To Steer or Not to Steer? Mechanistic Error Reduction with Abstention for Language Models
Authors: Anna Hedström
Salim I. Amoukou
Tom Bewley
Saumitra Mishra
Manuela Veloso
Venue: ICML 2025 poster (2025)
Keywords: mechanistic steering
intervention
error mitigation
language models
Primary area: deep_learning->large_language_models
TL;DR: A general-purpose steering method to safely reduce errors in language models with calibrated constraints

Abstract: We introduce Mechanistic Error Reduction with Abstention (MERA), a principled framework for steering language models (LMs) to mitigate errors through selective, adaptive interventions. Unlike existing methods that rely on fixed, manually tuned steering strengths, often resulting in under or oversteering, MERA addresses these limitations by (i) optimising the intervention direction, and (ii) calibrating when and how much to steer, thereby provably improving performance or abstaining when no confident correction is possible. Experiments across diverse datasets and LM families demonstrate safe, effective, non-degrading error correