Mechanism of Task-oriented Information Removal in In-context Learning
Authors: Hakaze Cho
Haolin Yang
Gouki Minegishi
Naoya Inoue
Venue: ICLR 2026 Poster (2026)
Keywords: Mechanistic Interpretability
In-context Learning
Large Language Model
Primary area: interpretability and explainable AI
TL;DR: We propose a new perspective of the in-context learning mechanism as a task-oriented information reduction.

Abstract: In-context Learning (ICL) is an emerging few-shot learning paradigm based on modern Language Models (LMs), yet its inner mechanism remains unclear. In this paper, we investigate the mechanism through a novel perspective of information removal. Specifically, we demonstrate that in the zero-shot scenario, LMs encode queries into non-selective representations in hidden states containing information for all possible tasks, leading to arbitrary outputs without focusing on the intended task, resulting in near-zero accuracy. Meanwhile, we find that selectively removing specific information from hidden states by a low-rank filter effectively steers LMs toward the intended task. Building on these findings, by measuring the hidden states on carefully designed metrics, we observe that few-shot ICL effectively simulates such task-oriented information removal processes, selectively removing the redundant information from entangled non-selective representations, and improving the output based on the demonstrations, which constitutes a key mechanism underlying ICL. Moreover, we identify essential attention heads inducing the removal operation, termed Denoising Heads, which enables the ablation experiments blocking the information removal operation from the inference, where the ICL accuracy significantly degrades, especially when the correct label is absent from the few-shot demonstrations, confirming both the critical role of the information removal mechanism and denoising heads.

Published as a conference paper at ICLR 2026
MECHANISM OF TASK- INFORMATION REMOVAL IN IN-CONTEXT LEARNING
Hakaze Cho
Haolin Yang
Gouki Minegishi@
Naoya Inoue!.2
JAIST "RIKEN
UUnieesstty of Chicago
*University of Tokyo
Verb subspace
yfzhac@jaist. ac. jo haolinyang2D0 2001 eaco. edu sinegishi@webie to.koo.acc ip
naoya wewaiiejasss.....e jp
ABSTRACT
In-context Learning (ICL) is emerging few-shot learning paradigm based on modern Language Models (LMs), yet its inner mechanism remains unclear. In this paper, we investigate the mechanism through novel perspective of information removal. Specifically, we demonstrate that in the zero-shot scenario, LMs encode queries into non-sclective representations in hidden states containing information for all possible tasks, leading to arbitrary outputs without focusing on the intended task, resulting in near-zero accuracy. Meanwhile, we find that selectively remov- ing specific information from hidden states by a low-rank filter effectively steers LMs toward the intended task, Building on these findings, by measuring the hid- den states on carefully designed metrics, we observe that few-shot ICI. effectively simulates such task task-oriented information removal processes, selectively remov- ing the redundant information from entangled non-selective representations, and improving the output based on the demonstrations, which constitutes a key mech- anism underlying ICL. Moreover, we identify essential attention heads inducing the removal operation, termed Denoising Heads, which enables the ablation ex- periments blocking the information removal operation from the inference, where the ICL. accuracy significantly degrades, especially when the correct label is ab- sent from the few-shot demonstrations, confirming both the critical role of the information removal mechanism and denoising heads.
INTRODUCTION
In-context Learning (ICL) is a promising application of modern Language Models (LMs), in which sequence of input-label pairs (demonstrations) concatenated with a query is fed to the LMs to predict the query label. However, the inner mechanism of ICL remains unclear, despite some progress (Zhou et al., 2024), including: linking ICL to specific input components (Min et al., 2022; Yoo et al., 2022; Pan, 2023; Kossen et al., 2024), relating ICL-style inputs to pre-training data (Li & Qiu, 2023; Gu et al., 2023; Han et al., 2023b; Li et al., 2024; Cho et al., 2025b), analogy to simpler algorithms (Zhang et al., 2023; Dai et al., 2023; Xie et al., 2021; Han et al., 2023a).
Among prior work, mechanistic interpretability studies (Elhage et al., 2021; Chan et al., 2022; Reddy, 2024; Wang et al., 2023; Singh et al., 2024; Cho et al., 2025a; Yang et al., 2025; Minegishi et al,, Yin & Steinhardt, 2025; Bakalova et al., 2025) reduce ICL to functional LM components (e.g., attention heads), capturing many phenomena and establishing causal roots to ICL accuracy. Mainstream interpretations attribute ICL Induction Heads (Elhage et al., 2021; Reddy, 2024: Cho et al., 2025a; Yang et al., 2025) (introduced in $2), which copy the most relevant label token from demonstrations to the outputs. However, such explanations fail in unseen label scenarios (Fig. 15), i.., the correct label is absent (Minegishi et al., 2025; Cho et al., 2025a) where ICL accuracy drops but remains well above the zero-shot level (Table 6), implying additional supporting mechanisms.
Therefore, we propose new perspective to interpret ICL, shown in Fig. 1. Specifically, we argue that ICL should not be viewed as "copying new information to the output (Cho et al., 2025a) or learning new tasks (Li et al., 2024)", but as removing task-irrelevant information from the query to highlight the specified task. In detail, since the previous works demonstrate that various kinds of information are encoded in various subspaces in LM's hidden states (Saglam al., 2025; Zhao

---

Published as a conference paper at ICLR 2026
A
"Donald Trump"
B
Demonstrations, T"rumpp"
C
Joe Bides-Male Mate
Tripgittt propecio))
Human Male
Presidant
Yoeicht Pikuzswa-Mai
Rightingule iraalle
Male
Head
Previous Token Masked
Dona Id Trump
Man e
Donald Trusp
Low projection layer with inner dimension
Demo.
Dieoo
T Task Verbalization Subspace
Model Output: "President"
Model Output:
"Male"
Iepat: tolkers
Prump
Figure I: (A) A zero-shot query is encoded into a non-selective semantic representation containing all possible label information on various subspaces, making the output arbitrary among these labels. (B) Demonstrations help LM filter the label information, saving only the task-related one on the specific subspace (termed Task- Verbalization Subspace (TVS)). leading to the specific output. (C) We explicitly find the TVS by injecting low-rank filter into the residual stream of zero-shot inputs, and train only the filter to drive the final outputs towards the ground-truth labels.
et al., 2025), we hypothesize that: LMs encode zero-shot queries with superposed information from all possible subspaces that mix task-specific and task-irrelevant information, often causing zero-shot outputs to yield plausible but arbitrary and unexpected answers (e.g., "Donald Trump, label:" - "President" instead of "Male", illustrated in Fig. and demonstrated in Fig. 2). Meanwhile, task- specific information is concentrated in one of these low-rank spaces (termed Task- Verbalization Subspace (TVS)) in the hidden states, which leads LM to output in the expected pattern but covered by the noisy information in the zero-shot scenario. To validate this, shown in Fig. (C), we inject a low-rank filter into the last token's 's residual stream of zero-shot inputs, and train the filter with the ground-truth output recover the TVS. Surprisingly, filters preserving only 0.7% of dimensions boost accuracy from near-zero to a remarkable level, showing that removing the orthoggooa irrelevant information suppresses arbitrary outputs and enforces task speciie predictions.
Based on such findings, we generalize the task oriented information removal from the injected zero- shot settings to vanilla (i.e., un-injected) few-shot settings. As shown in Fig. (B), we observe that LMs, guided by few-shot demonstrations, implicitly drive the hidden states towards TVS calculated independently in the previous low-rank filter injection experiments to produce task- specific outputs. Moreover, we also confirm a consistent behavior in the aforementioned unseen label scenario. Fur- thermore, we identify a set of attention heads (termed Denoising Head in this paper), which are highly independent from the input labels and induction heads, conducting such task- infor- mation removal by re-encoding the queries' information. Such -oaallooalizttoon enables ablation experiments by zeroing these heads' outputs, which results in substantial accuracy degradation, es- pecially in unseen label scenarios, where the accuracy drops nearly to zero, strongly indicating the task-oriented information removal as an essential mechanism for ICL.
In summary, the main contributions of this paper are: (1, $3) We propose a novel and systematic evaluation framework to measure the task-oriented information removal dynamics in hidden states, which is a versatile methodology for not only the ICL scenario. (2, $4.2, 4.3) Based on the proposed evaluation framework, we propose a novel ICL mechanism from the task-oriented information re- moval perspective, where demonstrations remove the task iask-irrelevant information from the query to drive LM's 's output on the specified task. (3, $4.4) We identify denoising heads responsible for task- oriented information removal, enabling subsequent ablation to verify their effectiveness. We further address induction heads' limitation on unseen labels by showing that ablating denoising heads (also the information removal) sharply reduces accuracy, and collapses to zero unseen label scenarios.
2 BACKGROUND
In-context Learning (ICL) (Radford et al., 2019). In an ICL scenario, given & input-label pairs {(x,, yt) y: as the demonstration and a xy as the query, a concatenation [x1, V1.... Tye yks I.p] is fed into LMs for yo corresponding to x.q. ICL enables LMs to perform diverse tasks without param- eter updates, drawing significant research interest, particularly in mechanism analysis. However, current studies, especially those focusing et al., 2021; Wang et al., 2023; Reddy, 2024; Singh et al., 2024; Cho et al., 2025a), cannot account for all ICL. phenomena, leaving them an incomplete explanation of ICL behaviors as described below.
attention components such Induction Heads (Elhage
2

---

Published as a conference paper at ICLR 2026
Induction Heads-based Mechanistic Interpretation for ICL. In- duction Head (Elhage et al., 2021) is a family of attention heads identified in LM, primarily responsible for prefix recognition and suffix replication. Specifically, for an input string shaped as (A, B,A]. induction heads add the information of B, which is the suffix of the previous A, to the residual stream of the last A, so that drive the output towards B. Such behavior aligns with the form of ICL, where the r,s, especially the consistent structural final token (i.e., "." in "label:") (Cho et al., 2025a), serve as the As, and the y:8 serve as the Bs. The induction heads retrieve the most similar s,s with Zig and copy the corresponding y/ to the output. However, such a framework has serious issue: it determines the final answer
O-shot Output Logits for "Donald Trump
Noue: Some sudjective lertta are cruited
17-
Output
16
Outgat Lagits
Republican
Expected
President
American
12-
****tt
Humen *e**ppt
Male:
10
Figure 2: Logits distribution (selected) of zero-shot input only by copying the tokens that have appeared in the context; thus, "Donald Trump, label:".
if the correct label token does not appear in the demonstrations (termed Unseen Label Scenario), then the framework predicts ICL to fail. But this is not the case in reality, although the accuracy in the unseen label scenario is significantly harmed, but basically not zero (refer to Appendix A.3), which prompts for new investigations to supplement the induction head framework.
3 METHOD: TRACING THE TASK-ORIENTED INFORMATION REMOVAL
In this section, we propose a systematic evaluation framework that traces the task-oriented infor- mation removal. Following this framework, in $4, we undertake a comprehensive investigation of task-oriented information removal in the ICL setting. While our discussion centers on the ICL sce- nario as the prototype, we believe the framework extends naturally to a wider range of scenarios.
Preliminary: verbbaaebali Subspace (TVS). As shown in Fig. 1 (A), an LM encodes zero- shot query T.g into a non-selective semantic representation N2 E Rd after transformer blocks, where the output derived from such hy by the remaining layers is unlikely to be the desired answer to Zig. as demonstrated in Fig. 2. In such a scenario, we hypothesize the existence of a low-rank subspace in the representation space encoding the task-related information, equipped with a projection matrix W E IRddd that projects 1/ to remove task-irrelevant information, thereby redirecting the final output derived from h1 W towards the task-specific answer. As shown in $4.2, such W defines the task and also the "verbalization mode" (i.e., how the output is expressed, such as "positive" vs. "4" in sentiment analysis), for which we term W as Task- Verbalization Subspace (TVS).
Step 1: Finding the Explicit TVS in Zero-shot Hidden States. As shown in Fig. 1 (C), we explicitly assume the existence of TVS parameterized low-rank filter WeneWee: dec RRdxr, .Rexdd and verify this assumption by an injection method: we inject Wen:War into the residual stream of the inputs' last token (where the output expected) in specific layer I, and interrupt this last token's access to previous tokens in the subsequent layers to block the context-related additional information gain from the inputs afterward the filter to keep the attribution clear. Given some zero-shot prompts and ground-truth responses, with all other parts of the LM frozen, we train the W WeneWaee on zero- shot inputs towards corresponding ground- -ouund-tuuthha responses (refer to Appendix A.2 for details).
Step 2: Tracing the Implicit Task-oriented Information Removal towards TVS. We then assume that LMs intrinsically drive the hidden states towards TVS in the uninjected inference with the help of demonstrations. To validate this, we propose two carefully designed geometric metrics of the few-shot hidden states, utilizing the trained W one Wece in Step 1. In detail, given a Nammount set of hidden states H = [K( N from the last token of k-shoo ICL inputs after / transformer blocks:
Eccentricity:
To measure the magnitude of information removal, calculate the eccentricity as the covariance loaded ratio on the first principal direction of Hi,,, indicating the enrichment, anisotropy, of information on single linear representation (Engels al., 2025). A higher eccentricity indicates a purer representation with less extraneous information.
Covariance Flux on TVS: To measure the correctness of information removal, we calculate the ratio of task-related information, we project all the h/- E H onto the W Was with r' trained on layer in Step I, and calculate the covariance ratio of H' Waec against H (details in Appendix A.3). A higher covariance flux suggests that a larger proportion of the information in H.. is task-related.
3

---

Published as a conference paper at ICLR 2026
In summary, intuitively shown in Fig. 23, eccentricity quantifies the concentration of information into a single feature, thereby indicating the magnitude of information removal; and covariance flux evaluates whether the task-related information is preserved, i... the correctness of the information removal. Appendix G relates these covariance metrics to entropy, a standard measure of information.
Step 3: Building the Causal Link between Information Removal and ICL Performance by De- noising Heads. To test whether the detected information removal process indeed has a causal sig- nificance, i.e., whether it actively influences accuracy, merely constitutes byproduct of accuracy improvement from other mechanisms, we conduct a causality evaluation which actively suppresses such mechanisms. Since the aforementioned two metrics are not directly controllable, we utilize the attention heads as the handle for such causal evaluation. In detail. we quantify each head's 's contribu- tion task-oriented information removal by ablating it and re-evaluating the metries on the hidden states produced by the ablated layer. Then, we label the heads that contribute substantially to these metries as "Denoising Heads (DH)", then ablate all the detected DHs and evaluate the ICL perfor- mance to verify the causal link. The design of the technical details relies in part on the conclusions from Step 2, as described in $4.4.
4 TASK-ORIENTED INFORMATION REMOVAL IN IN-CONTEXT LEARNING
In this section, we conduct comprehensive experiments apply the aforementioned evaluation framework to trace the task-oriented information removal dynamics in the ICL scenario.
4.1 EXPERIMENT SETTINGS
Models. We mainly conduct experiments on 6 modern LMs detailed in Appendix A: Llama (v3.2- 1B, v3-8B, v3-13B Instruct) (Grattafiori et al., 2024); Qwen 2.5 (3B, 3B Instruct, 7B) (Team, 2024; Yang et al., 2024). We default to reporting the results Llama 3.2-1B (more results in Appendix I).
Datasets. We utilize 6 classification datasets: SST-2, SST-5 (Socher et al., 2013), MR (Pang & Lee, 2005), FP (Malo et al., 2014), AGNews (Zhang et al., 2015), Subjective (Wang & Manning, 2012) 2); and 3 non-classification datasets: country-capitals (icyrockcom, 2011), 1), prople-profession (I (oouue- nan et al., 2022), opus-100 (Zhang et al., 2020). Unless specified, we report the results on SST-2
Others. To verify whether the LM spontaneously produces task-related outputs, we calculate the accuracy by greedy decoding, where hard matching of the model output among all the vocabularies is utilized for the accuracy, instead of the restricted decoding, where only the most likely output in the pruned output candidates selected. Refer to Appendix A. for the prompt templates.
4.2 STEP 1: FINDING THE EXPLICIT TVS IN ZERO-SHOT HIDDEN STATES
In this section, following Step in $3, we show that explicitly removing information from the or- thogonal complement of the injected TVS in the zero-shot hidden states guides the LM to recognize the intended task rather than producing arbitrary outputs, suggesting zero-shot hidden states contain task-related information with redundant information interfering with the output, and filtering out such redundancy helps LMs focus on the target task.
Existence of Explicit TVS in Hidden States. We conduct the injection-and-train experiment men- tioned in Step of $3, with validation accuracy with various I and on SST-2 and Llama 3.2-1B shown in Fig. 3. where, globally, compared zero-shot accuracy. filtering the hidden state while explicitly assuming the existence of a TVS of max-rank! 2 can significantly improve the output accuracy from the open-end decoding (mentioned in 1). Such results confirm our hypothesis: se- lectively removing information from zero-shot hidden states steers outputs toward the task, inspiring a possibility that ICL implicitly applies this procedure, as verified in $4.3.
Wene Weec is Information Removal. One suspicion is that W W may not significantly remove information, such as when the principal component direction of h is highly aligned with the eigen- vector of W W dec- We rule out such doubt by: (1) Calculating the remaining covariance-load ratio
'Notiee that even if the is sufficient large, the effective rank of W Ware can also be small, so the is the maximum possibile rank. (Original embedding dimension 2048.)
4

---

Published as a conference paper at ICLR 2026
Focentrinng (bbrienee Redio PCL.
2.6
Layer
0.40
Layer
00-
0.20
8.5-
Upen ene. Accusiy
Covadiesun Flus through
0.30
0.20
0.4
6.3
0.16-
0.2
0.10
0.3
16
Number Sbots
Number of Shots
Number of Shots
Figure 4: Test results of (Ieft) open-end accuracy against demonstration numbers k. (middle) ec- centricity of hidden states point cloud against demonstration numbers on various layers, (right) covariance flux through the catched Wen W against demonstration numbers l on various layers.
out of the top-r principal components of hys, as lower bound of information removal by Wone Wa dec with maximum rank r (explained in Appendix B, and numerically visualized in Appendix D, as
shown in the diamond size of Fig. 3, suggesting effective information removal by W ene W dec- (2) Calculating the cosine similarity of Weme's eigenvectors and the principal components of the hidden states, as an estimation of the positive gap between the actual information removal and the lower limit, shown in Appendix B. In summary, WeneWac is an effective information removal while en- hancing the zero-shot accuracy.
Wdec Controls the Verbalization Mode. Notice that, in the training of the W not only is the task- related information (as shown Fig. (B)), but also the verbalization mode, i.c., how the task-related infor- mation transferred into output tokens (e.g., into "pos- itive/negative" or "+/-") is defined in the trained pa- rameters. This is also why verbalization". Moreover, we find that the verbalization mode is mainly controlled by the Waec: In detail, we first train the Wene Wiee filter on SST-2 using the stan- dard verbalizations "positive" and "negative", then freeze either Wene or Wae and fine-tune the remaining one to transfer the outputs to symbolic verbalizations "A" and "B". The results, shown in Table 1, indicate that fine- tuning only Was successfully transfers the verbaliza- tion into symbolic form, whereas Wene fails. This sug- gests that Wene extracts task-specific but verbalization- irrelevant semantics from hidden states (otherwise, freez- ing will not prevent successful verbalization transfer), while Wass maps them into the target verbalization by aligning hidden states with the specified output unem- bedding vectors (Yang al., 2025), consistent with prior findings (Tao et al., 2024).
Zero shipt (open-end)
Encodling Magnita Goe Gut or lome
0.8
0.6
Accuracy
0.4
WeneWass as "task-
16
0.2
2018
0.0
0
2
6
8
10
12 14
16
Injected Layer Number
Figure 3: Filter-injection evaluations on various layers and ranks. Marker size: the remaining covariance out of the top-r principal components of the point cloud of hy Refer to Appendix for numerical results. Encoding Mag- nitude: the quality of the hidden states the current layer sentence encod- ing of the query, emerging simultane- ously with the test accuracy, calculated follows Cho et al. (2025b).
4.3 STEP 2: TRACING THE IMPLICIT TASK-ORIENTED INFORMATION REMOVAL
In $4.2, removing the TVS- orthoontll information produces task-specific output, which serves as efficient adaptors for LM to specific tasks, and motivates to hypothesize the mecha- nism ICL with few-shot demonstrations similar to such task- oriented information removal. In this section, following Step 2 in $3 to measure the two geometric metrics (i.e., Eccentricity and Covariance Flux) of the few-shot hidden states from uninjected inference processing, thereby verifying the hypothesis shown in Fig. 1 (B): LMs autonomously remove the redundant information out of the TVS with the help of fho-shot demonstrations produce task-specified ICL outputs.
Table 1:
Fine-tuning results with parts of the filter frozen, on Llama 3.2-1B and SST-2.
Trained Part Both
Wone
Wase
Accuracy
0.88
0.00
0.84
5

---

Published as a conference paper at ICLR 2026
0.6-
Uccontreelty Nar Rant on
through Mau
0.5
Eccontrcity (aa Rati on
0.4--
W..
0.5
Rodke, sas
0.30-
0.4
0.33
0.4
0.3
0.30
0.3
020-
0.2
0000
0.3
010
15
10
15
Layer Todex
Layer Indax
Luyer Indax
Layar Indaxx
Figure 5: Eccentricity and covariance flux w.r.t.
Figure 6: Eccentricity and covariance flux w.r.t. layer on MR, with random label, unseen label, and normal settings.
layer on MR, with instruction texts, demonstra- tions, or plain zero-shot inference.
Language Models Intrinsically Compress Hidden States towards TVS. We test both the metrics on various and I, with results as well as the output accuracy shown in Fig. 4 for Llama 3.2- 1B and SST-2 (refer to Appendix I for more cases). Globally, the amount of demonstration (k) increases, the task-oriented information removal primarily occurs in the middle-to-late layers, causing an increasing eccentricity and covariance flux. In detail:
Eccentricity: As shown in Fig. 4 (middle), with sufficient demonstration numbers (k), in the later layers, the eccentricity increases against k, reaching a maximum of around 60%, showing a highly anisotropic information compression with the help of demonstrations. Specifically, on certain datasets such as SST-2, the eccentricity exhibits a distinctive nonmonotonic decrease- and-increase pattern against k. This suggests that information removal initially compresses from the first principal component of zero-shot hidden states, which is understandable since the input distribution may be disaligned with the task, and confirms an important conclusion: task-oriented information removal primarily compresses from the task inreevateee directions (Yang et al., 2025; Kirsanov et al., 2025) of the hidden state point cloud, as discussed Appendix C.
Covariance Flux: As shown in Fig. 4 (right), also in the later layers, the covariance flux in- creases against k, suggesting that LMs correctly preserve the task-related information while removing the task-irrelevant one with the help of demonstrations. Moreover, the covariance flux of the later layers closely tracks the accuracy (Fig. 4 (left)), with both reaching their peak and then saturating at the same point, which indicates that the alignment of hidden states toward TVS constitutes crucial mechanism shaping the inference output?.
Additionally, such findings concur with previous works, where the early layers contribute to task- agnostic low-level semantic encodings (Jawahar et al., 2019; Chen et al., 2023; Wang et al., 2023; Cho et al., 2025a; Yang et al., 2025), thus task-related behavior such as task-oriented information removal, can not be significantly observed in the early layers by our metrics. Conversely, in later layers, high-level features are being processed, causing the task-related operation to obvious.
Effect of Instruction. In practice, instruction text describing the task (e.g.. "Please predict the sen- timent of this text:") can be utilized instcad of the few-shot demonstrations in the inputs. Therefore, examine whether such instructions produce the task-oriented information removal functionally similar to the few-shot demonstrations by measuring both metrics on the instructed inputs (config- urations detailed in Appendix A.1). As shown in Fig. 5, hidden states with 8-shot demonstrations exhibit obvious morphological differences and stronger information removal over the 0-shot infer- ence with without instruction text. Also, hidden states with instruction, even if the label spaces are indicated (e.g.. "Please predict in Positive and Negative"), show information removal dynamics almost consistent to the zero-shot inference (Kirsanov et al., 2025), despite the elearly higher accu- racy (refer to Appendix A.3). Such observation suggests that the information removal is only evoked by few-shot demonstrations, with a different mechanism from instruction.
Effect of Random Labels and Unseen Labels. Previous works demonstrated that the correctness of labels presented in the demonstrations influences the inference dynamics and output accuracy insignificantly (Min et al., 2022; Yoo et al., 2022; Pan, 2023; Cho et al., 2025a). Therefore, we measure both the metrics with label tokens randomly sampled from all possible labels (detailed in Appendix A. well as the unseen label settings, with results shown in Fig. 6. Focus on the cocentricity results, hidden states with randomized labels exhibit weaker information removal than
Thhe two differ in form, which natural since accuracy is nonlinear metric (Schaeffer et al., 2023).

---

Published as a conference paper at ICLR 2026
4.0%
Relative Change (%)
2.0%
0.0%
-2.0%
-4.0%
-6.0%
Eccentricity Covariance Flux Accuracy
-8.0%
-10.0%
10 12 13 14 16 18 20 22 23 24 25 Ablated Attention Head Index
26
27
28
30
Figure 7: Ablation results for the two metrics and output accuracy of every head in Llama3.2- 1.naa3.2-1BB Layer 9 8-shot SST-2 (relative the clean run). A smaller value indicates a more severe drop with ablation, i.c., this attention head contributes more significantly to the metric.
the plain 8-shot inference, suggesting that mismatched labels weaken the impact of demonstration, leading to weaker task-oriented information removal, which echoes previous works (Cho et al., 2025a) showing that mismatched labels neutralize the functionality of demonstrations. In contrast, the demonstrations with unseen labels show a stricter removal, and we infer the reason demon- strations with smaller label space actually specify a narrower task, causing more information to be identified as redundancy. More evidence is shown in Fig. 53, where such an effect is weakened on multi-way tasks than on 2-way tasks, where the removal of each label has a large impact on the task scope. Overall, task-oriented information removal appears across all label settings, differing only in magnitude, regardless of the labels' completeness or alignment to the demonstration. The above de- grading configurations merely shift the information removal away from the optimal range, resulting in reduced accuracy (we list the output accuracies in these configurations in Appendix A.3).
4.4 STEP 3: CAUSALITY TEST BY DENOISING HEADS
We have shown that selectively removing information from zero- shot hidden states boosts accuracy the injected settings, and few- shot learning under un unjeneected settings implicitly simulates sim- ilar process. This section therefore investigates the causal role such an operation. As outlined in Step of $3, first identify the model components responsible for this removal, thereby paving the way for subsequent ablation analysis to examine the significant accuracy influence, especially under the unseen label settings. The experiments in this section default using 8-shot inputs.
Number of Heads
2
Denoising Heads
Anti- Aati-Denoosing Heeds
Identify Denoising Heads in LMs. Following the ablate-and- remeasure method mentioned in $3, set of representative results on Layer 9 is shown in Fig. 7 (refer to Appendix for other settings). Because eccentricity trends have phase-tram mhase-transition pattern², we use covariance flux to identify significantly contributing attention heads (i.e., Denoising Heads (DH)), with some (e.g., #5, 7, 12, 15, 20, ...) showing clear contributions to both metrics and accuracy. Setting" +3.5% the thresholds, we observe the distribution of the DHs, and also the anti-DHs whose ablations increase the covariance flux remarkably, as shown in Fig. 8 (refer to Appendix for more settings). While the DHs can be observed in almost every layer, their numerical advantage against the anti-DHs emerges only in the middle-to-late layers, where task-oriented information re- moval becomes apparent discussed in $4.3. This further suggests the transition from early-stage task-agnostic encoding (Cho et al., 2025a) to later-stage task-related filtering: the former, most
12 14
Layer Number
Figure 8: Counting of DHs and anti-DHs w.r.. layers.
"As noted in 84.3, a contributive operation may reduce eccentricity, but in later layers (e.g.. Layer 10), once redundancy is sufficiently removed and task relevant information aligns with the first principal component, the contributive information removal begins to increase the eccentricity.
"Note that the goal of this experiment is to identify a subset prominent denoising heads for visualization or causal analysis, rather than to exhaustively capture all potential candidates. Therefore, discussed in Appendix F, the threshold should be relatively selective but not extreme value. Based on the visualization in Fig. 20, consider 3.5% 5% (mentioned helow) be ideal choice.

---

Published as a conference paper at ICLR 2026
heads conduct non-selective query encoding, leading to anti-DHs; in the latter, more DHs play selective and decisive role. Moreover, during this experiment, we find more interesting attention heads as shown in Appendix F.
Denoising Heads are Independent of Induction Heads. To demonstrate the independence of information removal behavior and also DHs against the induction heads, we observe the overlap of induction heads and the DHs. In detail, we calculate the magnitude of induction for each head as the sum of attention scores from all the label tokens to the last token, and visualize it together with
..0000.0..1 ..000..0
14
+000+0+0000000L
M0..0.e.
Layer Index
10
oooo
O
the ablation effects on the covariance flux, as shown in
o000
DOO
Fig. 9 (refer to Appendix I for other settings), where we find that: although induction heads and task-oriented in- formation removal emerge in similar layers, these atten- tion heads rarely overlap, which clearly suggests that: DHs, and their task-oriented information removal effect, an independent and novel operation evoked by the ICL- prompted LMs.
15 Head Index
25 Anti- Den--Deni
Dencising
Overlap of Denoising Heads among Tasks. To iden- tify whether the evoking of the DHs is task-specific or task-irrelevant, which suggests In-weight Learning (IWL) (Chan et al., 2022: Reddy, 2024; Chan et al., 2025) or in-context learning characteristics, we calculate the overlap count of the DHs identified on all the task pairs as [DA n Dal where the D or Dr is the DH set de- tected on the task A or by bottom-K K covariance flux relative change after ablation, as shown in Fig. 11 with
-10% -5%
0%
5%
10%
&Covartance Flux (Relative Change Ablation)
Figure 9: Head wise (scatter size) in- duction magnitude and (color) covari- ance flux relative change after ablation.
Attention Scores CLayer 9, Head 15)
4:35
K = 1%. In the results, we observe several common DHs across different dataset pairs, indicating that they exhibit ICL properties by extracting and discriminating at least two task information from the context and lever- aging it for operation. In contrast, most DHs are dataset- specific, reflecting the IWL property but still evoked by ICL. demonstrations: on mismatched datasets, these heads are inactive, neither hindering nor facilitating information removal (e.g.. Layer 9 Head 20 as a DH for sentiment- analysis in Appendix D), thus challenging current strict separation of ICL and IWL. These findings suggest that task-oriented information removal is a hybrid of ICL and IWL, supporting the previous works that ICL capability arises from latent tasks acquired during pretraining (Li et al., 2024) and is further strengthened by demonstrations (Yang et al., 2025; Cho et al., 2025c).
(Xllantion
Toker Indes LAltoaation Bey!
Figure 10: Attention map of common DH (Layer 9, Head 15). White dotted lines are the position of label tokens.
Attention Pattern of Denoising Heads: Local Re-encoding. To find how the DHs conduct the task-oriented information removal op- eration, visualize the attention maps of common DH (Layer
5575
47
9 Head 15) of Llama 3.2-1B, as shown in Fig. 10 (refer to Ap-
pendix A.4 for detail, Appendix for more cases). Surprisingly. although task-oriented information removal is a highly context- dependent operation the ICL-based common DH, the DH exhibits a local attention pattern. Specifically, significant attention scores of the last token are almost confined the query tokens (ignoring the attention sink (Gu et al.. 2025)), thereby forming local re-encoding pattern. In such processing, as demonstrated in Appendix D, DH appropriately identifies and enforces task-relevant information by selective attention calculation, where the vector extracted from the last-token hidden state by W Wx of the DH may serve indicator for locating this informa- tion, since serves an important part of the attention calculation, which is decisive for selecting the key tokens that contain the related information.
XB
11
47
sub), AONows
10
18
47
10
14
47
888122 SSFS
MR Pe AttNlees Subj.
Figure 11: Overlap of DH over all dataset pairs.
8

---

Published as a conference paper at ICLR 2026
(spet-end)
lopet-ondi
Loss
10
26:48
4
6
8
8192
8
10
12
14
16
8 10
12
14
16
Injected Layer Number
Injected Layer Number
Figure 12: Filter-injection results on country-
Figure 13:
Filter-injection results on the people-
capitals task. In cross-entropy loss.
profession task. In cross-entropy loss.
Task-oriented Information Removal as Key Mechanism for ICL with Unseen La- bel. Identifying the DHs responsible for the task-oriented information removal enables ab- lation experiments to evaluate the significance of the operation to ICL. Therefore, we remove DHs from the inference, specifically, setting the outputs of all heads with covariance flux rel- ative change below 55 to zero vectors, and report the resulting accuracy in Table 2 (refer to Appendix for non-average results), where when demonstrations at least one demonstration shares the same la- bel as the query (Seen Label), zeroing out the DHs significantly but not critically reduces ac- curacy compared randomly selected heads, since the induction heads provide a strong sup- portive mechanism in such cases. the unseen label setting where induction heads fail, DHs become decisive: ablating them almost elimi- nates accuracy,
Table 2: Ablated inference accuracy (%) of DHs, averaged on all 6 datasets. Layer: the ratio of the layer scanned for DH / total layers. w/o DH: ac- curacy with DHs ablated. w/o RH: accuracy with ablation of randomly sampled attention heads of equal amounts to DHs each layer. P-value: the probability for "w/o RH" to sample a value less than "w/o DH" (i.e., the likelihood of DHs being randomly sampled). (Due to computational constraints, we only evaluate Llama 3-13B on SST-2.)
Model
Demonstration
8-shot w/o DH
8-shot wio RH
randomly sampled, or
Layer
Configuration
8-abot
P-value
LJana
3-2-18
161T6
Randem Sample
71.02
55.04
67.29,
7
Scen Label
73.40
56.52
69.02s.72 72
4-1o
Unseen Label
14.54
1.06
10.65,e
2x10-2
Lama 3-00
7/32
Random Sample
72.05
76.3% wn
3x11-6
Seen Lahel
80.47
75.11
79,70, 80
3
Unseen Label
21.66
7.52
18.94,
2x
Qwenn 25-38
18/3 18/36
Random Sample
73.97
68.41
74.31.22
2x
Seen Label
76.41
70.31
76.36)
Unseen Label
23.49
26.82..8
34m0-
without exhaustively iden- tifying all DHs This shows that DHs are the primary source of accuracy in unseen-lahel sce- narios, effectively acting as the main comple- ment to induction heads (Cho al., 2025a).
1.lmma3 Qwen2.5
Sik-ins'
18/36
Seen Lahel
Random Sample
78.86
77.24
77.52
75.57
77,28, .00
78.05c
0.18
0.25
Unscen Label
48.70
37.51
46.324.2 02
2400
138 los'
13/55
Random Sample
76.86
71.58
77.83,
3 8
Label
72.16
81.20,
Unseon Label
29.59
10.35
32.13
4x10
Amplifying the Outputs of DHs Boosts ICL Accuracy. As
prototypical empirical application utilizing the discovery of DH, we try to amplify the output of DH on 8-shot inputs. i.e.,
multiply a scalar (1 + A) on the outputs of DHs detected sim- ilarly as the ablation in Table 2. The results with various À are shown Fig. 14, where a moderate amplification con- sistently increases ICL accuracy. Especially in the random- label scenario $4.3, DH amplification yields a markedly stronger effect, consistent with Fig. 6, where information moval weaker than in the true-label setting. This amplifi- cation provides frugal, plug-and-play way to boost ICL ac- curacy and mitigate label noise without extra computational overhead, while reinforcing the causal link between information removal and ICI. accuracy.
Accuragy
0.84
0.82
0.8
B-thot Sendom Labels
0.78
0.0
0.3
1.0 1.5
2.0
DH Amplification Factor
Figure 14: DH amplification sults on Llama 3.2-1B and SST-2.
DDue to computational constraints, only identify the denoising heads some of the layers of these models, shown in Appendix the ablation results here do cover all denoising heads.

---

Published as a conference paper at ICLR 2026
5 CONCLUSION AND DISCUSSION
Conclusions. This paper proposes a novel perspective to interpret ICL inference as a task-oriented information removal from the query's hidden states. In detail, we first demonstrate that injecting ex- plicit low-rank filters into the zero-shot hidden states to reduce their redundant information improves aceuracy. We then show that few-shot ICL spontaneously performs this process, identify the DHs responsible for it, and confirm both the independence from the induction head, and the significant effectiveness of information removal for ICL tasks by ablation experiments.
Comparison and Connection to Previous Works. This paper is related to the two categories of previous works: (1) Task vector-based mechanism. Our analysis of the attention patterns shows that denoising heads access subspaces of the last hidden states through W Q Wr K for the re-encoding
operation. The W WK thus acts as an operator extracting task representations to trigger and guide the denoising operations. This view suggests new direction for task-vector research: identifying the subspaces that purify the task representation from the coarse-graings hidden states, and finding the components that mediate their effects (Yang et al., 2025; Yin & Steinhardt, 2025), rather than only relying on coarse steering. (2) Induction heads-based mechanism. As mentioned, current induc- tion head-based works slough over the case of unseen labels and resort to vague explanations (Cho et al., 2025a), which our paper addresses. From our ablation study (Table 2). ICL behavior can be attributed almost fully to induction and DHs, with significant bypasses since ablating DHs in the unseen label scenario reaches near-O accuracy. Although induction heads contribute more to accuracy, the DH, the complementary mechanism identified when they fail, remains meaningful.
Failure Case: Clustering vs. Translation. Notice that the task-oriented information removal in- vestigated in this paper essentially a dimensionality reduction operation, where it is conceivable that classification tasks, which cluster a vast input space (i.e., the whole set of the input sentences x) to narrow label space, precisely align with such a dimensionality reduction. While, some works identified translation operation (Merullo et al., 2024; Jiang et al., 2024; Bu et al., 2025) in hidden states directing entities' semantics towards their attributes, especially unique ones (called "Fact Re- call" (Zhang et al., 2025), e.g.. "Japan" "Tokyoo"",, where the clustering operation as presented in classification tasks can not be applyed since the mapping from the input space to the output space is bijection. Therefore, the task-oriented information reduction process observed in this paper is unlikely to apply to the bijection scenario, as information is not removed: input can be losslessly reconstructed from the output. We demonstrate this point by repeating the filter-injection experi- ment shown in $4.2 on the country-capitale task as shown in Fig. 12, where no loss lower than the O-shot baseline can be obtained by any filter, even if nigh-dimensional (not necessarily high-rank) ones. As a comparison, we repeat the experiment on similar fact recall task but with a clustering structure, which maps person's 's name to their profession (e.g.. "F. Nightingale"">"Nuss shown in Fig. 13, evaluation results better than 0-shot can be obtained by low-rank filter, which confirms our idea that the task-oriented information removal does not occur in bijective ICL tasks, while clearly highlighting the distinction between these two types of tasks. Some works on synthetic datasets also discuss the uniqueness of such full-rank translation scenario (Dong et al., 2025) and obtain similar conclusions. We develop such discussion on a generative scenario in Appendix H.
As
L Limitations. (1) Long-term effect of head ablation. In Fig. 7, we identify DHs by ablated metrics only on the current layer's hidden states. However, since the effect of ablation may propagate to deeper layers, the DH sets could be underestimated. Exhaustively measuring all layers would be costly, yet our ablation already shows that these heads, though not the whole set of DHs, produce clear and significant effects on the outputs. (2) Fine-grained mechanism. We propose a prototype mechanism for DHs the extraction of denoising signals from some subspaces of hidden states. A more detailed investigation is needed to validate such a mechanism prototype for DHs. (3) Efficient localization of DHs. In $4.4, we adopt a naive ablation-remmaaureeenn method, which is costly applications (Cho et al., 2025b). Future work may utilize gradient-based
for Docalization-controlliii methods, or leverage DH characteristics, such as the attention pattern in Fig. 10. for more efficient localization. (4) Complex information bottleneck. In this paper, we utilize a linear low-rank filter as the information bottleneck as shown in Fig. 1 (C). This essentially assumes that the features on these subspaces are linearly separable in the linear space, as illustrated in Fig. (A). However, some works (Engels et al., 2025; Modell et al., 2025) show that features may also be embedded on manifolds and be nonlinearly separable. Therefore, extending the discussion to more complex tasks may require a more complex nonlinear information bottleneck.
10

---

Published as a conference paper at ICLR 2026
ACKNOWLEDGMENTS
This work was supported by the JST FOREST Program (Grant Number JPMJFR232K, Japan) and the Nakajima Foundation. The authors would like to sincerely thank the chairs and reviewers of ICLR 2026 for their thoughtful and insightful feedback on this paper, their perceptive reviews and discussions have greatly improved this work.
THE USE OF LARGE LANGUAGE MODELS
In this paper, LLMs are used and only used polish writing.
REFERENCES
Aleksandra Bakalova, Yana Veitsman, Xinting Huang, and Michael Hahn. Contextualize- then- aggregate: Circuits for in-context learning in gemma-2 2b. In Second Conference on Language Modeling, 2025. URL https: //wp://eoee/eeeeeeeeemmee net/ forum? (orum?id=rrMAAHHReSS
Dake Bu, Wei Huang, Andi Han, Atsushi Nitanda, Qingfu Zhang, Hau-San Wong, and Taiji Suzuki. Provable in-context vector arithmetic via retrieving task concepts. In Forty-second International Conference on Machine Learning, 2025. URL https: : /oppnreeevvvveeeeeeeeeeeeeeeeeee ew. net/ / forum? d=d= DbUmeNnNpt.
Bryan Chan, Xinyi Chen, András György, and Dale Schuurmans. Toward understanding in-context vs. in-weight learning. In The Thirteenth International Conference on Learning Representations, 2025. URL httph:tt////mm httpp:://ppereeeeeete wpwpreveeee..e.eeeopeeeeeeoe...m
Stephanie Chan, Adam Santoro, Andrew Lampinen, Jane Wang, Aaditya Singh, Pierre Richemond, James McClelland, and Felix Hill. Data distributional properties drive emergent in-context learn- ing in transformers. Advances in Neural Information Processing Systems, 15:18888-18881, 2022. URL attps::/azzivs org/ abs /205/ 05055.
Yixiong Chen, Alan Yuille, and Zongwei Zhou. Which layer is learning faster? a systematic ex- ploration of laser-wise convergence rate for deep neural networks. In The Eleventh International Conference Learning Representations, 2023. URL http::s::///ppneeeee...... net net/forumt forum?
id= JQFB.
Hakaze Cho and Naoya Inoue. Staice: Standardized evaluation for classification task in in-context learning. arXiv preprint arXiv:2501.15700 2025. URL 15708.
org//bs///////.aoooooo........ abs/2501. 2501.
Hakaze Cho, Mariko Kato, Yoshihiro Sakai, and Naoya Inoue. Revisiting in-context learning infer- ence circuit in large language models. In The Thirteenth International Conference on Learning Representations, 2025a. URL https:://///
http:ttt//ppeereeeeeeee /ttp////ep//eeeee//////e/ee.o.et net/ wttp://wwww.eeeeeotteeeeeeeeeeee
Hakaze Cho, Peng Luo, Mariko Kato, Rin Kaenbyou, and Naoya Inoue. Mechanistic fine-tuning for in-context learning. arXiv preprint 20X.::25055.1233 2025b. URL abs /2005 14233v1.
Hakaze Cho, Yoshihiro Sakai, Mariko Kato, Kenshiro Tanaka, Akira Ishii, and Naoya Inoue. Token- based decision criteria suboptimal in in-context learning. In Luis Chiruzzo, Alan Ritter, and Lu Wang (eds.), Proceedings of the 2025 Conference of the Nations of the Americas Chapter of the Association for Computational Linguistics: Human Language Technologies (Volume Long Papers), pp. 5378-5401, Albuquerque, New Mexico, April 2025c. Association for Computational doi: 10.18653/v1/200 naacl-long //aclantho org 2025. naacl- -oo.l-oong... 278/.
Linguisties. ISBN 8799-88891760 1177771886 189-6.
URL https:
Damai Dai, Yutao Sun. Li Dong, Yaru Hao, Shuming Ma, Zhifang Sui, and Furu Wei. Why can gpt learn in-context? language models implicitly perform gradient descent meta-optimizers. In ICLR 2023 Workshop on Mathematical and Empirical Understanding of Foundation Models, 2023. URL https: htttps://arxiv www.iiooorg/aaaee aba /20ls//22222 2222..0552 10559.

---

Published as a conference paper at ICLR 2026
Yuxin Dong, Jiachen Jiang, Zhihui Zhu, and Xia Ning. Understanding task vectors in in-context learning: Emergence, functionalityy, and limitations. arXiv preprint arXiv:2506.09045. 2025.
URL http:///axiiy org/ abs/2506. 00255666004450 09048v1.
Nelson Elhage. Neel Nanda, Catherine Olsson, Tom Henighan, Nicholas Joseph, Ben Mann, Amanda Askell, Yuntao Bai, Anna Chen, Tom Conerly, et al. A mathematical framework for transformer circuits. Transformer Circuits Thread, 1(1):12, 2021. URL https:// cransformer-circn wwtpuiits.pub//000 http://221//raamooo//eeeeee
html.
Joshua Engels, Eric J Michaud, Isaac Liao, Wes Gurnee, and Max Tegmark. Not all language model features are one-dimensionally linear. In The Thirleenth International Conference on Learning Representations, 2025. URL https: /pooreeeeeveeeeeeeeee net/ forum? 63 4AM.hb.
Aaron Grattafiori, Abhimanyu Dubey, Abhinav Jauhri, Abhinav Pandey, Abhishek Kadian, Ahmad Al-Dahle, Aiesha Letman, Akhil Mathur, Alan Schelten, Alex Vaughan, al. The llama 3 herd of models. arXiv preprint arXiv:2407.21788, 2024. URL 21783v3.
org/ absgg//b////0000/0 2207.
Xiangming Gu, Tianyu Pang, Chao Du, Qian Liu, Fengzhuo Zhang, Cunxiao Du, Ye Wang, and Min Lin. When attention sink emerges in language models: An empirical view. In The Thirteenth International Conference on Learning Representations, 2025. URL /tpp:////////...e..//// net/ net/forune Eorum? id=7 4ONNTTJTEN
Yuxian Gu, Li Dong, Furu Wei, and Minlie Huang. Pre-training to learn in context. In Proceedings of the 61st Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), pp. 4849-4870, 2023. URL https: : //tpaiii.gg//aaa.aa//o/oo/oooo/a
2305. 09137.
Chi Han, Ziqi Wang, Han Zhao, and Heng Ji. Explaining emergent in-context learning ker- nel regression. arXiv preprint arXiv:2305. 12766, 2023a. URL https:/ /atpiv///avvvv.// org//brggss.o.o
2305. 12766.
Xiaochuang Han, Daniel Simig, Todor Mihaylov, Yulia Tsvetkov, Asli Celikyilmaz. and Tianlu Wang. Understanding in-context learning via supportive pretraining data. In Proceedings of the 61 Annual Meeting of the Association for Computational Linguistics (Volume I: Long Papers),
pp. 12660-12673, 2023b. URL https:/ wawxiv.vvvvv.////////...///aaavv org/ abs
Roee Hendel, Mor Geva, and Amir Globerson. In-context learning creates task vectors. In Houda Bouamor, Juan Pino, and Kalika Bali (eds.), Findings of the Association for Compu- tational Linguistics: EMNLP 2023, pp. 9318-9333, Singapore, December 2023. Association
for Computational Linguistics. doi: 10.18653/w12023 http://////....ninnnneneeeeeeiee fndingg--emnlp6224
URL https:
//aclahtholoogy.or//20000 http://222......nn.... findings-ennininnn emnlp. 624//p
icyrockcom. country-capitals, 2011. country- capptala...a......m..
URL
com/ com.o//oc//////cccoooooooo
Ganesh Jawahar, Benoît Sagot, and Djamé Seddah. What does BERT learn about the structure of language? In Anna Korhonen, David Traum, and Lluís Mårquez (eds.). Proceedings of the 57th Annual Meeting the Association for Computational Linguistics, pp. 3651-3657, Florence, Italy, July 2019. Association for Computational Linguisties. doi: 10. 10.18653/1//P1-1133 URL https: //////aaanttttttt www.llogoy.....ooo..ooooo wrg.orggg///0 91566///
Yibo Jiang, Goutham Rajendran, Pradeep Kumar Ravikumar, Bryon Aragam, and Victor Veitch. On the origins of linear representations in large language models. In Forty-first International Conference on Machine Learning, 2024. URL
net forum?id=
ottTw4Mghk.
Diederik Kingma. Adam: A method for stochastic optimization. arXiv preprint arXiv:
2014. URL https:/ / arxiv. org/ abs /abe/22 /11/1111..99 6980.
Artem Kirsanov, Chi-Ning Chou, Kyunghyun Cho, and Yeon Chung. The geometry of prompt- ing: Unveiling distinct mechanisms of task adaptation in language models. In Luis Chiruzzo, Alan Ritter, and Lu Wang (eds.), Findings of the Association for Computational Linguistics:
12

---

Published as a conference paper at ICLR 2026
NAACL 2025, pp. 1855-1888, Albuquerque, New Mexico, April 2025, Association for Compu- tational Linguistics. ISBN 111998889977--99559 doi: 10.18653/v 1/20:/1//2222...// 1/2022.innnnng.sss...... findings-naacl.100 nancc. URL
org. htteias.fiiinnnngneeee www.iinnnnnannnn.nnnn...m
Jannik Kossen, Yarin Gal, and Tom Rainforth. In-context learning learns label relationships but is not conventional learning. In The Tweifth International Conference on Learning Representations, 2024. URL https:t////. //axivv org/ abs 12337....3..
Morgane Laouenan, Palaash Bhargava, and Etienne Wasmer. A cross-verified database of notable people, 3500bc-2018ad, Scientific Data, 91))2990, Jun 2022. ISSN 2052-4463. doi: 10. (0.1038//41157-022-00133 //doi. oro.orgg///o 10. 2000///45590 0010770022200-----2000
Eyméoud, Olivier Gergaud, Guillaume Plique,
URL https:
Jiaoda Li, Yifan Hou, Mrinmaya Sachan, and Ryan Cotterell. What do language models learn in context? the structured task hypothesis. In Proceedings of the 62nd Annual Meeting of the Association for Computational Linguistics (Volume Long Papers), pp. 12365-12379, 2024.
URL https:://///cct http://aaaaatthh aclanthologyy 3zgg2024.aaaee long. pd..
Xiaonan Li and Xipeng Qiu. Finding support examples for in-context learning. In Findings of the 2023. URL https:
Association for Computational Linguisties: EMNLP 2023, pp. 13539.
//arxiv..or
Malo, A. Sinha, Korhonen, Wallenius, and Takala. Good debt or bad debt: Detecting semantic orientations in economic texts. Journal of the Association for Information Science and Technology, 65, 2014. URL http: /ttp/aaavvv///////////.//..a wwwpxiiivorrr..oooooooo abs////b///// 1307 5336v2.
Jack Merullo, Carsten Eickhoff, and Ellie Pavlick. Language models implement simple Word2Vec- style vector arithmetic. In Kevin Duh, Helena Gomez, and Steven Bethard (eds.). Proceedings of the 2024 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies (Volume 1: Long Papers), pp. 5030-5047, Mexico City, Mexico, June 2024, Association for Computational Linguistics. doi: 16.22443/ naacl-long.281. URL http:::p///acaaaaaooooopooooee/e org/2024 www.aaaalllloooo 1o1g.
Sewon Min, Xinxi Lyu, Ari Holtzman, Mikel Artetxe, Mike Lewis, Hannaneh Hajishirzi, and Luke Zettlemoyer. Rethinking the role of demonstrations: What makes in-context learning work? In Proceedings of the 2022 Conference on Empirical Methods in Natural Language Processing, pp- 11048- 11064, 2022. URL https: pestps://azeer /ttp://aaavvve/aa///a/eeee..aaea oor. abs 220222222222 12837.
Gouki Minegishi, Hiroki Furuta, Shohei Taniguchi, Yusuke Iwasawa, and Yutaka Matsuo. Beyond induction heads: In-context meta learning induces multi-phase circuit emergence. In Forty-second International Conference on Machine Learning, 2025. URL forum? iidummid--ii -eeeiid--iio Xw01vF13al
Alexander Modell, Patrick Rubin- DelannDe,,nchh, and Nick Whiteley, The origins of representation manifolds in large language models. arXiv preprint arXiv:2505118235, 2025. URL https:
Tlaxxi.orggeee abs /500. 8233..
Jane Pan. What in-context learning "learn"" in-context: Disentangling task recognition and task learning. Master's thesis, Princeton University, 2023. URL https://aaxiv org/abs/
09731.
Bo Pang and Lillian Lee. Seeing stars: Exploiting class relationships for sentiment categorization with respect to rating scales. In Proceedings of the 43rd Annual Meeting of the Association for Computational Linguistics (ACL'05), pp. 115 2005. URL http:/ /ttt:://arxivv /rgg//gggao.... abs/
cs/0506075vl.
Alec Radford, Jeffrey WU, Rewon Child, David Luan, Dario Amodei, Ilya Sutskever, et al. Language models are unsupervised multitask learners. OpenAl blog, 1(8)99 2019. URL https://cán. openai wtt/ Lww.uaag--ooeee//aaaaeeeeeeeeeee models_ aae_l___ree__ee htt.:aawww...urrrreeeeeeeeaaaaaa
Gautam Reddy. The mechanistic basis of data dependence and abrupt learning in in-context classification task. In The Tweifth International Conference on Learning Representations, 2024.
URL /https://arret .org htsgg/bbs22113 03002.
13

---

Published as a conference paper at ICLR 2026
Baturay Saglam, Paul Kassianik, Blaine Nelson, Sajana Weerawardhena, Yaron Singer, and Amin Karbasi. Large language models encode semantics in low dimensiioin linear subspaces. arXiv preprint arXiv:2507.09709, 2025. URL http: /ttp///axvvvv/vv////v//e../...va org/ attaa/ass/////////// 007000.990222
Rylan Schaeffer, Brando Miranda, and Sanmi Koyejo. Are emergent abilities of large language models a mirage? In seirth-eevntth Conference on Neural Information Processing Systems, 2023. URL httptttt/////. opwnrevieeevveeee /
net/ perrummiddITTTT SedTTT99eedDD...
Aaditya K Singh, Ted Moskovitz, Felix Hill, Stephanie CY Chan, and Andrew M Saxe. What needs to go right for an induction head? mechanistic study of in-context learning circuits and their formation. In Forty-forst International Conference on Machine Learning, 2024. URL https: / //arxiv. org. abs/ 10bbs/244 2404444000000 07129.
Richard Socher, Alex Perelygin, Jean Wu, Jason Chuang, Christopher D. Manning. Andrew Ng. and Christopher Potts. Recursive deep models for semantic compositionality over a sentiment treebank. In Proceedings of the 2013 Conference on Empirical Methods in Natural Language Processing, pp. 1631-1642, Seattle, Washington, USA, October 2013. Association for Computa- tional Linguistics. URL https:/ www. aclweb. org/ anthology/DD3 -1100
Junyi Tao, Xiaoyin Chen, and Nelson F. Liu. Inference and verbalization functions during in- context learning. In Yaser Al-Onaizan, Mohit Bansal, and Yun-Nung Chen (eds.), Findings of the Association for Computational Lingnistics: EMNLP 2024, pp. 16394-16421, Miami, Florida, USA, November 2024, Association for Computational Linguistics. doi: 10. 11533/122/2 findings-emnlp.557. URL https::/accaasee hwwpellooo.oooooog/eeee 2004 windiigs-ennnnnnen 957/.
Qwen Team. Qwen2.5: A party of foundation models, September 2024. Utthttps: /qwenlmm Mathub.io/blle hwtpg///we22/////
Jörg Tiedemann. Parallel data, tools and interfaces in OPUS. In Proceedings of the Eighth International Conference on Language Resources and Evaluation 12) 2012. URL http:/ //tp://wwwww. www. 1 wwee-ccooooo
Lean Wang, Lei Li, Damai Dai, Deli Chen, Hao Zhou, Fandong Meng. Jie Zhou, and Xu Sun. Label words anchors: An information flow perspective for understanding in-context learning. In Proceedings of the 2023 Conference on Empiriaal Methods in Natural Language Processing, pp- 9840-9855, 2023, URL attpss://arxee orgg abs 2305. 14160.
Sida Wang and Christopher D. Manning. Baselines and bigrams: simple, good sentiment and topic classification. In Proceedings of the 50th Annual Meeting of the Association for Compu- tational Linguistics: Short Papers- Volume 2, ACL '12, pp. 90" C94, USA, 2012. Association for Computational Linguistics. URL https: http://wwwwww.nneeeeeeeeee
org/ ort/papez/ /aper/
Sang Michael Xie, Aditi Raghunathan, Percy Liang, and Tengyu Ma. An explanation of in-context learning as implicit bayesian inference. arXiv preprint arXiv:2111.02080 2021. URL https:
/ //arxiv. org/ abs 2111. 02080.
An Yang. Baosong Yang. Binyuan Hui, Bo Zheng, Bowen Yu, Chang Zhou, Chengpeng Li, Chengyuan Li, Dayiheng Liu, Fei Huang, Guanting Dong, Haoran Wei, Huan Lin, Jialong Tang, Jialin Wang. Jian Yang, Jianhong Tu, Jianwei Zhang, Jianxin Ma, Jin Xu, Jingren Zhou, Jinze Bai, Jinzheng He, Junyang Lin, Kai Dang, Keming Lu, Keqin Chen, Kexin Yang, Mei Li. Mingfeng Xue, Na Ni, Pei Zhang, Peng Wang, Ru Peng. Rui Men, Ruize Gao, Runji Lin, Shijie Wang, Shuai Bai, Sinan Tan, Tianhang Zhu, Tianhao Li, Tianyu Liu, Wenbin Ge, Xi- aodong Deng, Xiaohuan Zhou, Xingzhang Ren, Xinyu Zhang, Xipin Wei, Xuancheng Ren, Yang Fan, Yang Yao, Yichang Zhang, Yu Wan, Yunfei Chu, Yuqiong Liu, Zeyu Cui, Zhenru Zhang, and Zhihao Fan. Qwen2 technical report. arXiv preprint arXhv:2407.106711 2024. URL 10671v4.
http:// //aaaiivvvv/ v.xiv.oo org/
Haolin Yang, Hakaze Cho, Yiqiao Zhong, and Naoya Inoue. Unifying attention heads and task vectors via hidden state geometry in in-context learning. arXiv preprint 25ti::2505..855. 2025. URL http: / www./rrg//////oo/o//o.oo.eeeee// absaabss5555 18752v1.
14

---

Published as a conference paper at ICLR 2026
Kayo Yin and Jacob Steinhardt. Which attention heads matter for in-context learnin?? In Forty- second International Conference on Machine Learning, 2025. URL htttp::::/ppeeeeeltttt/
Kang Min Yoo, Junyeob Kim, Hyuhng Joon Kim, Hyunsoo Cho, Hwiyeol Jo, Sang- Lee, Sang- goo Lee, and Taeuk Kim. Ground-truth labels matter: A deeper look into input-label demon- strations. In Proceedings of the 2022 Conference on Empirical Methods in Natural Language Processing, pp. 2422-24377 2022.
URL httpt:tttt......oottt
abs/2205 ....126868 12685.
Biao Zhang, Philip Williams, Ivan Titov, and Rico Sennrich. Improving massively multilingual neural machine translation and zero-shot translation. In Proceedings of the 58th Annual Meeting of the Association for Computational Linguistics, 2020. URL https:/ pttt:p:s/aacaattolooooo
org/ 2egg20200 acl-main. 148.
Ruiqi Zhang, Spencer Frei, and Peter L Bartlett, Trained transformers learn linear models in-context. arXiv preprini arXiv:2306.0992 09927, 2023. URL httpst://aaaiv...rrttttet wtt.ooo////ab/a//ooaa 22066 09927.
Xiang Zhang. Junbo Jake Zhao, and Yann LeCun. Character-level convolutional networks for text classification. In NIPS, 2015. URL https //www///wwww/// wwt.:eeenn.ccco.......o/ooaaaaaa
Ying Zhang, Benjamin Heinzerling, Dongyuan Li, Ryoma Ishigaki, Yuta Hitomi, and Kentaro Inui. Understanding fact recall in language models: Why two-stage training encourages memorization but mixed training teaches knowledge. CoRR, abs/2505.16178, May 2025. URL https://
orgi 10. 48550/arXiv 2505 16178.
Haiyan Zhao, Heng Zhao, Bo Shen, Ali Payani, Fan Yang, and Mengnan Du Beyond single con- cept vector: Modeling concept subspace in LLMs with gaussian distribution. In The Thirteenth International Conference on Learning Representations, 2025. URL https: /opprr///e/ee..ew...
Yuxiang Zhou, Jiazheng Li, Yanzheng Xiang, Hanqi Yan, Lin Gui, and Yulan He. The mystery of in- context learning: A comprehensive survey on interpretation and analysis. In Yaser AI-Onaizan, Mohit Bansal, and Yun-Nung Chen (eds.), Proceedings of the 2024 Conference Methods in Natural Language Processing, pp. 14365-1433 14378, Miami, Florida, USA, November 2024. Association for Computational Linguistics. doi: 10. 121188655v112222 htt/2//22..mmmmaaiia999999 URL https: / /acllalee anthol logyyyooyyyoooooo wogg/0222 emnle-mmee ... 795/.
Empirical
15

---

Published as a conference paper at ICLR 2026
Appendices
Table 3: Prompt templates used in this paper.
Dataset
Prompt Template (Unit)
Label Tokens
SST-2
sentence: [z] senntm [y] \n
negative, positive negative, positive negative, neutral, positive
MR
review: [x] sentiment: [y] \n
FP
sentence: [x] sentiment: [y] \n
SST-5
sentence: [x] sentiment: [y] in
poor, had, neutral, good, great world, sports, business, science objective, subjective
AGNews
news: [x] topic: [y] in
Subjective
revlew: [x] subjectiveeness:
[y] \n
cauntry-capitals
country: [x], label: [w] \p
people-professon
name: [r], label: [y] in
opus- 100
sentence: [ø], translazion:
[y] in
Table 4: Instruction used in Fig. 5.
Dataset
Instruction
SST-2
a helpfill assistant. predict the sentiment the following sentence:
MR
You are a helpful assistant. Please predict the sentiment of the following sentence:
Basic
You a helpful assistant.
prodict the sentiment the following scutence:
SST-5
You are a helpful assistant. Please prodict the sentiment of the following sentence:
AGNews
You helpful assistant. Please predict the category of this
Subjective
You are a helpful assistant. Please predict the subjectivity of this sentence:
w/ Label Space
SST-2
You helpful assistant. Please predict the sentiment of the following sentence positive and negative:
MR
You are a helpful assistant. Please predict the sentiment of the following sentence in positive and negative:
FP
You helpful asistani. Please predict the sentiment of the following senience posilive, neutral, and negative:
SST-5
You are a helpful assistant. Please predict the sentiment of the following sentence in poor, had, neutral, good, and great:
AGNews
You helpful asistanii Please predict the calegory of this
world, sports, business, science: You are a helptul assistant. Please prodict the subjectivity of this sentence in objective and subjective:
Subjective
Table 5: Models and corresponding check- point names used in this paper.
A EXPERIMENT DETAILS
Model
Checkpoint
All the models and datasets are loaded from Hug- gingFace, with checkpoint names listed in Table 5.
Llana 3.2-1B
met 1iss-111a w1w.s/ wlsmmmmmaaaaaee 3.. 3-2210
Llama 3-8B
mata- MMteeMeeataaa-a---aaeea
3-13B
elinas/fll aaaa://1aaaa--3----- 3-133---n3
The Llama 3-13B Instruct is quantized to INT4.
Qwen 2,5-38
Owen:/wen: 2,5-3
Owen 2.5-3B Instruct
twen/2wen2.55 S-3--tsrret
Qwen 2.5-7B
Qwen/Qwer /wer. 2.5-7B
A.1 PROMPT TEMPLATE
Seen Label
In this paper, build the input prompt from Cho & Inoue (2025), detailed in Table 3. Moreover, in the experiments shown in Fig. 5, utilize the instructions as shown in Table 4, with and without label spaces provided in the instruction.
Joe Biden F. Nightingale
Politician
Nurse
Yukichi Fukuzawa
(Politician)
Unseen Label
We illustrate seen unseen label scenarios in Fig. 15. In the seen case, the query's ground-truth answer appears at least once in the demonstration, activating induction heads for di- rect copying. In the unseen case, the answer is absent, and induction heads lose their functionality (Cho et al., 2025a).
Joe Biden F. Niihhtingale Maurice Ravel
Politician
Nurse
(Musician)
Figure 15: Examples of seen la- bel demonstration and unseen label demonstration.
Also, a random label prompt utilized in $4.3 is built by randomly sampling the labels presented in the demonstrations in the label space. For example, for the prompt shown Fig. 16, we randomly (with probability 50%) flip the "positive" to "negative" and "negative" to "positive".
A.2 TRAINING DETAILS OF Wene Waec ($4.2)
As shown in Fig. (C), in the experiment of $4.2, we train two contiguous linear layers in the residual stream of the LMs, with only the first linear layer (parameterized by Weme) attached with a bias term. During the training, only the two linear layers are unlocked for parameter update. We sample 2048 zero-shot training examples, and train the filter on Adam (Kingma, 2014) with learning rate 10 momentum factor 31 = 0.9, B2 = 0.999. After the gradient calculation of every update the parameter once, i.e., we utilize pseudo batch size of 32. The
32 training samples, filters are trained for 4 epochs. After the training. we test the model on a 512-size hold-out test set by strict token matching across the entire vocabulary space.
16

---

Published as a conference paper at ICLR 2026
sentence: 's rollicking adventure for you and all your mateys regardless of their ages sentiment: positive', (n
sentence: playing a role of almost bergmanesque intensity ... bisset is both convincing and radiant sentiment: positive),
sentence: robust and seary sentiment: positive',n
sentence: addictive guilty pleasure sentiment: positive',n
sentence: chance to find love in the most unlikely place sentiment: positive',n
sentence: but because of the startling intimacy sentiment: positive
sentence: the movie 's seams may show ... but sentiment: positive',n sentence: if tragic) ) sentiment: negative\,n sentence: likable story sentiment:
Figure 16: The input for attention visualization.
A.3 DETAILS FOR ECCENTRICITY / COVARIANCE FLUX AND EXPERIMENTS OF $4.3
We intuitively illustrate the eccentricity and co- variance flux metrics in Fig. 23.
Table 6: Accuracies (%) in all configurations shown in Fig. 5 and 6. Ins.: with basic in- struction; Ins. (LS): with instructions and label space prompt; Unseen: with unseen label settings; Rand y: with randomly sampled demonstrations label tokens in the original label space.
The Calculation of Covariance Flux. Given the last token hidden state set H {h: Ji=1 from layer and k-shot ICL prompts, we recall the low-rank filter obtained in $4.2 (indepen- dently trained from O-shot setting) as Wene and Waec. Then, calculate the mapped hidden state as _= ( W Ji and calculate the covariance matrix of the mapped set D Cov [H] also the covariance matrix of the original set as DL,k= = (ov Then, we calculate the covariance flux as:
Dataset
O-shos
O-shot Ins.
O-shot Ins. (LS)
8-shot
8-shot Unseen
S-shot Rand y
SST-2
4.49
22.27
48.83
87.40
15.14
77.44
LInna 3:2-111
MR
0.00
42.19
46.68
90.23
44.92
88.77
1.17
12.30
15.82
73.14
65.01
SST-5
17.97
AGNews
0.20
2.34
15.23
71.78
23.83
66.21
Subjoctive
0.00
0.00
0.00
61.43
0.00
90.78
Average
0.98
13.31
24.09
71.03
14.53
64.31
SST-2
24.61
K2.71
IJama 3-811
MR
FP
27.34
25.98
22.66
82.71
9.57
$7.03
| |
SST-5
0.20
0.00
23.63
45.31
6.74
40.23
AGNews
0.98
9.77
75.59
33.69
48.73
Covariance Flux
(1)
Subjective
Average
7.65
28.29
24.32
77.64
21.66
61.07
where the || ll. is the nuclear norm, i.e., the
Illma 3-131 Ins.
SST-2
MR
63.48
11.13
5.66
1.56
49.80
$8.79
79.79
76.86
35.64
29.59
79.39
80.08
sum of the singular values.
SST-5
4,30
0.00
42,58
47.85
7.03
44.34
AGNNws
13.67
24:22
14.65
68. 75
$8.79
60.16
Subjective
0.00
0.00
0.00
79.79
0.00
53.81
Experiment Details. Based on the same 512-
Average
72.69
32.75
65.48
size test set with Appendix A.2, we sample demonstration sequence for each test sample with & demonstrations. Then, on the specified layer, extract the hidden states from these 1024 test samples to measure the metrics.
SST-2
Qwen 2--38
MR
28.13
61.52
84.38
91
50.98
83.01
FP
8.40
31.05
72.85
78.51
25.00
55.86
SST-5
0.00
41,99
48.14
5.37
41.41
AGNews
Subjective
0.00
0.00
0.00
62.79
0.00
52.54
Average
13:44
27.86
$7.29
74.84
29:82
62.14
Accuracy with Instruction and Label Con- figurations. As supplementary information, we list the accuracies in the input configura- tions shown in Fig. and in Table
Qwen 2.5-318 lox.
SST-2
MR
56.05
52.93
82.81
89
90.33
69.04
85.16
13.48
53.71
66.21
87.59
77.73
76.27
SST-5
0.39
1.17
33.01
50.78
16.50
43.85
AGNNws
1.37
38.48
59.57
75.35
48.92
$3.91
Subjective
0.00
69.33
53.71
Average
57.29
SST-2
48.05
20.12
$4.77
93.07
$4.98
75.20
Quenn 2.5-7B
MR
69.53
0.59
4.30
92.
64
83.40
A.4 DETAILS
0.78
14.65
71.88
68
26.07
41.50
SST-5
FOR ATTENTION VISUALIZATION IN FIG. 10
AGNows
0.20
0.30
35.74
75
46.09
44.82
Subjective
0.00
0.00
0.00
66.41
0.00
55.47
In the attention visualization, we input 8-
Average
24.25
78.38
53,52
77.25
48.70
65.54
shot ICL prompt as shown in Fig. 16 into Llama 3.2- and extract the attention scores from the specified attention head.
'Notiee that the bias terms in the linear layer do affect the covariance, so omit them here.
17

---

Published as a conference paper at ICLR 2026
verbelleet cellicttoon Subopare
Lcce, Reduce
Informationtee verbaliration rition Sabsptce
Ecte. Increase
Verbalaatinn Subapace
A
B
orl orlented Information Removaa
Pinoppl Compoeent
Nas-lask
Information
Demonstration Numbers
An illustration of task-oriented information removal with nonmonotonic eccentricities against the number of demonstrations. The ellipsoids refer the hidden state point cloud with two ground-truth labels (distinguished colors), which is separated even no demonstrations are given, according to previous works (Cho et al., 2025a; Yang et al., 2025).
Figure 17:
B THE INFORMATION REMOVING MAGNITUDE OF LOW-RANK FILTER
Principle of Covariance Loaded as the Lower Bound of Information Removal. Given that information theory suggests the covariance of distribution can approximate its differential entropy (i.e., information content), we can compute the upper bound of the covariance remained after the filtering as lower bound the information removed by the filter. Evidently, this covariance upper bound can be taken the variance captured by its top-r principal components.
We utilize such principle to estimate the gap between the real information removal to the lower bound: if the eigenvectors of Wene fall within the top principal component subspace of the hidden states point cloud, thus we judge that Wene can better preserve the information of point clouds, and vice versa. Therefore, map every eigenvector of Wase to the orthonormal basis spanned by the top-64 principal components the hidden state point cloud, and calculate the ratio vector norms before and after the mapping, as shown in Fig. 25 30 for all the datasets Llama 3.2-1B. In the results, the norm ratios remain low, suggesting that not all the covariance on the top-64 principal components of the hidden state point cloud can be preserved through the Wene filter, i.e., the Wone filter is an effective information removal towards the hidden states.
Although the TVS is composed of two parts W ene and Wacs merely confirming that Wene performs significant information removal is sufficient to demonstrate that projecting the hidden state onto the W enc dec substantially reduces the amount of information contained in the hidden state point cloud.
C VISUALIZATION: THE DIRECTION OF INFORMATION REDUCTION
In $4.3, observe that the eccentricities have nonmonotonie pattern against the number of demonstrations on SST-2 and Llama 3.2-IB, while in some of augmentation results of Appendix e.g., results MR and Llama 3.2-1B (Fig. 47), such nonmonotonic pattern can not be observed.
Our explanation that: as shown in Fig. 17 (A), in some datasets, the distribution of the hidden states sentence embeddings (Cho al., 2025a)) of zero-shot queries does not dominate on the task subspace, i.c., the first principal direction of such hidden state point clouds is orthogonal to the TVS?. So, the early information removal when few demonstrations are given from direction near the first principal direction, which reduces the covariance loaded on the first principal direc- tion. i... reduces the eccentricity. Such removal gradually reduces the dominance of bosk-irreeevant information, causing the first principal component of the hidden state point cloud to progressively approach the TVS, as shown in Fig. (B). this point, the eccentricity reaches its minimum
In this visualization and the experiments of this section, we implicitly make the assumption that TVS maximizes, or at least preserves, the separability of clusters produced by queries of different labels. This assumption is acceptable: if TSS were to confound this separability, the mapping results on TVS would fail to effectively distinguish different lahels, which would contradict the high accuracy observed in Fig.
18

---

Published as a conference paper at ICLR 2026
O-shot
2-shol
4-shol
64-shot
O-sbol
2-shol
4 4-shol
6d-sbol
Figure 18: Visualization the last token's 's hidden states from Layer 13 of Llama 3.2-1B, (upper) on SST-2 with nonmonotonic eccentricity, and (lower) on MR with monotonic eccentricity. The colors refer to the queries' ground-truth label.
and then begins to increase (Fig. 17 (C)) gradually. While, other datasets, the distribution of hidden states of zero-shot queries naturally dominates on or near the TVS, that is, the information removal begins from Fig. (B), causing a monotonic increase in the eccentricity.
We prove aforementioned inference by visual- izing the last token hidden state point clouds from Layer 13 of Llama 3.2- IB on SST-2 (nonmonotonic) and MR (monotonic) with various demonstration numbers, shown Fig. 18. In this visualization, on SST-2, the separability occurs on the 3rd principal component at the beginning of demonstrating, and turns to the 1st principal component on k 4, where
Attention Scores (Layer 6, Head 11)
825
20
Tolen Index (Altwition Query)
80
the eccentricity reaches the minimum. However, on MR, the separability occurs on the 1st principal com- ponent at the beginning. causing monotonic eccen- tricity. Such observations corroborate the process il- lustrated in Fig. 18 and confirm an implicit yet im- portant property: orisntree information removal preserves the distribution along the separable direc- tions of the hidden state point cloud, while com- pressing the distribution along the non-separable di- rections.
120
Token Index (Attention Key)
Attention Teetmap (Layer & Head 11, Query, lws token)
0.10
000
Theee Jibunciks Kast
Figure 19: (Upper) attention map; (lower) at-
Moreover, we consider the reason for such a distri- bution difference SST-2 and MR as the difference in the inputs. We observe some inputs in both datasets, as shown below:
tention scores last token (":"", as the tention query) of Layer 6 Head 11.
(Test samples from SST-2) video, and.
stirs us as well.
all of Dean's mannerisms and self-indulgence,
(Test samples from MR.)
Audiard successfully maintains suspense on different levels throughout a film that is both
gripping and compelling.
The problem with the mayhem in Formula 51 is not that it's offensive, but that it's boring.
Doesn't tt deliver a great story, nor is the action as gripping as in past Seagal films.
19

---

Published as a conference paper at ICLR 2026
spegin, of sentece mosippe ple ebureble expressions of pure movie sentiment posliive
lalse starts populated charatlers nearty impossible about sentment sentence is small but rewarding comady that takes aim contemporary souther scolescence and never lets up. sentient:: posiiiee open sentiment: negattva
sertence: by central potthaa"
serience la con it and very st in its dielogue, this indie fick never found it oudience e probally becouse i exiremely hard relete to any of the charatters sontimant: negative
sentence can wetch, gia gle and gel an adrenaline boost without feeling liee you 've complesely lowered your entertainment slandards sentiment: pos live sentence tojin the pan
great monster sentence: called jor brb nis the movie sentment: negative
flick have come love sentiment: negalive
sentonce hare Venoocinng Interestn and most sentiment:
<peern text sertence: Issit all sericusly sentment: negattvv
sentonce: to ented enough and sendment: positive
sentence: movie staris legend ends with story
etched would impossible to believe ifit sentiment negative
sontonce: surprtiiggty emic dlaagpointment sentientt: negative
sentence
sentiment postivve
in both animation and storytelingg.. sentiment; negalive
sentence: the emperor" 's club any time sentment; posiitre
sontimental has
bue actors pick the sentment: positive
sentence: home movie is swae gesssr and something well worth your yourgmall
contiment:
<hhagin, of sodp sentance hhart w armiiigg non jod gment cin sentment: positive
sertencc ill lacks the utter suthorky of genre gem sentiment: negative
sentence eting memories rendered with clarity that it's filall heapened only yesterday sentiment: posiivee sentence freedom the ir erian people already possess with or without access to the bellot box sentiment: posilive sentence: filed with more holes than
sentiment: negative
sentence really. really good sentirent: postive hungry portions
"sentment: negative
sentence the wonderfully lush mor vem call ar pure punk ex exstential ism, and mss rams and her co -w filer. lf liana d ogn have dram ized the alian war ner which feltikee arswer sentence cean be classifed as one of those alternate rea (mogess
wel
sng sentiment: posilive
except that would have worked so much Beenn dealing in only one meaty sentiment:
muc-ttene
Figure 21: Attention score visualization of DH (Llama 3.2-1B Layer 9 Head 15), where the last token serves the attention query.
MR examples show clear sentiment tendencies, absent in SST-2, likely explaining the hidden state distribution difference between the two datasets. Moreover, such distributional property, i.e., noiae--nise--atio describing whether the zero-shot hidden states are in the status of Fig. 17 (A) or (C), can be designed into a metric to characterize the task difficulty. We leave such a discussion to future work.
D CASE ANALYSIS FOR DHs' MECHANISM
In this section, we provide prototypical evidence for the mech- anism of DH, i.e., locating the important query tokens with task-related information by the attention scores, where the hid- den states processed by the W WK serve as a detector such tokens. In detail, visualize the attention scores of Llama 3.2-1B Layer 9 Head 15 on the last tokens in some cases from SST-2, shown in Fig. 21. In the visualization, is obvious that the attention scores are concentrated on some sentiment- related tokens, which contain the task-related information for the sentiment analysis task defined on SST-2. This result con- firms that DHs can leverage attention scores to correctly filter hidden states generated by tokens containing task-relevant in- formation, thereby amplifying task-related representations, so as to relatively reduce task-irrelevant information. In this process, can equivalently interpret W WK as extracting information from a certain subspace of the last-token hidden state, which en- codes the criterion for determining task information, enabling the subsequent dot- dot-product operations with each hidden state vector to select task-relevant information.
Accuracy (Unseen Label)
Boben wis DEl Boboit wio RK
0.20
0.15
0.10
0.05
-0.4-0.2 0.2 044 0.8 1.0 Ablation Threshold
Figure 20: DH / RH ablation re- sults against ablation threshold.
E DISCUSSION ON THE SELECTION OF ABLATION THRESHOLD
The ablation experiments in $4.4 utilize a fixed threshold of -5%, which might be suspected to be arbitrary. Therefore, this section aims to demonstrate that the ablation results insensitive to this threshold, showing that any mild threshold is sufficient to distinguish DH ablation from random ablation. In detail, vary this threshold and retest the results of ablating DHs and random heads
20

---

Published as a conference paper at ICLR 2026
with the same amount of DH. The results Llama 3.2-1B SST-2 unseen setting are shown in Fig. 20, where thresholds between -0.2 and 0 (note that we use the relative change rate of covariance flux the metric, this is a fairly broad range) all successfully identify the causal effect of DHs against RHs. While, if the threshold is too strict (extremely small values), no head will be ablated, and overly loose threshold will cause many -0.05 within this range as the experimental setting.
all heads to be ablated. Therefore, select
F "IMPLICIT STEERING HEADS" DISCOVERED IN $4.4
Since we test the ablation effect on the accuracy of all the attention heads in $4.4, we can detect more important heads rather than induction heads or denoising heads as an interesting supplement. As shown in Fig. 59 64, ablating Head 11 in Layer 6 causes very significant drop in accuracy; therefore, we examine its attention map under the aforementioned setting shown in Appendix A.4, shown in Fig. 19. We find that the attention map exhibits localized diagonal pattern that recurs periodically with the location of label tokens. Ignoring the attention sink (Gu et al., 2025), this pattern reflects the behavior of the head: locating tokens in the preceding context that identical to the current token (more evident in Fig. 19 (lower), where nonzero attention scores appear almost exclusively at the ":" positions, identical to the current token). Consequently, the attention map produces periodic diagonal pattern around each label token, since the tokens at these positions are exactly the same.
Intuitively, at the final token (":",, this attention head copies information from all preceding "." hidden states to the current position, where, each "." stores the inference result of the previous shot round (e.g., in an 8-shot input, due to the causal mask, the 8th "." position is effectively the output position of all preceding tokens, i.e., a 7-shot ICL input, and thus stores the previous round's inference result). In other words, this attention head functions similarly to "task vector steering": implicitly steers the hidden state of the previous ... (commonly used as a task vector in prior work (Hendel et al., 2023)) to the current "." and aggregates it into updated task vector. This may partly explain why more demonstrations can yield better accuracy, requiring further discussion.
G GROUNDING THE METRICS TO INFORMATION MEASUREMENT
Since utilize covariance-based metrics to measure the information-baat based quantity, which is usu- ally measured by entropy, here we prove that the covariance a linear-scale surrogate of entropy.
Notice that we need to handle the scenario with low-rank inputs (e.g., the point set mapped by the low-rank filter Wene W dec). we define entropy on Hausdorff measure, instead of the typical differen- tial entropy defined on Lebesgue measure, to avoid the entropy calculated being -C.
Definition 1 (Hausdorff differential entropy on d-dimensional r-rank subspace). Let E R2d be random vector sampled from Gaussian X ~ NN,, E), where the rank of E is r & Let H" denote the r r-dimensional Hausdorff measure, embedded the subspace M μ + im()). If p is the
density of X on H", the Hausdorff differential entropy of X is defined as
bow (X) (x)=-} p(x) log p(x) (z).
On such entropy measurement, we can build the link to the covariance.
Theorem (Non-zero eigenvalues as Hausdorff entropy estimator). Let x: E Rd be random vector sampled from Gaussian X ~ (H, Σ), where the rank of E is r & d. Let Ai...., X > 0 as the non-zero eigenvalues of E. Then the Hausdorfs differential entropy hyr (X) is given by
hag (X) (log 2n + 1)
log A
2
2
The Theorem shows that: the covariance loaded on each principal direction (Ax) can be a positive correlated measurement of the information (entropy) contribution (log X;) on such direction, which is the theoretical grounding of our metrics design.
21

---

Published as a conference paper at ICLR 2026
Table 7: Fine-gree Fine-grained data for Table 2.
Random Sample
Unseen Labels
Seen Labels
8-shot w/o DH
8-shot w/o RH
8-shot w/o DH
8-shot w/o RH
8-shot w/o DH
8-shot
8-shot
8-shot
8-shot
w/o RH
SST-2
87.40
61.42
84.041.u 61
15.14
4.78
17. 17.42..18
87.79
62.10
68.731.84
Llama 3.2-1B
MR
90.23
81.25
88.60
44.92
1.27
28.01 28.01
90.53
81.64
65.542.10
FP
73.11
67.38
73.26%.69
0.39
0.00
0.68 0.71
75.00
67.97
59.424.41
SST-5
42.19
30.08
39.282.08
2.93
0.29
3.46 1.34
48.63
33.98
61.79;.77
AGNews
71.78
36.72
63.87a.17
23.83
0.00
14.3210.83
76,95
39.94
77.322.25
Subjective
61.42
53.42
1..711.81
0.00
0.00
0.00 0.00
61.52
53.51
81,30s.9s
Average
71.02
55.05
67.29
14.54
1.06
10.65
73.40
56.52
69.02
SST-2
91.31
86.23
90.94..76
27.14
2.83
26.464.39
91.89
86.91
91.50
MR
93.07
91.31
92.80p.4s
52.83
33.69
40.6714.61
93.46
91.60
93.124.54
Llama 3-8B
FP
82.71
79.59
p2.35
9.57
4.69
8.84 0.76
84.96
82.13
85.47g.40
SST-5
45.31
43.16
45.73
6.73
3.91
6.01 1.29
54.39
51.95
54.83
AGNews
75.58
60.74
p..95p.9
33.69
0.00
31.672.83
80.27
66.70
78.30
Subjective
77.83
71.29
71.562.54
0.00
0.00
0.00 0.00
77.83
71.39
74.974.61
Average
77.64
72.05
76.38a.9e
21.66
7.52
18.9 18.943.98
80.47
75.11
79.70
SST-2
91.80
70.60
92.30p.4z
21.88
0.68
49
92.09
71.09
92.65g.54
Qwen 2.5-3B
MR
89.06
19.941.14
46.00
0.88
48.24 18.24
91.11
81.44
90.33
77.73
79.00
79.45
23.92
27.25
15.31
79.49
80.37
80.35
SST-5
49.71
40.53
47.13
5.47
1.07
5,43 2.19
55.76
46.09
53,442.04
AGNews
74.80
74.90
74.221.88 .B3
43.65
38.96
38.462.21
78.02
78.52
77.42
Subjective
60.74
64.36
62.81 1.68
0.00
0.68
0.00 0.00
62.01
64.36
63.942.52
Average
73.97
68.41
74.31
23.49
11.59
26.823.82
76.41
70.31
76.361.77
SST-2
90.33
89.94
90.78p.uz
69.04
38.28
66.957.u
90.43
90.04
89,96g.sb
Qwen 2.5-3B Ins
MR
89.84
85.53
88.66 38.651.us
64.8s
29.49
66.546.87
89,94
86.13
89.266.32
87.89
85.94
p.
77.73
73.82
73.653.01
88.57
87.89
88.24g.96
SST-5
50.78
48.54
49.96g.55
16.50
10.06
13.97 2.32
56.44
$4.59
56.33a.34
AGNews
75.29
75.29
14.311.20
48.92
43.26
43.654.0s
78.32
78.22
78.091.25
Subjective
69.33
68.16
71.357.54
15.14
30.17
13.18 3.43
69.43
68.26
66,441.16
Average 77.24
75.57
77.28
48.70
37.51
46.324.51
78.86
77.52
78.05
Proof. Since E has rank r, write its eigen degemmeccomooitionnn
Σ == 2 OT.
A, diag (Mg ,.).
On the Hausdorff measure 7t" on M, the probability density function of X is
(-5 - 11) E (x 11)
p(z) (2T) det 1/2 exp
(5)
where E is the Moore-Pentn Penrreee pseudoinverse of E.
The Hausdorff differential entropy is therefore
hur (X) = - Eloo pXX]
(6)
log(2 log (A,) E 1 T 1)]
T (x
x~x
Since E inverts A, on the image of E and annihilates the orthogonal complement, obtain
E xxx [[ - 4)) Ty (r u)] = tr(=+)) = tr((,) = r.
(8)
Therefore,
ho (X) = log(2Tr) + log (er + r
r
(9)
2
= (log 2n + 11
+
log A
(10)
2 1=1
22

---

Published as a conference paper at ICLR 2026
Seeatbaily Oumere RA00011000
Lose
Lobtr
3:2
No Shots
Number Stons
Nanter Shoiss
Figure 22: Eccentricity results of 3 non-classification tasks. (Left)
(Middle)
100s-100 translation: English to Chinese; (Right) country-capital
H PROTOTYPE OF INFORMATION REMOVAL ON GENERATIVE SCENARIO
In $5, we discuss some infinite label space set- tings, i.e., the country-capitals task and the people- profession task, but still on one-token or few-token labels. Therefore, in this section, we generalize these discussions to the generative tasks. In sum- mary, we observe similar information removal dy- namics on generative tasks with classification tasks (Fig. 4 (middle)). However, as acknowledged the Limitation (4) ($5), we can not obtain linear in- formation bottleneck to evaluate the correctness of such information removal (i.e., Covariance Flux). Therefore, this experiment serves only as a proto- typical observation intended to motivate subsequent research within our framework.
Nigh Eccentricity
Low Eccentricity
High Covurtance Flix
Fow cowcow.fee Flow Flux
Figure 23: Diagram for eccentricity and co- variance flux metrics. The green plain refers to the TVS (Wens Waec) obtained in $4.2.
Specifically, perform tests the opus-100 (Zhang et al., 2020; Tiedemann, 2012) En- glish-Chinese translation dataset and Llama 3.2-IB that follow the same procedure of eccentricity calculation of Step 2 described in $3, yielding the results shown in Fig. 22 (middle). Note that trans- lation is not a bijective task (i.e., a single translation may correspond to multiple possible source sentences). Therefore, the translation task exhibits clear ceommation-rmoove trend. This is intu- itive: with the prompt template "sentence: [original text]. translation: [translated text]", the target language is not explicitly specified in zero-shot inputs. Thus, at the last token, the model encodes verbalization patterns corresponding to all potential target languages, with the default pattern dom- inating. Once some demonstrations are provided, non-target verbalizations are removed. If the specified target language difffes from the "default" pattern, this produces the decrease-anddincreass pattern as observed, following the description in Appendix C.
Such results directly confirm the information removal dy- namics in task recognition driven by ICL demonstrations for generative and non-bijective tasks. However, it is con- ceivable that the outputs of such generative tasks are dis- tributed on a manifold (to be compared, the outputs of classification tasks are distributed in the space spanned by the unembedding vectors of their labels). Therefore, utilizing simple linear filter to actively remove task- irrelevant information and locate denoising heads is diffi- cult, as shown in Fig. 24, which echoes our Limitation 4. Future work can intuitively utilize more complex infor- mation bottlenecks to extend our framework to the non- linear tasks.
Blask
Loss
15
Injected Layer Number
Figure 24: Filter- cilter-injection evaluations
Moreover, we repeat the experiment on the people- profession task and country-capital shown in Fig. 22 (left)
opus-100 100 Baglish-Chiness, transla- tion task. In cross-entropy loss.
and (right). In these results, can observe clear information removal dynamic in the peo- ple-profession task, while the country-capital task shows no visible interval of increasing eccen- tricity, which is consistent with earlier discussion in $5.
23

---

Published as a conference paper at ICLR 2026
I SUPPLEMENTARY MATERIALS OUTLINE
Augmentation Results for Fig. 3 ("Filter Injection"). We repeat the experiment shown in Fig. on all the mentioned settings, shown in Fig. 31 36, which are consistent with Fig. 3.
Augmentation Results for the Scatter Size of Fig. ("Filter Injection: Covariance out of Rank r*). We explicitly visualize the numerical results of the lower-bound of information removal (i.e., the covariance rate out of rank) shown as the scatter size in Fig. 3, as shown in Fig. 42 46
Augmentation Results for Table ("Symbolic Fine-tuning"), We repeat the experiment shown in Table Llama 3-8B and Qwen 2.5-3B, shown in Fig. 39, which consistent with Table 1.
Augmentation Results for Fig. 4 ("Eccentricity and Covariance Flux against k*). We repeat the experiment shown in Fig. 4 on all the mentioned settings, as shown Fig. 47 49. The results are consistent with Fig. 4.
Augmentation Results for Fig. and 6 ("Eecentricity and Covariance with Instruction and Various Labels"), We repeat the experiment shown in Fig. 5 and 6 on all the mentioned settings, as shown in Fig. 53 58. The results are consistent with Fig. 5 and 6.
Accuracy with Instruction and Label Configuration in Fig. 5 and 6. We report the test accura- cies on the input configurations in Fig. 5 and in Table 6.
Augmentation Results for Fig. 7 ("Finding Denoising Heads"). We repeat the experiment shown in Fig. on all the datasets with 8-shot inputs and Llama 3.2-1B, Llama 3-8B, Qwen 2.5-3B, Qwen 2.5-3B Instruct Fig. 59 82.
Augmentation Results for Fig. ("Layer Distribution of Denoising Heads"). We repeat the visualization shown in Fig. 8 on all the datasets and Llama 3.2-1B, Llama 3-8B, Qwen 2.5-3B, Qwen 2.5-3B Instruct in Fig. 86.
Augmentation Results for Fig. 11 ("Denoising Head Overlap among Datasets"). We repeat the visualization shown in Fig. 11 Llama 3-8B and Qwen 2.5-3B in Fig. 40.
Augmentation Results for Fig. 9 ("Overlap of Induction Heads and Denoising Heads"). We repeat the visualization shown in Fig. on all the datasets and Llama 3.2-1B, Llama 3-8B, Qwen 2.5-3B, Qwen 2.5-3B Instruct in Fig. 87 90.
Augmentation Results for Fig. 10 ("Attention Map Visualization"). shown in Fig. 10 more 2 denoising heads shown in Fig. 41.
We repeat the visualization
Augmentation Results for Table 2 ("Ablation Experiment"). We list the ablation results on individual datasets rather than the average ones in Table
Augmentation Results for Fig. 12 and 13 ("Factor-recall Filter Injection")). We repeat the periment shown in Fig. 12 and 13 on Llama 3-8B, Qwen 2.5-3B and 7B as shown in Fig. 37 and 38.
'The curve with r = 8 is usually plotted at higher resolution. i.e., one point is drawn for each layer (if 3f 8, we sometimes draw one point for each 2 layers). Therefore, in some cases, the 8 curve appears above curves with lower ranks since the serce plot is usually convex.
24

---

Published as a conference paper at ICLR 2026
PC Stor Rank
PC Nerm Baakkk
Narn Rank
Nara Bf
Nome Dank
Tigeiimniin 47.4 PR (Diegua Weees
Tlamnwcio
TC Noom
0:24
Nomm
0.42
0.26
0.24
0.33
0.33
2.15
0.22
5.20-
0.34
10
15
30
15
20 25
Inpected
1xye EAd LOg
11pe5ted Layur
Expecied Loyer uober
tajedaad Layor
Figure 25: The cosine similarity between all the cigenvectors (each for scatter) of W specific layers and the subspace spanned by the top-64 principal components of the hidden state point cloud, measured by the ratio of vector norms before and after mapping the principal subspace. On Llama 3.2-IB, SST-2, repeated on various inner ranks of TVS, i.e., the column dimensionality of Wene-
Koen Rask
PC Bank
Noen Rook
Ro
Nome Bank
18 20 (00gb Nove
TC Nom
Panuee Noma
0.22
0.32
5.24
0.22
0.15
20
10
Inpected Layer Nurther
Dypeciol Capee
Injezed Lapor Ntrrhor
Dxjected Lagee Nonnerr
byjetted Laper
Figure 26: The similar result with Fig. 25 Llama 3.2-1B, MR.
PC Novta of Rask
2C of Back
PC Nourn of Razk
Rieeennte Nirm
PC Nera Back
0.33
PC None of Dank 16
0.32
2,20
6.19-
6,16-
5.30
0.27
0.24
0:33
100
10
100
10
Injected Nurther
Exjected Nember
Iijettdd Laper Nuncher
Figure 27: The similar result with Fig. 25 on Llama 3.2-1B, FP.
of Breneerr
Telee (c62e4 Ntre
0.23
0.28
Wire of Riuu Saameette
0.32
5.20
2.10
0.20
DC
C.37
0.15
10
Inpected Layer Namber
Lageted Lagne Namber
Irpecsed Lager Nantaee
Sapeted Logne Namber
lajedied Layer Starber
Figure 28: The similar result with Fig. 25 on Llama 3.2-IB, SST-5
PC Yorm of Rusk
ICNern Bakk
PC of Rese
PC Nors of
PC Nome Bank ic
0.30
6:23-
0.22
5.20
Nire NC Sletrreeee
2.33
0.22
0.25
0.23
0,20
10
Figure 29: The similar result with Fig. 25 on Llama 3.2- IB, AGNews.
11SSbe TCT 010344 1000
2.24
dee TC Diggoa
TC TC Eevenerann
0.20
0.33
0.28
C220
0.25
Tejected Lager Sterber
Tejocted Lagor Narber
Tejected Lager Ntecher
Tijected Lague Nimbbrr
Iijaceed Laper Nurther
Figure 30: The similar result with Fig. 25 on Llama 3.2-1B, Subjective.
25

---

Published as a conference paper at ICLR 2026
Supplementary Materials
Zeredbat enpeb-end) Eocriing Magull Cop Out of Berk
2 Siaeday Magetde Coc Detor BAA
0.5
Eacoding
0.6-
Accurazy
Aptaruuy
0.2
2000
2044
2040
0.0
0.0
10
32
14
Injected Layer Number
Inpected Lay Number
Iajected Layer Number
SST-2
FP
0.5
Zero Lapetngg
0.8-
0.3
Accurasy
Accuratty
0.4
0.3
2040
10
12
16
16
6
10
12
14
16
2
4
12
16
Injected Layer Number
Inpected Lay Number
Injected Layer Number
SST-5
AGNews
Subjective
Figure 31: Augmentation results for Fig. 3 Llama 3.2-1B.
Zoro
Zedoo
Zerobat Excadin Siccolla
Eacadag Aipiiio
Sngoda Ragnkede
Cop Ryo nazk
0.8
Cu Baak
0.5
Accuracy
Aucurais
0.2
0.2
0.0
0.0
0.0
25
Lajected Layor Number
Jnjected Lay
Lajected Layer
SST-2
MR
FP
0.5
Dacodiyg Magnlingo
Une Cugik AiZA
0.8
Uve out Back
0.8
0.6
0.3
Acouracy
Accursy
0.4
0.1
0.2
0.0
20
25
30
10
15
20
25
30
10
20
25
50
Injected Layor Number
Injected Layer Number
Injected Loyer Number
SST-5
AGNews
Subjective
Figure 32: Augmentation results for Fig. 3 on Llama 3-8B.
26

---

Published as a conference paper at ICLR 2026
Zeeschet trpee enc)
Mugti
0.5
Bark
0.8
of
0.5
Aocarary
0.6
0.8
Acturacy
0.4
0.2
20
20
30
40
50
10
20
30
40
50
10
20
30
Lnjected Layer Number
Injected Lay Number
Lajected Layer Number
SST-2
MR
FP
Aeti-da teplieerdd) Daoidday Magpltudd
Zapi aast-aatt capet-zzah
1.0
Zigurolot lopan soAll
Tricetine Magnsttue
Cacading Magahrude
Accuracy
Accurass
0.6-
0.0
0.0
0.0
30
50
10
20
Injected Lagar Number
Injected Layer Number
Injected Layer Number
SST-5
AGNews
Subjective
Figure 33: Augmentation results for Fig. on Llama 3-13B.
Maynitude Coe of Bazkk
Eeceding
0.8
Coc DutorBask
0.5
Accuuaryy
0.4
204-
0.2
10
15
20
25
30
5
10
1.5
20
25
30
10
15
20
Injected Lager Number
Injected Layer Number
Enjested Layer Number
SST-2
MR
0.5
Zarbotas (ipeoeedi
Zero-abit (ipas-edd
Zarp book lape--spdi
0.4
0.8
Accurucy
0.6
0.2
0.2-
10
15
20
25
30
15
20
Injected Lagor Number
Injected Liyier Number
Injected Layor Number
SST-5
AGNews
Subjective
Figure 34: Augmentation results for Fig. on Qwen 2.5-3B.
27

---

Published as a conference paper at ICLR 2026
Zipodbat Dasatay Maynitudh
Zere-shel Bryedinn Magetute
Zerohit (opersend)
Deoutiy Maynfauk
0
Col Our Batkk
Co. Dut Bukkk
0.5
Basa
Acouracy
Accurcyy
Accuzucy
2048
2043
2040
0.2
0.2
0.0
0.0
0.0
15
20
25
35
30
15
20
35
10
20
30
Injected Layor Number
Injected Layer Numbor
Injected Layor Number
SST-2
MR
FP
0.5
0.5
0.4
Acoureyy
Acouracy
Accursey
0.3
201-3
0.2
15
20
25
30
35
10
15
20
25
35
0
10
15
20
30
35
Injected Layer Number
Inpected Layer Number
Lajected Layer Number
SST-5
AGNews
Subjective
Figure 35: Augmentation results for Fig. 3 Qwen 2.5-3B Instruct.
bitt-lat eepenvelll
Zero shatt Cppen-ord
Zieo (xpetvend)
Eacoding Naqultuda
Secoding Magaaee
Escading Magetrudk
0.8
O
Bank
Cae Out
0.5
Qut Rask
Accuracy
Ancuracy
0.6
Arcurssy
0,0
0.2
2008
0.2
200c
0.2
2048
0.0
40
0.0
0.0
Lajected Layer Number
Injected Lay Number
Lajectod Layer
SST-2
MR
FP
Zerosden
0.5
Exceding Naguntuda
Goe Out Bank
ONE Bask
Cad Cur of Baai
0.8
0.4
Accursty
Ancuraccy
Aocurwor
0.3-
0.2
0.4
0.1
20122
0.2
4/4
5
30
15
25
30
25
10
15
25
Injocted Layer Number
Injected Layer Number
Injected Laver Number
SST-5
AGNews
Subjective
Figure 36: Augmentation results for Fig. on Qwen 2.5-7B.
28

---

Published as a conference paper at ICLR 2026
2,055
204
2763
4112
4110
15
20
25
Loger
Dajocted Lager
Llama 3-8B
Qwen 2.5-3B
Qwen 2.5-7B
Figure 37: Augmentation results for Fig. 12 on models.
Sypasend
Tank
>abotppe-edd
16
14-
12
Jark
20
15
20
10
15
20
25
Injectedd Lagrer Number
Injected Layer Number
Injootee Lager Number
Ilaama 3-8B
Qwen 2.5-3B
Qwen 2.5-7B
Figure 38: Augmentation results for Fig. 13 models.
MCK 0516 85572
Layer
SST:2,
Layor
1.0
1.0
XCR DETC
0.8
0.75
0.70
0.8
Accuracy
0.6
Aceurney
0.8
0.4
0:46
0.4
0.41
Sub AoNowe DP
Wib, AUNows EP
0.2
0.2
27
0.0
0.0
Both
Trained Part
Traized Part
2810
Xin
19
3512
5513
17 AcDilaa Skaj
Augmentation results for Table (left) on Qwen 2.5-3B, (right) on Llama 3-8B.
Figure 39:
Figure Augmentation results for Fig. (left) on Qwen 2.5-3B, (right) on Llama 3-8B.
Attention Scores LLayer 9, Heed 6)
Attention Scores (Layer 9, Head 20)
025
20
20-
Taken lodex (Atrentun Quary)
Indox (Attantion
68
80
ALL
0.55
2.8
120
20
60
50
60
1.0
120
100
Tolon Index (httectton Key)
Taken Index Ulttention Key!
Figure 41: Augmentation results for attention visualization on (left) Layer 9, Head 6, (right) Layer
Head 20, with the inputs shown in Fig. 16.
29

---

Published as a conference paper at ICLR 2026
1.0
1.0
Conntea Our SUUE
1.0
2.8
0.8
10
10
Layer Nomber
LasKe Mknterr
Eqaated Lager Nandor
Typetad Layse NoRber
Uppeaed Lager
1gedte Lager Panbor
SST-2
MR
FP
SST-5
AGNews
Subjective
Figure 42: Numerical results of covariance out of rank on Llama 3.2-IB.
Conmees 04L BaKK
1.0
3.0
6.
2.8-
0.0
0.
0.
20
10
20
10
20
20
3oydted Layee Nomoer
fepeted LovK Nomber
Is-ded Lover Narder
bypetel Lawe Norsee
Inpeted Lover Numter
SST-2
MR
FP
SST-5
AGNews
Subjective
Figure 43: Numerical results of covariance out of rank on Llama 3-8B
CoNcoaate O0L- Buak
0.8
16
64
0.
0.0
20
Ioaded
ctaected Sumber
Igaded Numberr
Injected
Liger
Igedee Namber
SST-2
MR
FP
SST-5
AGNews
Subjective
Figure 44: Numerical results of covariance out of rank on Qwen 2.5-3B
1.0
1.0
ChRNsEae OREe of Back.
1.0
Beckk
3.0
0.0
0.0
0.0
10
20
30
10
20
10
30
20
30
10
20
13
20
30
SST-2
MR
FP
SST-5
AGNews
Subjective
Figure 45: Numerical results of covariance out of rank on Qwen 2.5-3B Instruct
1.0
3.0
1.0
2.0
2.8
0.8
0.8
0.
10
15
20
10
Layer Nander
Loore Namber
Egaated Laovr Ninder
Typendd Lays Nurher
Tipeaadd Lagur Nemker
SST-2
MR
FP
SST-5
AGNews
Subjective
Figure 46: Numerical results of covariance out of rank on Qwen 2.5-7B
30

---

Published as a conference paper at ICLR 2026
Lioer
Number STAAKS
Ninter Shots
Kunter Shotts
SST-2
Eowesster Ohiaaoo Etati 04 PC1
0.8
0.3
Numberr St 30
Number State
Nunber dEStata 11
Brcerde Sinnerr GuAti un PC32
0.34
Cyste Oyst-sed
0.14
128
350
32
1232
Nuumber
Mumber Stats
Nanber
FP
Eoresiaty Narioo Tattl 00 2011
Opit-464 Acourses
02
12B
256
26
128
24
120
SST-5
0.0
6.0
0.30
0.25
0.9
0.55-
122
122
Nanibor
Number
AGNews
2C1
Lager
Openr
Nambber dEStons 24
Noxtherd of Shonss PS
Norther of
Subjective
Figure 47: Augmentation results for Fig. 4 Llama 3.2-IB.
31

---

Published as a conference paper at ICLR 2026
Liotr
433
Namber StAts
Nimber of Shons
Kurber Stots
SST-2
Eowastor (lecen Etalic PC1)
Opsta 4o4 Mer2200
0.3
Jusneer SEStao 30
Nambbrr of State
Nunder of S1Stata 01
Chaations Brmattee t2rech
0.23
10:35
64
120
Shumber Shwor
Mumber
FP
Eoreuriity Narioo Batto en PC11
118
SST-5
Securratty RN213
0:5
14
Nimborof
Nunber
AGNews
Lager
Consteuue www.ddoddd through
3.6
6--
Opesk
Nonter
Norbver of..terStooe.. G1
Nonther www.berrthheeee
Subjective
Figure 48: Augmentation results for Fig. on Llama 3-8B.
32

---

Published as a conference paper at ICLR 2026
133
Laye
Lapt
Oyen 409 Nrcurv
2.30
6.25
0.24
6:15
0.09
Namberr of Sho15
Nanther of Sheees
Nonter Shets
SST-2
0.13
1.75
1.00
0.22
Numberr State 50
Maambber Shooe
Number of State
3.000
Eocerrdc Nateere Statee 2015
3.875
833
880
8:33
05 32
Namber
Shite
FP
0.35
0.25
16:
433
SST-5
0.25
6.38
6.10
22
AGNeWs
Layve
Laser
Open Accueccy
0.2
0:1
6:8
Namter Shors
Nonther of Staee
Notther of Shote
Subjective
Figure 49: Augmentation results for Fig, 4 on Llama 3-13B.
33

---

Published as a conference paper at ICLR 2026
Lioer
09
0.266
Ope cnd Arrunna
Rocauncte Mierne Balle
mm
Nondber orateer 03
Nanber Shots H6
Number ocshoss
SST-2
0.4
Opitvedd
6:25
3.55
Namtber Shote (0)
Number Shata
Nunber 575t
Trceededs Taate RC12
2.35
Open-ern and
3:3
2.09
0102.0
3632
10.32
120
226
Ximberaf State
Nenbber
FP
Rasto PP
0.2
022
Acoumcs
3.2
830
0102 6/
26
128
10:42
64
120
SST-5
0.30
0:5
Recurraity
939
00224
2622
Norber
AGNews
Lover
Lyyer
0.12
333
Nomtber of STLEEO
Numherr Shonss Hi
Numter Styts
Subjective
Figure 50: Augmentation results for Fig. on Qwen 2.5-3B.
34

---

Published as a conference paper at ICLR 2026
Laye
1.40
033
1.40
855
Number 16500351 14
Nonbor of State
Sondersf B0
SST-2
0,722
1.45
0.12
222-
8.25
0.000
2.1
10.70
0.750
8:38
Manter Shoos
Marbor
Nambbr Shcta
0.0
6.05
0.7
0.1
0052
123
355
250
12+
FP
4.43
3.5
0.--
Opere Aoomrr
0:38
0.0
124
254
SST-5
3.37
3.30
0.3
0.0
0.5
12
Munber
Nunbbr
AGNews
Loyer
Layer
Accuney
Nimher Shors
Nunther of 2i
Narther of
Subjective
Figure 51: Augmentation results for Fig. 4 Qwen 2.5-3B Instruct.
35

---

Published as a conference paper at ICLR 2026
0.33
Looer
0.03
0.23
Number Strrk
Nurberr MunneerfSSboss 14
Nunber Stotss
SST-2
Brweneery Roati
Compleses Secalted dertseddhheeot
0.2
0.00
Nattber Shoca (d
Number Stwwa 30
Nambber Shuta
64
2.83
Rematted
Oyst
0.39
1102
123
355
1632
68
120
250
32
Shunber
Mumber
FP
0.00
1.0
0.35
2.81
4.0
12.00 08
124
16:40
124
246
SST-5
C4
0-4
Sccntraaty
0.19
3.0-
122
122
Nanbbr
Number
AGNews
Lower
Lyyer
3.30
8.5
Nomtber of STEERO G1
Nunter of Stots
Subjective
Figure 52: Augmentation results for Fig. on Qwen 2.5-7B.
36

---

Published as a conference paper at ICLR 2026
Enrqutiig fhe Satto Pd1
0:23
2.30
Labes
6:23
555-
Con Plts theuugh
0.25
Plux theuugh
3.20
9.13
Doseltadiyy Obe
6.15-
0.35
230
0:33
Cayer Tedex
Tager Tralex
Cayer Index
Lagen Trales:
SST-2
Ecoontay (Nar Rutto 2011
0.6
0.5
2.15
8.5
0.5
The thruuh Ri.
2.40
Staven Lobels
6:3
Ter
0:3
2.5-
6.2
MR
Bonantooy Mar Satto PC13
0:20
6:20
3.55
Fiux through
8.1.
3.2
6.1.
2.00
2.2-
6.12
6.12
6.te
Cayer 2ndex
Layer Trdex
Cager Iidex
Loyer Trdex
FP
Exventiiy the Safto on PO1
Incentradiy Satton 2000 PC1)
332
Gabor who Eoit
OUbbE Stavee Lobil
throug
2.00
6:3-
6.4
Tlxe
12
6.2
62
SST-5
Bouanitiity (Nla Sarto PC13
6.7
Dabec
Spard
Pard Labels
Tiu through
2.22
3.20
2.20
15
13
15
Layyer
Layer
Lager
Layer
AGNews
Eonanitlly (fr Satto 1013
cooeeninntty tik (betto oa
Achel with bafee Labal
6.5
Cras
Goe Flox thrugh
Flux thmuggh
2.
6.1
6.1
Cayer Todex
Layer Trdex
Lopre Trdlex
Eayer Todex
Subjective
Figure 53: (Left 2) augmentation results for Fig. 5, (right 2) for Fig. 6 on Llama 3.2-IB.
37

---

Published as a conference paper at ICLR 2026
Somerreity tke thetts on N010
Spuetriity Rbe Bagt on PO33)
9.20
Sotatted thooogh
Retaiied thaoogh
0.20
020
92
0:15
0.2
0.0
Luger Codex
Layer Index
Luget Codex
Laper Index
SST-2
1.2-
Cre Rematted Dhroaith
9.20
0.8
0.30
0.00
0.C-
0.25
2.20
0.20
0.13
Con.
0.-
0.2
0.30
Loder
Layer Dadex
Lagor Iodex
Layer Index
MR
0.8
0.00
0.5
0.33
Romuined through
Coe Remained theuggh
9.85
9.83
Excenssote
220
2,20
0.35
2.10
Layar
Cayer
Layer
Cayer
FP
Ecoanteig in
un
0.33
Onr. Remalted through Ni.
Back Tdlel
Noto Nemalted through
0.30
2.05
0.23
0.4
2.20
2.30
0:35
32
32
Lopee Index
Layer Index
Lapec Index
Layer Zodex
SST-5
Domiined themuugh W. 21.
den
0.25
Eoontraat Ratio
8.80
0.4-
Jubict and loll
Beastnnd Cheuugh
0.4
9.85
0.30
0.20
0.2
2.15
E100
Layse Tedee
Layer
Tnder
AGNews
Cav, Reraited through Wia Mio
1.0
3.A
On: Remo Retostte-ddi througgh
Seccenserr Sla
8.8
0.
0.c.
3.135
0.2
0.100
0.-
1.00
20
30
10
20
10
26
24
10
200
Layer Ihdle
Eayer Indexx
Layer Indee
Caper Iodee
Subjective
Figure 54: (Left 2) augmentation results for Fig. 5, (right 2) for Fig. 6 on Llama 3-8B.
38

---

Published as a conference paper at ICLR 2026
Sowerriity Obe Baith 1010
Somerriity Obe Batto PV33
9.20
Romalee chanough
9.20
Romahed
0.-
0.-
0.15
0.3
Luger Lndex
Layer Index
Luger Cadex
Laper Indexx
SST-2
2.89
Baday
1.50
0.30
1.50
0.25
Remalted
0.75
0.75
2.00
0.20
0.66
0.00
Laper Index
Liger Index
Lagor Iodex
Layer Index
MR
9.30
Romuined (hrough Ni.
0.28
Coe Remained theuugh 1h.
Lobel
2.5
Excenstary
1.0-
0.15
Layer
Cayer
Tayer
FP
2.40
Ner Hend tarough Rh.
9.8
2.00
0.00
44
0.4
8.20
0.20
Lapee Index
Layer Index
Lapec Iodex
Layer 2ndex
SST-5
Eoontrrstt en PCI1
0.75
0.23
Deminne themugg
Juliet and lare
Col Denstned theuggh
Dubaoc Unarn Lands
0.20
1.5
1.175
2.15
1.-
21.50
1.0
2.10
0.5
Ucaess Labce
30
33
Layse Indee
Indes
AGNews
Cov. Renaind thnoggh Ni.
0.C.
Tel- Outict yno Here Ficann
Pari
2.43
OuDoo and Acien Bankian Labile
0.5
Cre. Renaind thoouhh
3.30
0.4
0.23
Scconsiie
220
a
0.-
0.15
01-
20
1.0
20
20
10
10
28
20
40
Layre Trddes
Dayerr
Tagerindes
Caper Trules
Subjective
Figure 55: (Left 2) augmentation results for Fig. 5, (right 2) for Fig, 6 on Llama 3-BBB.
39

---

Published as a conference paper at ICLR 2026
Browedtitt (ee Ohe Bhath on 1010
0.35
Eloenedyyy ote Reets no nott
0.33
andl
Remaled tiro
0.23
0.33
0.20
0.15
9.25
0.35
0.20
0.45
0.05
Luger Ladex
Lopes Indox
Luget Codex
Lages Indkox
SST-2
9.45
2.45
Cac: Bumuiee theough W...
0.22
0.34
Cvlent
0.40
thougg (2
0.20
0.11
9.85
0.80
0.31
0.11
3.25
0:31
0.10
0.00
0.23
0.15
0.15
Laper Iodex
Layer Index
Lapor Iodex
Layer Inden
MR
2.45
Ove Domuined through Me. S..
Coe Demalted through 11 Ma
Lobel
Epoastricty (Oe Rast
2.85
2.05
3.230
0.175
2.15
3.1.0
10
Layer
Layer
Layer
FP
Domuned (laug thrugh Wow Wr
0.225
0.225
Eccnnttin (Og Bush
0.40
Demsiined Chough
0.33
0.225
0.175
0,200
0.300
0.320
0,30
2.375
0,300
0.130
Lapee Index
Layeer lodex
Layer Index
Layeet ladex
SST-5
0.24
0.24
or Eal
0.20
0.30
0.22
Bemstred theugh
Delact Miren Labols
0.30
0.18
2.55
0.30
Epantraat
0.34
0.34
0.22
0.33
2.35
o.re
0.15
2.10
sobel
tobe Crane
0.31
Layse
Indwe
Index
AGNews
2.49
Cor. Rutaand thnough Wi. 2ie
2.5
en Fool
Spiies
0.22
Ecconstate Rutto
Ger Rentated though
0.23
0.16
1.3
0.2
Eccenstore
0.34
0.2
0.22
0.15-
0.10
0.08
0.1
25
24
Layne Trdtee
Laywr Indet
Layer Indwe
Laywer Indes
Subjective
Figure 56: (Left 2) augmentation results for Fig. 5, (right 2) for Fig. 6 on Qwen 2.5-3B.
40

---

Published as a conference paper at ICLR 2026
Brcseieking thhe Botto PC11
Ecoenttatt oht Rodts 30
0.20
fix piaeee
0.33
0:25
0.30
0.20
Eluc
020
0:25
0.15
0.33
0.25
0:55
0.03
Luger Lodex
Lopes Todex
Luger Codox
Lapes Tndex
SST-2
3.45
nebit lac.
0.25
Rebit Iis.
0.25
3.85
Col. Flax througg
0.33
Elax 1i0-tthruuhhhhh
0.35
9.00
04:38
0.23
3.30
0:35
Epeataiitt
0:20
0.35
0.13
2.35
9.30
Lapee Index
Liyer Indox
Lagor Todex
Laycz Index
MR
2,300
2.025
Coboe patted Label Spray
0.22
Peflic
0.25
Eweatriit Obe Rulb
9,775-
0.30
Dvn Elux (2oough
0.23
Cre Flux through
0.35
2.05
0.22
0.28
Eecentreety
0:32
0.15
0.10
0.13
20
Layer
Layer
FP
0.20
Cus, Flss Damnggh 111
3.00
3.399
2.55
0.23
thruggh
0.23
Eccenntely
2200
3.175
2.45
0:30
2.1.0
0:10
Lapee Indox
Layer lodes
Layer Index
Loyez Indck
SST-5
2.55
sefic Jod
0.7
0.25
tha Rado
2.50
2.35
0.5
Dublet and
Rutta
2.00
9.39
CoN Flax throogg
0.5
8.00
2:30
9.5
2.55
2.33
0.2
0.1
Indox
Layer
AGNews
0.42
0.45
2.50
11.02
Sandin Label.
0.45
2.55
0.35
0.25
0.25
0.33
0.33
Eeconsttty (Na,
0.35
0.23
0.00
0.25
Cov. Flax
0.38
2.23
0.28
0.13
0.15
10
20
30
15
20
30
Layve Trdlew
Leywer Indes
Layer
Layser Indes
Subjective
Figure 57: (Left 2) augmentation results for Fig. 5, (right 2) for Fig. 6 on Qwen 2.5-3B Instruct.
41

---

Published as a conference paper at ICLR 2026
Browtriity Ober Bhets 1010
0.55
1.5
1.4
0.20
0.25
0.25
0.20
0.33
0.35
0.03
Luger Ladex
Lopes Todex
Laper Tndok
Lager Indox
SST-2
9.45
0.-
3.43
Ouboit and lar
Con. Remuted Etarugg
Con: Bertatte the Bhrrough
0.29
02
0.2
0.13
Lapee Index
Layer Dadex
Lagor Iodex
Layer Zadee
MR
Demuine (Lrough V...
0.20
0.5-
0.6-
Batto
0,30
Or Remalned therugh
2.25
0.23
0.20
0.3
Layer
Cayer
Tayer
FP
2.45
1.75
Our: Bemoatted throuughh Mi..
1.0
Back
0.S.
1.25
0.00
1.40
0.G-
Net
Eucontsity
0.4
0.0
0.25
0.2
Laper Index
Laper lndck
Lapec Index
Layer Zodex
SST-5
2.50
Hars.
Ecantriayy Rutto
0.5
Oae. Humutedd bargugh
Da Ressited themoggh
220
0.2
2.3
0.125
0.130
sobic Xre
3,075
15
15
Indww
AGNews
Outict yoo
0.63
OvDos and teri
Car. Retaand thnough Ni.
8.8-
furee Fapeer
Cor. Rentateed thnough Ri.
Acces Bank Labils
2.39
0.30
0.c
0.30
0.29
Eqcontatty
Rocunsture
0.15
9.33
20
18
15
10
20
18
17
200
Layer Trddes
Eayerr Tiudao
Caper Ttdlen
Subjective
Figure 58: (Left 2) augmentation results for Fig. 5, (right 2) for Fig. 6 on Qwen 2.5-7B.
42

---

Published as a conference paper at ICLR 2026
Layer 0
Assndae by
bocecde Cernecsons
Chazge
03.9
0.80
ma
Aboate Atteedee Bied Iode
Attondee TTaad Index
Layer 1
Ercuntrccyy
Saleon Charge (34)
10.00
2.0%
14
1.30
18
20.23
Allendicnn Itaval Inddox
Layer 2
Iedlactinn Megrctede
Layer 3
0,002
2.155
0.004
Atrecten
4.7%
Guan
Attendoe TSnnal trdixx
Layer 4
11.5%
Poneectety Accatsry
0.31
Chanoe
5.0%
0.34
4.5%
Abated Antetton Beat Iafex
ATtERtii Read Invir
Layer 5
4.7%
2.5%
2.78
Addentton Slead lades
Layer 6
0.30
IT 19
Layer
Albertn Spuma
Caange
Road Traee
Atbortion Clead Indios
43

---

Published as a conference paper at ICLR 2026
Layer 8
Intuttie Naptiche
Contana
10
Mosted Mlvetion BSed Erdo
Atfertion Stoad ladix
Layer 9
Nagaltade
4.9%
2.9%
0.85-
Civsranca Thu
Layer 10
Anaracy
2.7%
Abudied Allention
Alternoe Stad Indot
Layer 11
Induttiee Napstaaee
2.5%
42.9%
Musted Alveiii Boed Erdek
Attretton Elaad Indee
Layer 12
Clange 158
0.0
20
2044
Layer 13
Intacios Magghtute Indactoc Comeezan
Chagge
2.00
Abtited Ameettonn Hoad Trdns
Atbenston (Tead TEdRE
Layer 14
Iedadioo Mageltze
Abtecdenn Scora
2.%
0.90
Attortion
Iados
Layer 155
7.5%
3.99
Fock Fire Dre temo
2.5%
0.95
15 10 1/118
06
Attonriin Tiene Irddrc
Figure 59: (Left) augmentation results for Fig. (right) induction score of each attention head on Llama 3.2- 1.2 SST-2.
44

---

Published as a conference paper at ICLR 2026
Layer 0
King m.d
1.
Ubg
Aboate Attredie Tied Indr
Aetuntion Thood Indee
Layer
0.24
2.8%
11
0,00
3.88
12
Allentiinn ISoaal Irdeo
Layer 2
0.25
Iedaction Megested
23.95
Layer 3
585
10.00
52.8%
Com
Alsentien Indis
Attendoc TSanal Endix
Layer 4
2.00
Wosee Ameetton Hoad Tr00s
ATSEEDIO Hoad (nvins
Layer 5
Indacioo Magalada
2.95
Contraci
Abaate Mivodee 1ond Trdee
Attoedtio (Tane Indee
Layer 6
3.25
11
Indactio Carredbbar
23.95
Scoeeddy
1o Alsentian Head Indls
Mlsted Allontie (hedd Ladks
Layer 7
Intactio Sageloce
Gootune ka
120%
tlead
45

---

Published as a conference paper at ICLR 2026
Layer 8
Intutine Naptiahe
Change
3.8%
23.8%
Mested Mivetio ised Erde
Atfertion Stoad Iadix
Layer 9
4.7%
Ielatos Clane
Actertion
Layer
Domenniety Acrumyy
Indacton Megnaads
4.0%
Abisted Amertion Hoad Trdex
Attorntion Clone Index
Layer 11
Hapaiake
03.8%
Layer 12
Daage Charge
0.70
4.0%
Hoad Traex
Attenntion TTane Indee
Layer 13
Conrllzze
Abaled Allection Hond 1200
Alteriinn Stoad laAks
Layer 14
6.7%
Foomusiity
Nagataate
2015
-0.0%
Layer 15
5.9%
2.9%
Iaductice Cotrectians
Acterle
2.5%
Alated Allxtite Bhedd Ladk
12
Allantion Stoad Inaios
Figure 60: (Left) augmentation results for Fig. 7, (right) induction score of each attention head on Llama 3.2-1B, MR.
46

---

Published as a conference paper at ICLR 2026
Layer 0
Trventncty
Magatrate
Chagge
2.8m
[F]
daice
Alcoted Alveniin theed Icoa
Lea thoud Lunde
Layer 1
3.95
2.5%
0.9%
2255%
-5.9%
23.99
2.99
Scoeerdty
42.9%
Aboatd Altedien 1Sed TrOr
Attondee ITAnd Tndee
Layer 2
Scome
02.8%
0.33
10.33
13
Layer 3
4.15
0.000
760
0.00
0,00
Consrbtte The
0.00
0.003
Layer 4
Iedattoo
12 19
Layer 5
Intacioo Magahuue
Chargee
A. 1
Ablattd Ateettinn Hend Traw
Atbennton Cland Indet
Layer 6
Moguutale
F
10 1e TE IT TE
Layer
6.7%
Inaactio Sigghhute Inaevtio Comeetaass
Change
Albertan
Hoad Trates
Atbortion Clead Inaloc
47

---

Published as a conference paper at ICLR 2026
Layer 8
Intutine Naptiafe
Contania
Change
3.90-
Mostel Alteaiin Bedd
Adtertion Sload ladox
Layer 9
Nagaladda
Cirsranca Tla
to
00:1
Layer 10
Ercentricty
21/70
Jaleoa Chaoge
0.00
Alcated Artustio tlond
Alternon Staad Indot
Layer 11
Iadactic Hoganade
Coudisee has
Aftretton Elead Indee
Layer 12
2.5%
D4lbbr Chagge
Condutace
2044
Layer 13
6.7%
Eomeudeity Accemcs
Intactio Magghtute Indactoc Comeezan
Altrrtao Scoral
Chasge
0.0%
Aiiated Amrettonn Hoad Trons
Atbendton STead Iedee
Layer 14
0.79
Induliee Nagataade
2.0%
Abuuked 12000
Attortion Slead ladox
Layer 15
Domesricer
2.70
Aramay
Amerttinn Hond Traies
Attentiin Tiane Irdiec
Figure 61: (Left) augmentation results for Fig. 7, (right) induction score of each attention head on Llama 3.2-1B 1B, FP.
48

---

Published as a conference paper at ICLR 2026
Layer 0
PM1
10.05-
1.44
23.85
33.95
0.00
Altnnden Iadre
Aftendien Tanad Indox
Layer
Kouudeen Magi
3ARDON Chagge 780
tha
3.955
0,00
Layer
Abeated Aisetion Indes
Layer 3
0.00
douttie Comeetarn
Telethe Chargg
0.7%
2,0%
Atreaiin
2,00
Micded Hoad Szades
Atlendiie Toxnal Trdixx
Layer 4
0.37
7dktio Chaoge 1961
6.0%
18
Layer
by
Intacioo Magahude
Misatuns
Abaad Minedee Boed Tod
Atbennton Cland Indet
Layer 6
Magalak
21.8%
33.95
Allvntie Ladks
Allendicn taxall tndis
Layer 7
Inatatio Stgghtute
Charpp 120
Conatiee
4.7%
Micied Atrection Hoad Toales
Atturtion Slead Indio
49

---

Published as a conference paper at ICLR 2026
Layer 8
Intutine Naptiahe
4.8%
4.8%
10
Mested Mivedi Bod
Adtortion Sload Iadox
Layer 9
indactoo Nagelada
2.8%
1.8%
U
Abaated Aiteeee trdes
Albertion tlone tndee
Layer 10
4.7%
Layer 11
Inkelkke Crewten
2.99%
-.99
Emeerritt
Abated Atteetvv Hadd Indre
Atbrestinn Eload Irdee
Layer 12
150
Consriace tha
6.%%
9 2 Jue
ladis
Layer 13
4.10
0.8
2.0%
0.
Hond Iodex
Attantionn STane Italic
Layer 14
Maptiako lakatike Correctanss
2.8%
3.55
2.8h
-3.8
Abcoted Alveliee Bhad lnba
Alturtion Stead ladis
Layer 15
Indactic Magucaaee
04300ve Ohaege
33.0%
13 14
Aterttion Hoad Tradir
Figure 62: (Left) augmentation results for Fig. (right) induction score of each attention head on Llama 3.2- SST-5.
50

---

Published as a conference paper at ICLR 2026
Layer 0
0.22
0.000
22.
2.86
12
Allentionn Iooal Indox
Layer
0.00
Chaogg 7914
h
Layer 2
Indaction Meggctak
0.08
Abcated Absodion Iodes
Slund
Layer 3
0.000
0.00
Aflenticn Hooal Invix
Layer 4
Charge
2.8%
Comeeriity
Alrated Aitestie Haed Tndee
Atlendic 1orad Didix
Layer 5
Comeenicar
Thlahe Clange 150
2. R.
0.0%
Abaueed
Aldontion Slead ladie
Layer 6
0.14
Dilltin Change
1.5%
Ablated Attretee 1ood Indre
Ansention Tied Tndee
Layer? 7
by Contaace
Iedactio Magetade
Zaletho Chagge
5.5%
11
14
Aftertion Stead Iudos
51

---

Published as a conference paper at ICLR 2026
Layer 8
10.05
Irdanton Segetone
Contasi
0.00
Mested Mivetii isdd
Adtortion Stoad tades
Layer 9
Ohange
23.95
Layer
Domennicty Acrumyy
6.0%
Inductice Cornectoo
Chaage
Abuilidd Allention Hoad Lodox
Alterton Stead Indot
Layer 11
3.7%
Foomushity
Iedactic Megrctede
Changg
v
2.00
13 1E
Layer 12
4.8%
Comeraas
Maated Aitvetiee 1oad Traer
Altrettnn ETANE TOONE
Layer 13
7.5%
Indactoo Mageluue
3.%%
2.9%
5.55
-2.5%
Abtated Alvodee Indes
Atbordton 11ane Iudee
Layer 14
Irdacie Comeazan
Domnstety
Layer 15
Indatie Veggcake
600
4
1..0
Conertuce
005
Mbaked Atrentoon Hoad Ioole
Atsentian
Figure 63: (Left) augmentation results for Fig. 7, (right) induction score of each attention head on Llama 3.2-1B, AGNews.
52

---

Published as a conference paper at ICLR 2026
Layer 0
Magataak
148%
23.9
25.95
Scoeerdyy
0.00
Ababed Attredee 1oed Irdr
Atteeder Tinad Indie
Layer
0.06
0,00
-355
0.04
23.95
0,00
0.000
Aftondien 1Shad
Layer 2
$3.95
Indactinn Houphhute
iha
Caaoge
1.8%
0.55
Layer 3
6.7%
Charge
2.7%
n 0
2.75
Miided Atrection Hoad Izdlex
Acsuntic Head Indixx
Layer 4
3.00
Indactio Magecaade
0.35
15
1 18
Layer 5
Intacioo Magahuue
23.9%
13.9%
21.0%
33.95
Ababdd Miredee Tadee
Attirntion Cload Indet
Layer 6
23.95
23.9%
18.01 13
Layer
2.99
Srome
Iedietiv Commeraas
Attrentin Elead Indert
53

---

Published as a conference paper at ICLR 2026
Layer 8
15.95
Inturtie Nagticht
Contaan
Mosted Alvetion Used ToOK
Attortion tadox
Layer 9
7.55
Chatgg
3.95
2.99
0.9%
Acterlion
-3.5
Layer
Inductice Nagtiaaee
Change
1.00
Alaatdd Arsiition Fland Sidex
Attorntion Eland Indet
Layer 11
Iedastio
Charge
0.0%
Layer 12
200
Cramattens
Ohaege
0.0m
Aterrtinn Hoad Traee
Attertiinn TTane Irdee
Layer 13
Accemn
Abulted Allection Hoed 1200
Alteriinn Stead Lados
Layer 14
Nagataate
Chasge 1961
Conrtizze Tka
15
Layer 15
1.%%
Inductico Cocretzar
1
Mirrban
-300%
to 1015
Attoontin Tiene Irdeec
Figure 64: (Left) augmentation results for Fig. (right) induction score of each attention head on Llama 3.2- BB, Subjective.
54

---

Published as a conference paper at ICLR 2026
Layer 9
Infariie Naptiste
Courtezes
Indutine Corattnns
A00ee Road Troes
Attrrntion BlAK todet
Layer 11
4.7%
2.75
Attertien Sooe
11.0%
Abulied
Altentani Stead Lakii
Layer 13
Clange 1h11
3.8%
Inducticn Cornetnen
2.5%
0.0
Aboodie 1Sed Indrs
Attention Stund Indiox
Layer 1.5
Indictic Sagazade
20085
Alcoted Alveliie BSed lcda
Allerttinn Head lndis
Layer 17
Consttate Thx
Layer 19
Chagge 132
Modted 16000
Altertion Stoad Lobox
Layer 21
031
Change 786
Bomecricty
2.70
Figure 65: (Left) augmentation results for Fig. 7, (right) induction score of each attention head on Llama 3-8B, SST-2.
55

---

Published as a conference paper at ICLR 2026
Layer 9
4.7%
Indatia Hagaiads Cornectans
Polethe Chaoge
6.0%
2.7m
Acnemec
Abcdee Road Indes
Atbertton Stead ladix
Layer 11
160
4.7%
Indacton Nagaliada
2.7%
[
4
2.7h
4.5%
Concriaten 7kx
20
Layer 13
Caaqee 786
$0.95
Eeseunccy
2.80
2000
Altated Alluntie
12
Alteroon Staad Indot
Layer 15
Indactiee Magriede
4.0%
12.0%
4.0%
Consriann
Woste Amertton Hoad Trans
Attreetion Elead trdee
Layer 17
Clanve 593
Acturdiee Sorea
3.79
400%%
20/4
Layer 19
Intactio Magghtute Inaaetio Comrezann
Albortan
6.0%
Monited Hoad Trale
Atbindton Claad Indec
Layer 21
Magacaae
222
-1.0%
2.76
-3.7%
22.000
Adtorstion slead Iades
Figure 66: (Left) augmentation results for Fig. 7, (right) induction score of each attention head on Llama 3-8B, MR.
56

---

Published as a conference paper at ICLR 2026
Layer 9
Indatic Hagaiado Correctans
Doarkeze Acarscy
Chooge
Musie Triies
Afterntin SlAae TOdOs
Layer 11
Indactoo Nagaliaaa
Consttate
Chasge
4.0%
20
Layer 13
13.9%
Erentricty
Inductic Cornectoon
12 Allentie
Alternon Stead Lndoo
Layer 15
2.0%
Indactiee Magriede
Contanc
pq..
Bo
Alcated
Adforttonn blead lades
Layer 17
Tidatte Clange 188
600
20-2
Layer 19
3.79
Intactio Magahuuee
Baleor Chaoge
Ablited Atrection Hond Tral
Atbendton Cland Indec
Layer 21
0.35
Laluttio Magakade
2.2%
330%
10
13 14
17
Figure 67: (Left) augmentation results for Fig. 7, (right) induction score of each attention head on Llama 3-8B, FP.
57

---

Published as a conference paper at ICLR 2026
Layer 9
Indatire Naptiste Indutine Cerwttens
Coudioee
Charge
WORE Road Troes
Attrrntion ElAN ToOeE
Layer 11
4.70
Actentiin Sooms
PHAli Change
Abulied 1200A
Altentan Stoad Ladio
Layer 13
Inducticn Cornetnen
3.9%
Attention Dlund Indiex
Layer 15
Indactice Hogaiaae Correctanss
Alcoted Alveliie Dead lcda
Allerttinn Head lndos
Layer 17
Indacton Magaltude
Chasgg 193
207%
Alsumm Scrua
mQ 18
2.7m
Consttate Thx
Layer 19
1.10
Change
Arretiin
Alternon Staad Lodox
Layer 21
Induttio Megnlaee
81
025
Conoriizes Tka
13 14
Figure 68: (Left) augmentation results for Fig. 7, (right) induction score of each attention head on Llama 3-8B, SST-5.
58

---

Published as a conference paper at ICLR 2026
Layer 9
Intatire Naptidds Cornetaas
4.7%
Tolethe Charge
0
1..0%
4.0%
Abcdeed Hoad Indies
Alberttin Stoad ladix
Layer
4.0%
Iadactoo Nagaladda
Charge (36)
11
0.75
Layer 13
23.35
11F
53.9%
Adtrodion Indie
Alteroon Staad Indot
Layer 155
11
23.8%
Mested Alteeiie Boed Erdok
Attrerton flese trder
Layer 17
Change Charge
Covaranea Thu
Layer
Domeniccy Arrmey
Indacioc Sagahtute Indacbo Comrezan
Mbdied Allection Hoad LOOOR
Atbendton Claad Indeo
Layer 21
Intactee Mtgpiade
4.70
400%
Conelezze
4.0%
12.00
Adtortton Sload Iadie
Figure 69: (Left) augmentation results for Fig. 7, (right) induction score of each attention head on Llama 3-8B, AGNews.
59

---

Published as a conference paper at ICLR 2026
Layer 9
Intuttie Naptiafe
Couattae Fkt
Alcaked Atcention Hond I2.lex
Adtortionn Slond Iadix
Layer
Actertion
12.0%
4.0%
OF OF
Layer 13
Inductice Nagsiaate
3.89
Soweerdtt
Aboated Atteede Toad Indr
Athintton Cland Indiet
Layer 15
Inleciea Mageashs
(50)
4.10
2.7%
607
1..0%
Layer 17
4.7%
2
Seuma
4.0%
Hoad Traeee
Attention TTANE Irdee
Layer 19
Jhlbbr Charge 136
2.70
Indactic Comeezann
4.00
4.7%
Alterton Staad Indot
Layer 21
Irdaatio Meggctade
Chasee 1941
Conatiane
825
3.mm
0.
Figure 70: (Left) augmentation results for Fig. 7, (right) induction score of each attention head on Llama 3-8B, Subjective.
60

---

Published as a conference paper at ICLR 2026
Layer 0
0.00
Seaeteer Corsersee
0,006
0.00
Layer 2
1.85
DAcca Magatzak
Abated Metiie Seed Indr
Layer 4
Afteatic Hood Index
6.7%
Doansiiity
0.10
tudution Megriaaee
Charge
4.7%
Layer 6
4.7%
1umb
Aoaeed Atrention Tined Trole
Layer 8
Aetraton Bbed Trdex
Rooeeticy Conetoae the
Iadatae Hagiinaa Curnekons
3ilchs Clarge (50
0,33
Absaked Attection Hoad Indis
Layer 10
0.38
Magucaae
0.0%
4.0%
Domeeticty
Layer 12
0.77
Chaoge
Jb Atrection Tond Irder
Layer 14
Artention Tleed Tndex
Clange 1941
Conatonce
Ga1c
0.00
0,000
Layer 16
4.70
2.7%
1.0%
60%
10 Alrectin Hoad IedUs
Altettin Head Inder
61

---

Published as a conference paper at ICLR 2026
Layer 18
6.7%
0.00
Conslizae
0112
Change
01000
Abuded Alrention Hond lzdke
Layer 20
Allvetice Taval Irdix
irdacioo Nagalida
Chasge 19
4.0%
Miverim Stare
3.7%
0.0%
Coualose Aorueyy
Wooted Attertion Hoad travs
Layer 22
Aftrrtion [leat triee
Indartine Naptiaake
Conduees iha
2ahoae Change
4.7%
Abusked Izdes
Layer 24
Lados
0.17
0.000
0,000
Aboated Alteeeen 1Sed Indos
Layer 26
Atlendes 1Stadd Tndix
Ementeccy
Inductice Correctenn
23.95
Atated Alletate tied Lo0ks
Layer 28
Altenton Sead Lndox
0.31
Indactic Magutaade
/Biated Intection Hond Trdott
Layer 30
Amsetion
3.79
Maptiske
17
Whrtte Antection Hond Irdot
Layer 32
ETAnd Triee
Iealstio Mogettuee
27
607
-1.0%
4.2%
Alrestion Indut
Layer 34
Eccasiiity
Iadatas Hugizaa
400%
2..%%
Hoad Irdert
Anwetton
Figure 71: (Left) augmentation results for Fig. 7, (right) induction score of each attention head on Qwen 2.5-3B, SST-2.
62

---

Published as a conference paper at ICLR 2026
Layer 0
23.0%
23.99
0.42
Sotectir Cornecaser
0.9%
0312
20.95
23.8%
91.%%
Lcbk
Layer 2
33.95
Leveancy
0.20
DAACE Magatzak
23.8%
0.15
23.95
Meated Mevdie Seed Irde
Layer 4
Abtetice Hood Intox
Vudti Megriaae
2.9%
11.0
2.00
Caverine
0.00
Layer 6
00175
D4102 Change
Acann
Woae Amertton lond traie
Layer
Jeteaton Bbod Trdiex
0.38
Iadatie Hagginda
Clargo (h
0.7
100%
nIL
Absseed Aitection Indet
Layer 10
Magataak
2.70
Maniitn Scoee
0,000
Abatad Aliection Nond Lndbo
Layer 12
Allentic tsoa Indox
4.7%
Indacten Hugiituta Dannkoon
Antratic Seora
Chaege
0
1..0
Conalites
Whrtte Attection Hond trdos
Layer 14
Ameetion
12.5%
Eccestticy
toutke Megra
Changee 159
11:10
1.7%
0.000
Alattd Aruutioo Head Iadex
Layer
Allendis 1aaal Irdex
Conrltte The
11.00
Tolbbe Comecton
Chaage
0.700
mm
0.20
63

---

Published as a conference paper at ICLR 2026
Layer 18
2.7%
Comentety
Change
Abuledd Aliention Hond Lodus
Layer 20
Aluzzian Hoad lindox
irdacioo
iedecion Comveaan
1.27
12.0%
Abuded Aliention Hond Locbux
Layer 22
Atbresttn [lond trdet
Conducee Tke
Joaeed Atrectinn Tindd Traee
Layer 24
Attreston [Toad troeet
02.9%
koudioo Magi Bode
mm
0,000
Layer 26
Change 7660
03.95
lnsuuncty Coverame the
Inductiee Cornetnon
23.55
Layer 28
Head
Comeuticty Acrmay
60%
Iededee rendan
Change
0.18
Ablaeed Atrection Tind trdex
Layer 30
Antention Heed Tndex
Iaductic Correczo
Clange
13.0%
Mudted Aliection Hond Lndbet
Layer 32
Allentan Stad Lndox
Intacioo Magalute
Charge
3.7m
10 Atrettion Tondd Trder
Layer 34
Atbertte TIaad Irdvet
P5a
0.%%
Figure 72: (Left) augmentation results for Fig. 7, (right) induction score of each attention head on Qwen 2.5-3B, MR.
64

---

Published as a conference paper at ICLR 2026
Layer 0
13.99
Inducton Correcbers
11.80
3.95
nam
0,004
Bsnd Todng
Layer 2
Jetiation Thod Todrss
11.8%
0.115
Inkurtes Siepeias
03156
00075
Mivertie Hed Irire
Layer 4
Hbod lndix
Change
2.8%
0.85
0.055
ledactes Cernetions
22.h
0,000
-.995
Corsrane Thus
0.005
0,000
Layer 6
3.9
0.14
Dan
0,000
235
Abouted Alvitite thad Icdo.
Layer 8
Atlvetice tooa Indox
Gomemnicy Coortoee the
Ialates Hagiinaa
Ohange
207
Layer 10
4.7%
Enceastitty
Magucade
Accencs
2.7%
0.0%
0.33
0.11
Hissted Attection Hond Iedii
Layer 12
Arseztion Head Irdex
0,00
Change
3.35
4.2%
amm
Mlated Moreete Indoe
Layer 14
Attondee TTout
4.15
Nuguizaa
Stene
4.70
600%
Layer 16
4.70
0.6
60%
634
0.0
Macaeed Atrention Hond Indie
Acsetiin Hend Index
65

---

Published as conference paper at ICLR 2026
Layer 18
4.0%
608
Abaated Atrettion Hond Irdex
Layer 20
Arwetiin Headd Index
6.7%
Chappe
2.7%
2.7%
4.0%
Abuded Aliention Hond Lndbes
Layer 22
Allentin Heat Lnako
4.15
Indactic Correctaons
Nagaiads
Broweshity
Abuded Aliention Hond Induus
Layer 24
Allentin Heat Inakox
6.0%
Chooge
4.7%
2.7b
Abaded Atrection Hond tzdee
Layer 26
Allvetice Haad bidox
laductic Haganade
Woated Attection Hoad Indos
Layer 28
Attiection Elaad trdee
Iedactic Megrchede
(hangg 193
0.2
Constiies The
0:5
6430
Layer 30
F
4.7%
-30%%
Layer 32
Dowerticrr Armmay
4.0%
Layer 34
Conrtizzs
Mirotte
1.0%%
10 Atvertionn Tond Traie
Antestion Thred
Figure 73: (Left) augmentation results for Fig. (right) induction score of each attention head on Qwen 2.5-3B, FP.
66

---

Published as a conference paper at ICLR 2026
Layer 0
23.85
boaccar Coreecsner
3.05-
23.95
0.90
Layer 2
Tedacaan Haperade
Abttted Altetiie tbed Iodks
Layer 4
Milatton thec Indes
Comeenicry Arama
0.05
Iecedter Megatrade
607
2.0%
0000
Abaaee Amrettion Hondd Irdex
Attedde 1TAnd Trdee
Layer 6
ledacia Cornecinn
mm
n Il
3.88
Layer 8
Indutiion Connecion
34022 Charge
600
chilky
No Atrection Tond Irder
Layer 10
Aftrodie ITaad Index
Diktow Clange 150
2.7%
Magelak CenReTTAR
0
Conaroane Phe
0000
0,000
Layer 12
4.7%
Naguiaaa
Change
4m
Moste Attertion Hoad
Layer 14
Abwitiin Heed Inver
12
Goavese rka
00075
4..0%
Motited Allection Hoed Ledie
Layer 16
Allastoo Meid Lndies
0.79
Cowesricer
Infaia Magriade
Charve
Bazze
0000
(oaated Attention Tland Traiic
Jehento 1brd Trdies
67

---

Published as conference paper at ICLR 2026
Layer 18
Comentety Gomrony
Amsaiion Seere
Cornecan
+4.0%
Abuled Aliection Hond Lodus
Layer 20
Aluzzian Hoad lindox
irtacioo Nagalada
Change
2.%
Briwertiiy Aboeed Atrentinn Tond trdes
Attreston [lead trdet
Layer 22
Condutse
60%
Abaded Alrection Hond Izoks
Layer 24
Altertion blead lndos
Frundee by
12.85
Ahabel Meriete Red Irdre
Layer 26
Anteetin Tlrdd
Indertiee Naptiake
Abouted Alvetite Bhad Indo
Layer 28
Alberttonn Head lndis
Indaciic Hagaiale Corraczans
Telezove Charge
2.5%
Allated Arssttin Head Index
Layer 30
Attiectinn Eland Irdox
Inlatic Hogaiabe Corractans
Change
Abcated Atrection Hoad Izdes
Layer 32
Attirntinn Elead trAo
Irdactoo Magetada
3.7%
Coeatate Fit
2.7%
Wotted Atrection Hoad trdos
Layer 34
Attertton Head tudo
Domesticty
Indattze Mughhaa
1.0%
Figure 74: (Left) augmentation results for Fig. 7, (right) induction score of each attention head on
Qwen 2.5-3B, SST-5.
68

---

Published as conference paper at ICLR 2026
Layer 0
0.34
0/113
23.05
0,004
0,00
Lodk.
Layer 2
3.95
0.8%
3.8%
Abaited Miviie Seed Inor
Layer 4
Afeetice Hood Intes
10.09
Covrrnne the
4.0%
5.015
Juans
0.20
Layer 6
0,00
Alanttn Scuee
Change
6076
Accrracy
Wotee Atrection Tind Trale
Layer 8
Afteddre Heed livex
344e0s Chroge 151
koudin Magi Aode
0.0%
8200
0,000
Layer 10
3.5%
Condttace the Gowunny
Change
Marree
Abuuted Alrection Hond Lnchee
Layer 12
Allvntice Iasal Indio
Eccardeity
Ioaale Magicldde
Change
0,000
Woated Attention Hoad trdvr
Layer 14
Alvedice Food Inver
Change
G2016
Rbaaed Atrection Head todes
Layer 16
Jetuntion 1had Indes
0.20
12.%
69

---

Published as a conference paper at ICLR 2026
Layer 18
Busett by
Corneian
1.2%
50%
Altated Alustin Heat Indes
Layer 20
Aluztian Hoad lindox
Nuneanily Accemsit
irtacioo Nagalada
nL
Akattd Arwettio Blad Isdex
Layer 22
Attrestion [load trdett
Abosted Alvefite Thed Icoo
Layer 24
Altertion blead lndie
koudion Magi
0,000
Layer 26
23.05
Inductiee Cornttnn
0.0
Layer 28
4.7%
Excnrdicty
Chrnge
Accency
2.775
Jboaedd Atrection Tindd Irdes
Layer 30
Attentiinn Tleed Ttdrx
Condlcsce
Abuuee Alreciion Hond tndie
Layer 32
indacioc Magalada
Accency
Abuued All Alrection Fond tadke
Layer 34
Attretton [TAnd Triee
80124
000
83075
Hood
Figure 75: (Left) augmentation results for Fig. 7. (right) induction score of each attention head on Qwen 2.5-3B, AGNews.
70

---

Published as a conference paper at ICLR 2026
Layer 0
Eowerratty
0.4
Iedaction Carrecteor
22.9%
0.80
Alteted Alvetine thed Ic0bs
Layer 2
Alaestian Head linkes
0.12
Iedacias Hagrande
1.80
Coveramm
Alisted miveiio Bsed
Atbeedice Food Intex
Layer 4
Ieacie Magataak
0,00
0,00
0,00
0,000
Abaate Alsetiin thnd Indo
Layer
Atlendien Haad Index
Comentiery
dudutoon Megrcadee
0.00
2012
Aliestion Loditt
Layer 8
Indadion Vagalade
Scees
4.0%
Constiios Thx
Layer 10
Iedaciio Cacrectaaa
Abauked Alrention Hond Indux
Layer
Abuztian Hend Index
Irdacino irdactos Comeezas
Palatre Charoe
200%
Nitelinn
Alated Anweroo Bead Ivies
Attrrnten [laa Irdve
Layer
0.17
Chtagg
Coveante The
0.000
0.70
L
2.5%
0305
Layer 16
Gooesticty Goudlsse
008
Wanated Acrention Hoad Trdeet
Actection Hoad Irddec
71

---

Published as conference paper at ICLR 2026
Layer 18
4.0%
Abudeed Aliention Hond Indos
Layer 20
Aluzziann Hoad lindox
Irtacioo Nagalada
4.7%
Iydeniev Cametaan
Mineitm
1..%%
Aboeed Atrection Tinod Trales
Layer 22
Atbrrston [load trdet
Nagalaae
lndactic Corractaans
Accemec
1baeed Atrection llndd Trans
Layer 24
Attrestinn [load tróet
0.000
Claroes Ph3
sauttee Comeitane
5.0%
0,22
Layer 26
Napatadee
Clasge 194
1.5%
Consrtace fha
Layer 28
Naptlade
34lan Chaoge
Comertiity Consrtices Thes
Layer 30
Clanee
Jetemiten Stume
Induciie Cormtnnn
1.0%
0.0
Layer 32
2.15
4.9%%
4.0%
0.6
Histed Atrention Hoad trdex
Layer 34
Atterdton Elaad Index
Conrtizzs
Mivettan
Abultd Alreciion Hond Iodie
Alsztian Hendltdee
Figure 76: (Left) augmentation results for Fig. (right) induction score of each attention head Qwen 2.5-3B, Subjective.
72

---

Published as a conference paper at ICLR 2026
Layer 0
23.9k
0.55
Iocecdir Coreersee
Chazge
0,00
0.00
Layer 2
Thua
Reverancy
0,00
Nagatzak
0.22
Abated Mitiiee Seed Inde
Layer 4
Afteaiie Hood Intex
Conrlezee
Changg
60%
0,00
1..0
6.04
0,00
Abisted Atrection Hoad Izdex
Layer 6
Atteedic Iaadd Indix
Indake Magectide
24480te Clange
2000
Layer 8
0.08
4.10
Chooge
20
2.7b
Actentes
Eowesteity
603
Wosed Atrertinn Tindd Trale
Layer 10
Antetiin llred liviex
4.7%
0.08
Indartie Megccaee
Bakov Change
13.0%
Consttuce
Abciked Altection Indes
Layer 12
Ialadas Higgarae
ContionsTrr
Layer 14
Eoaertecty Accence
0.6
60%
Intactes Cornetan
0.7%
002
46.%%
Aodted Aliection Rond Indes
Layer
Alazziian Hend Inndox
Indacioo Oevedaae
Chasgg
Wi Attertion Hond traee
Artertin
73

---

Published as a conference paper at ICLR 2026
Layer 18
600%
Enameneitt
Cornetan
2.7%
-4.%
Abuled Aliection Hond Lndio
Layer 20
Aluzzian Hoad lindox
6.7%
Eccerteity
Iydentiv Cameeaan
irtacioo Nagaluda
Accumec
2.7%
1..7%
-6.%
Abaeed Atrertion Tindd Traee
Layer 22
Atbrrston [lead trdet
6.7%
Conrtczas
4.7%
0.7%
4,7%
Abaded Airection Hond tzous
Layer 24
Allertion blead lndes
indutioo Magntada
1.5%
Conraaca ika
6.0%
-15%
Indoc
Layer 26
Arsentian
Hapalake
0.9%
Layer 28
1/15
Eocesteity
028
Magucaade
0.0%
000
Aiaated Atrection Hond Iedex
Layer 30
Arseztion Head Tridex
2.7%
Iaka Da
1.7%
-1.0%
3.7%
Ahddel Allection Hand Lndiet
Layer 32
Allentinn Stard Ladoe
Ixdacto Vagahste
Chatgg 191
0.0%
1.0%
Consrtizes Tie
Dommetiitty
Layer 34
2.0%
bopates Cornctun
Change
038
Audtal Aliectizn Road Inchet
Alaztian Headinde Index
Figure 77: (Left) augmentation results for Fig. 7, (right) induction score of each attention head on Qwen 2.5-3B Instruct, SST-2.
74

---

Published as conference paper at ICLR 2026
Layer 0
0,00
Seacter Coreecaee
0.90
Layer 2
25.99
Iaductan Sagarabe
13.9%
13.9%
Alcated Alterine tbed Ic0ns
Layer 4
Allatton thed Index
4.7%
-uage 7611
2.0%
Consllazes 7kx
Layer 6
0,02
Clange
2.5%
Score
0.35
Eowearitty
Abated Mitiedte Boad Irdre
Layer
Afhentie Boeu lnvrr
Iadatae Hagginda Curnekoos
Chargg (74)
13.0
2.8
Conslkeze
-2.0%
Musked Attection Izdis
Layer 10
Mapatakk
Abstad Aliection Hond
Layer 12
Allenticn tsoal Index
Indacten Hugiituta Danneion
Whatee Intection Hoad Trales
Layer 14
Amoetion
Bowerrecly by Jemmy
com
2.0%
20mm
0.00
0,000
Aussked Atrection Hond Izdex
Layer
Allendie 15tal Index
3.7%
Score
bddtze Grackas
1..0%
Emarrtiity
Accenics
20 A2 Aicention Hoaed LEA0e
Altostinn Head Index
75

---

Published as conference paper at ICLR 2026
Layer 18
Conaiazee
Change
4.0%
Abuded Alceciion Hond lo0ks
Layer 20
Allvetice Taval Irdix
irdacioo Nagalida
Atrersa Secres
4.70
Accmacy
Dn
Woaee Attertion Hoad travs
Layer 22
Attertion Elead triee
Indartiee Naptiaake
Chasge 744
Condissce ika
Abusked lndis
Layer 24
tlead Ludox
3.95
Iedaliaa Houradde
0.8%
B072
0,000
Ablated Altreden 1Sad Indes
Layer 26
Atlendes 1Stadd Index
2.550
Ementricty
Inductice Correcton
2.0%
0.5%
225%
Atatte Allettoe thed
Layer 28
Altenton Head Lndox
Indactic Magutaaee
/biated Intection Hoad Trdot
Layer 30
Amertion
lade Mapsiake
2.7
60%
1.0%%
Accerac
Abided Alrestion Indus
Layer 32
Charge..0 100
Domesticar Dooekoo
Iedadioo Magalidd
mmm
Layer 34
4.70
Brventicty
2.7%
1.2%
627
2.7%
0.0
Head
Anwettin Indin
Figure 78: (Left) augmentation results for Fig. 7. (right) induction score of each attention head on Qwen 2.5-3B Instruct, MR.
76

---

Published as a conference paper at ICLR 2026
Layer 0
33.91
Inductoo Xagatrate
0.99
00002
00000
Layer 2
Centran
Cermeber
Charge
00115
0000
Layer 4
2.8h
0.00
Ecoerancyy
0,000
Alcated Alletate thed Indos
Layer
Aftediie HTed lnver
3.89
Srowe
43.9
Layer 8
Rooeacicyyy Avmmy
3aledw Chroge
0.01
Abistedd Attection Hond Tzdex
Layer 10
Arteztion Head Irdex
4.70
Indactio Correcbear
Sdaati Change
Goonmticar Acoumyy
Abulted Alrection food Lnchee
Layer 12
Alsztiaa Hoad lindox
Iosale Mageclide
80
6000
2,m9
Attertion Hoad
Layer 14
Aivedice Food Inver
Inladee Mapituut
Chroge 154
2660
Layer 16
takkttee Comeitaan
Changge
Ecsnsbetty
Mosted Aflection Hoad Indee
Aloetton Head Index
77

---

Published as a conference paper at ICLR 2026
Layer 18
Cornecan
2.5%
6.0%
2.70
Altated Alustao tlead Indes
Layer 20
Aluzziann Hoad lindox
10.0%
Iedentiv Cameeaan
Irtaciio Nagaluda
Change
9.0%
4.7%
Accersty
4.0%
D
Abated Amwetio Bexd txdet
Layer 22
Attrrston [load trdet
2.7%
0.0%
Abidee Alrection Hond Izoes
Layer 24
Altertton blead lndos
Chaage
Insuancy Coverame tha
bescoa Magatak
0.130
1.2
3.8%
0.02
-0.85
0,000
Layer 26
3.79
Cornetann
6.7%
0.0
Layer 28
Htad
2.7%
0.25
3.0%
0.35
Jblaed Atrection Tond trdes
Layer 30
Arseation Tleed Tndex
la Corretnan
Change
2.0%
Eoonstaety Accino
Abulte Alrection Roedd t2d0e
Layer 32
Indacioo Magalude
Chaogge (50
5..0
Gonrteze
Masded Allectic Hond tz0ke
Layer 34
ETand Irdee
Inleten Hapdaaa
Figure 79: (Left) augmentation results for Fig. 7, (right) induction score of each attention head on Qwen 2.5-3B Instruct, FP.
78

---

Published as a conference paper at ICLR 2026
Layer 0
12.95
Setecaer Cornecseer
0012
23.86
0,00
-2.9%
Layer 2
15
Iedactas Highadd
0.12
0.00
3.0%
0,00
Abateed Movtie Sked Inde
Layer 4
Abeetice Hood Index
Change 7611
hotrle Nagtiakk
2.7
4.%%
Conattice hh
0,00
Layer 6
Choose
6.0%
Abard Amertton Bead lvdex
Layer
ARhoddee Heed liver
3.7%
koudinn Magi Aode
3ale2 Chroge R33
40h
mm
-4.0%
0,000
Layer 10
Magalak
Daltte Chaage
4.0%
0012
Abuited Allection
Layer
Allentic 250al DRAO
Cornehaa
Chagge
com
-2.0%
Aboiia Allention Hand Lndbes
Layer
Aluxtian Mead Iindox
Dommeticar
Channe
Alrustion Isous
Layer 16
6.7%
026
Change
4.7%
0mm
0.2
Anwittin
14
79

---

Published as a conference paper at ICLR 2026
Layer 18
6.7%
Consltaze
011
Change
Abuded Alcection Hond lo0ks
Layer 20
Allvelice Taval triix
irdacioo Nagalida
4.79
Chasge Chasge
Coualise Aommeyy
46.%%
Woaeed Attertion Hood travs
Layer 22
Attretton [lend traee
Indariie Naptiahe
Condusee hka
Abusked Alcention Indes
Layer 24
Iadox
10.09
Broentricty
Iedalca HiuraLe
0.12
2.5%
0,000
Akiated Artuntion Tland Isdex
Layer 26
Atlendes 1Stad Indix
Ementectyy
Inductice Correctenn
Atatted Allentte thedd LoOks
Layer 28
Altenton Head Lndox
Domemtity Acamyy
Inductine Nagslade
6.0%
Chaoge
60%
Jblntedd Ittection Tiead Trdee
Layer 30
Atbindton Eland Indeet
Chaqge 750
Inductiee Corntner
0.0
Layer 32
Atterdtinn Elane Index
4.7%
1.15
Boseniinly dy Anawnyy
Change
2.0%
Monted Atrention Hoad Irdex
Layer 34
Attertton [land Index
6,06
0/9
Conrtazze
Change
Abuuted Alrection Hond Indie
Alsztiann Head lndex
Figure 80: (Left) augmentation results for Fig. (right) induction score of each attention head Qwen 2.5-3B Instruct, SST-5.
80

---

Published as a conference paper at ICLR 2026
Layer 0
0031
23.95
31.9
0.00
Layer 2
Iedactaa Highadds
3.8%
Abated Motiie Seed Indr
Layer 4
Afredice Hood Intex
751
Domemtitty
hotrte Nagsiade
2.7
0,000
Layer 6
0.14
0.12
0,00
(biated Attection Iinad Irdex
Layer 8
Atlentien ESsal brdex
Dovetooe Acoumay
Change
0,17
60%
Abadeed Atrection Hoad Izdee
Layer 10
Allvetice Iaiad Iidix
2.75
Enceaskitty
Toutbe Megrctdde
Soora
0.0%
0,002
01:0
Layer 12
13-0%
11.79
0.000
1.2
8000
Abiated Artection Elaad bylet
Layer 14
Aftodde (TAvi
toutle Megra
4.7%
Komrboa Srene
0.20
0.00
0/76
2.76
4.7%
4.0%
4.79
0.00
Musted Atrention Hond Index
Layer
Allendies 1anal trdis
2.7%
Conelunce
bodatze Grackas
1.75
11.0
601
100 Atrention Tould Stalis
Altestian Head lndes
81

---

Published as conference paper at ICLR 2026
Layer 18
12.5%
160%
Boselt by
Corneian
5.0%
2.7h
R_
Th_
Altated Alustao Head Indes
Layer 20
Aluztian Hoad lindox
10.0%
irtacioo Nagaluda
Iydenie Cometaan
Accemii
607
Alattd Arwetiin Elaad Isder
Layer 22
Aitrrstion [load trdett
Choogt
2.8%
0.4
Aboated Alvetite Thed Icdo
Layer 24
Altentton blead lndoe
koudii Magi
3aleshe Change 101
0.0%
Domemtcer
0,000
Layer 26
21.8%
Change 7961
Inductiee Cornttnn
0.0
Layer 28
Ixdactic Corretbar
Chaoge Change
Eccarteity
0.35
Abatiad Aliection Hond Lndoe
Layer 30
Aluutiun Head lindox
Domesticty Actumyy
Indaciee Megzaads
Abrated Atrection Tindd Tradet
Layer 32
Atbernte E1and Itdet
1.27%
Conducsc the
Abuueed Alsection Hondd Indie
Layer 34
Altertinn Mead Indes
0.20
kouako Magutade
Change 84
Atrection Seeeus
10.%%
0.1
Domerbeit
0.000
Figure 81: (Left) augmentation results for Fig. 7, (right) induction score of each attention head on Qwen 2.5-3B Instruct, AGNews.
82

---

Published as a conference paper at ICLR 2026
Layer 0
Seactaer Coreeraser
13.95
0.89
0.00
0015
Layer 2
Iedactas Highadda
0.10
0,000
20.9%
13.00
22.m
0,00
Abatted Mondie Seed Inoe
Layer 4
Abeeiic Hood Inbox
hesrte Nagtiade
Caveriane
0.000
Layer 6
Conduaee
0,22
0012
0.00
Woaee Atrection Tond Troee
Layer
Afhodtee Hoed livex
4.7%
Intatee Hogthute
Consltate Fixs
0.0
0.15
-4.7%
Abssked Attection Hoad Izdis
Layer 10
6.7%
0.000
Magalak
4.7%
348tb Change
Abatidd Aliection Hond
Layer
Allenticn tssal Indox
Intacten Hugtituta
Chaage (50
Actoay
0.0%
0L1
Ahoaee Atrection Hond traeet
Layer 14
Amoetiin
Coneranes The
2.99
Layer 16
6.%%
33.%%
Eounsbett
Masked Atrection Hoad Iodies
Acsetion Index
83

---

Published as conference paper at ICLR 2026
Layer 18
600%
6.7%
Iotatee Cornetan
4.7%
4.7%
Abuled Aliection Nond Iodus
Layer 20
Aluztian Hoad lindox
Irdaciio Nagaluda
1..7%
Browariity
Aoaend Atrettin Tindd Trales
Layer 22
Atbrrston [load trdet
Abaded Alrection Hond tndee
Layer 24
Altertton blead lndes
Iedaction Magecade
0.2
2.8
L7
Iade
Layer 26
6.7%
Bommnticty
Hapaiake
Pka
4.0%%
Layer 28
Napttate
Layer 30
7,70
Insetion
12.0%
Dommrsicity
Layer 32
Intrche Comeiaan
Fue
0.
13
Layer 34
Conrtizas
1.78
0.2
10/ Amertion Tond Trdee
Anwettio TnnedTadee
Figure 82: (Left) augmentation results for Fig.
(right) induction score of each attention head on 84
Qwen 2.5-3B Instruct, Subjective.

---

Published as a conference paper at ICLR 2026
Eroding
Ohone Heads Sceeding
Dr Tasts Felihiertooooo
Las Nosia
Naska
Naader
Lap foadin
SST-2
SST-5 Figure 83: Augmentation results for Fig. 8 Llama 3.2-1B.
MR
FP
AGNews
Subjective
Deiliiy Lack
Assoseiinn say Sted
Karonienng Lond
Aisoric thaa
SST-2
FP Figure 84: Augmentation results for Fig. on Llama 3-8B.
MR
SST-5
AGNews
Subjective
eallh
Number
SST-2 Figure 85: Augmentation results for Fig. 8 on Qwen 2B5-3B (the threshold is set to +2.5%).
MR
FP
SST-5
AGNews
Subjective
Empoiric Mead
Eraer Houls
Layer
Saver
Layer
SST-2 Figure 86: Augmentation results for Fig. 8 on Qwen 2.5-3B Instruct (the threshold is set to +2.5%%
SST-5
AGNews
Subjective
85

---

Published as a conference paper at ICLR 2026
12
HO CHCCO
12 Yoand
Layer indox
10
Lager rodex
10
CLCOOO
cord Drg
1o0d Oroka ae O
5% @Cosrancc Ther (Sabitiva Change Aniitio)
0h LCwartnncs Flix (Reiativs Change Vi Anletion)
68
10%
(Courance Flux (tataitis Change Absitoo)
SST-2
MR
FP
12-
12-
Lapee Indox
*Oin Cal
Co CHIGHD O
10-
Lagrer Inder
10-
0-
Oc00eO Do
Dessiana
6% @Cosarance Flu (Rduuivvo Chinge Allitinai
0%
.1%
6%
10%
a0waninoo Flax (Relaties Change wi Allatioo
ACosarance Flux Gedulivo Change Allitic
SST-5
AGNews Figure 87: Augmentation results for Fig. 9 on Llama 3.2-1B.
Subjective
Gooooo
Layee Insore
Lagrer Instoss
18.
Omess
13
15
2000
11
0000
4-000000000
0--000RS-00 Co O
00000000
20
20
85
Dezolaing
Denshing
Denchilog
Deacisin
Dazolaing
SComrfance Tha (Baacho
aCwartance (lelatten Ablation)
aCmmlinns (Beathe Ablution)
SST-2
MR
FP
19
19
Lager lbd0
12-
Saperr todox
17-
Coo
13
20
36
10
25
20
30
Desctinn
Head Index
Anti Denatiing
Denshing
Hand Indea
Auti Denchltg
Desciehn
Hend Indox
Antii Dezoteing
1.%
0%
2%
10%
-00%
5%
0%
5%
10%
12%
5%
0%
3%
10%
Changn
Change
SST-5
AGNews
Subjective
Figure 88: Augmentation results for Fig. Llama 3-8B.
86

---

Published as a conference paper at ICLR 2026
24
22
20
Head Index
Heead Inder
-10%
-5%
dis.
5%
10%
100%
-0%
-00%
.6%
bis.
10%
JDmartaare Flex (Belaitiv Change Ablxtion)
(Omarrino Flex (heistivn Chonge wi Ablation!
anmarbaee Flex (Retadiiv Change wo Allition)
SST-2
MR
FP
34
24
22
26
10
5
Indas
-10%
.6%
5%
10%
0%s
Gis
.10%
.6%
10%
JDoustiance Plox (Belodive Change w/ Ablision)
AOwarrlaoee Flux Chelative Change wi Ablationt
aDwarlance Flax (Reladive Change Alliation
SST-5
AGNews Figure 89: Augmentation results for Fig. on Qwen 2.5-3B.
Subjective
26
26
26
24
0.0000
Dessnsling
Head Indws
Aniil Aeri--erraiinnggg
Dussising
Hoad Indes
Atill Decrnoinng
Desstiing
Hear Indie
Atiil Derniiinng
.10%%
.5%
dis
5%
10%
..0%
.6%
ols.
5%
10%
.10%
.%%
5%
10%
aDovatiacc Plux (eelodivv Change si Alliation)
aCovasiance Flax (Relativo Change wi Allintoo))
aCwaziance Plus (Relative Change Allation)
SST-2
MR
FP
26
26
24
0
00
24
M4
2
10-
14
Henri Inday
Demstenp
Fenndd Indert
Desstaing
Meari Indee
10%
5%
dis
3%
10%
.10%
-5%
0%
S%
10%
.10%
5%
9%
3%
10%
aDvaatunce Piaa Biduuivv Change vi Aliiaian)
#Coversince Flus (holatine Clange wi Ablationl
aCwaztune Flus (Relutive Change Aliutian
SST-5
AGNews
Subjective
Figure 90: Augmentation results for Fig. 9 on Qwen 2.5-3B Instruct.
87


Reviews:
[{"review_id": "oyjwFcxNvd", "reviewer": "Reviewer_M6i4", "summary": "This paper proposes a new mechanistic interpretation of in-context learning: rather than copying label tokens via induction heads, large language models perform a task-oriented information removal that compresses query hidden states toward a low-rank, task-verbalization subspace (TVS). The authors demonstrate (1) that injecting a trained low-rank filter into a layer’s residual stream converts near-zero zero-shot performance into strong task-specific outputs; (2) that few-shot demonstrations induce geometric changes in hidden states — increased eccentricity and covariance flux into the learned TVS — consistent with implicit information removal; and (3) that a subset of attention heads  causally contribute to this aligning operation: ablating them reduces covariance flux, eccentricity, and downstream accuracy. The paper thus argues DHs complement induction heads and together explain a broader range of ICL phenomena.", "questions": "Can you show that amplifying DH outputs (scale >1) increases Covariance Flux/Eccentricity and improves accuracy in settings where the model is weak (e.g., few-shot with noisy labels)?", "limitations": "", "rating": 6, "confidence": 2, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "The paper’s framing of the “information removal → task-verbalization subspace” is conceptually novel and shifts the focus from mere copying to selective suppression\n\nThe paper is well-written and easy to follow. The low-rank injection experiment is simple, interpretable, and effectively demonstrates that a small learned linear filter can steer outputs.\n\n\nThe identification of Denoising Heads (DHs) and the analysis of their interaction with induction heads provide a richer mechanistic understanding of in-context learning.", "weaknesses": "Ablating a head is a valid intervention, but zeroing a head output changes the residual stream and thus all downstream activations; the observed drops in Covariance Flux / Eccentricity / Accuracy may partly reflect these propagated network dynamics rather than a head performing a localized denoising operation.\n\nThe method appears to identify DHs only on a subset of layers. If many DHs remain unidentified, ablation results could be underestimated or misattributed. \n\n\nThe DH identification uses fixed relative-change thresholds (e.g., −3.5% / −5%). It is unclear how sensitive results are to threshold choice and whether effects are statistically significant across random seeds / datasets / prompts.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "Tk9d93p9RA", "reviewer": "Reviewer_TE1T", "summary": "The paper proposes a novel interpretation of the ICL mechanism by viewing it as a process to remove redundant information in the query’s hidden states for the targeted tasks. Specifically, the paper applies a low-rank filter on the hidden states for informational removal and finds it boost the performance on the designed tasks significantly. On top of that, the paper conducts further analysis to prove that a few-shot ICL implicitly performs a similar information removal process. Finally, the paper identifies attention heads that are responsible for such removal behaviors and shows that they are crucial for the success of ICL.", "questions": "What are possible sources of the accuracy improvement from instruction given that instructions do not seem to contribute to the information removal process?", "limitations": "", "rating": 10, "confidence": 2, "soundness": 4, "presentation": 4, "contribution": 3, "strengths": "- The paper includes well-designed illustrations that well support the claims.\n- The paper provides a perspective for demystifying ICL that is novel yet aligns with many previous observations.\n- To support the claim that ICL performs information removal, the paper provides decently comprehensive analyses that dives deep into the activities of the hidden states of the model using self-crafted analysis methods.\n- The paper includes experiments and discussions to compare their newly discovered Denoysing Heads against the previous induction heads.", "weaknesses": "The paper provides many insights on the mechanism of ICL, but the potential future directions built on these findings are less clear.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "VOP5vIevJg", "reviewer": "Reviewer_5eyE", "summary": "This paper investigates the internal mechanism of In-Context Learning (ICL) in large language models (LLMs) from a new perspective — task-oriented information removal. Instead of viewing ICL as pattern imitation or label copying via Induction Heads, the authors argue that few-shot demonstrations act as filters that suppress task-irrelevant information in the hidden representations.\n\nTo support this view, they introduce two novel probing metrics: Covariance Flux through the Task-Verbalization Subspace (TVS) and Eccentricity, which quantify how hidden-state variance aligns with task-relevant directions and how anisotropic (filtered) the representations become. Using these tools, they demonstrate that (1) LLMs spontaneously recover the TVS during ICL, (2) this process can be measured as an information-removal trajectory across layers, and (3) a new class of attention heads, Denoising Heads, drive this mechanism, overcoming the well-known limitation of Induction Heads when facing unseen labels.", "questions": "Suggestion:\n\n **Center the paper on the probing methodology.** \n\nIf the authors had focused the paper around the two new metrics (Covariance Flux and Eccentricity) as a general probing framework, the contribution would appear sharper and of broader relevance. The ICL mechanism and Denoising Head discovery could then be presented as compelling applications of this framework, rather than parallel findings competing for attention. \n\n**A more layered structure** -- with detailed exposition of the probing metrics in the main text and the some extended empirical findings moved to the appendix -- would make the paper both clearer and more impactful. You can organize the paper similar to [1].\n\nMinors:\n\n1. In Figure 3, I understand that the marker represents the lower bound of information removal with a value between 0 and 1. However, please include at least one reference marker (for example, the marker size corresponding to no information removal) so that readers can intuitively gauge the approximate lower bound portion of information removed.\n\n[1] Ren, Yi, and Danica J. Sutherland. \"Learning dynamics of llm finetuning.\" arXiv preprint arXiv:2407.10490 (2024).", "limitations": "", "rating": 10, "confidence": 4, "soundness": 4, "presentation": 2, "contribution": 4, "strengths": "1. **Novel probing metrics with clear interpretability.**\nThe introduction of Covariance Flux through TVS and Eccentricity provides a fresh, quantitative lens for studying internal representation dynamics of LLMs. These metrics go beyond uncovering new ICL mechanisms and identifying denoising heads, enabling a measurable understanding of how information filtering evolves within transformer layers.\n\n2. **New mechanism of ICL: task-oriented information removal.**\nThis paper shifts the focus of ICL mechanism from token-copying to information filtering, which deepens our conceptual understanding of ICL.\n\n3. **Identification of Denoising Heads addressing the Induction-Head limitation.**\nThe discovery of Denoising Heads is an insightful contribution. These heads operate locally and semantically, filtering query representations rather than copying lexical patterns, thereby explaining why LLMs can generalize to unseen labels -- something Induction Heads cannot do.\n\n4. **Strong empirical grounding.**\nThe experiments are extensive and solid.", "weaknesses": "**Overly dense and somewhat disorganized presentation.**\nWhile the findings are rich, the paper feels overly packed. The main sections attempt to cover TVS analysis, metric design, mechanistic ablations, and head identification all at once. The narrative flow occasionally sacrifices clarity for compactness, making it harder for readers to see the conceptual through-line.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "HGbXFs9KV5", "reviewer": "Reviewer_sEGe", "summary": "The paper argues that few-shot in-context learning (ICL) works by selectively removing task-irrelevant information from query representations, steering the model toward the intended task. In zero-shot settings, injecting a low-rank \"task-verbalization\" filter that projects onto a Task-Verbalization Subspace (TVS) dramatically improves accuracy even while preserving only ~0.7% of dimensions, while in few-shot ICL the model spontaneously moves hidden states toward this TVS, as measured by geometric metrics that rise in middle-to-late layers. The paper identifies \"Denoising Heads\" (DHs)—attention heads whose ablation disrupts this removal operation—which are largely independent of induction heads and show local re-encoding patterns over query tokens; ablating DHs significantly reduces ICL accuracy and nearly collapses performance in unseen-label settings, demonstrating the causal importance of this mechanism. The authors note this mechanism applies to clustering-style classification tasks but not bijective tasks like translation, with experiments conducted across multiple text classification datasets and models including LLaMA and Qwen variants.", "questions": "1. How sensitive are results to scanning all layers/heads? Could you provide one full‑layer run on a smaller model to confirm no hidden DH clusters?\n\n2. Do your metrics or DH patterns say anything in multi‑class generative outputs (e.g., natural language rationales)? If not, what would be needed?\n\n3. Any preliminary results on larger models (e.g., 13B/34B) or instruction‑tuned variants to test whether DHs persist or shift?", "limitations": "", "rating": 4, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "1. Task‑oriented information removal operationalized via a low‑rank subspace and two geometric metrics that correlate with accuracy and layer depth. \n\n2. identification and causal ablations of Denoising Heads, with independence from induction heads and a sensible local re‑encoding attention pattern. \n\n3. Explicit failure case on bijective tasks (translation/fact recall) and an explanation of why low‑rank removal should not help there. \n\n4. Broad, careful experiments across six datasets and three models, with appendix replications and unseen‑label analyses that stress‑test induction‑only stories.", "weaknesses": "1. Theory is largely heuristic. The link between covariance and “information removal” is argued but not formally proved; metric choices and DH thresholds (±3.5%) are somewhat ad hoc. \n\n2. Narrow task family. The focus is single‑label classification; reasoning, chain-of‑thought, or generation settings are not studied, and the paper itself notes the mechanism likely does not apply to bijective mappings. \n\n3. Scale and generality. Only up to 8B models are used. It remains unclear whether DH distributions and metric trends stabilize for larger base or instruction‑tuned LMs.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)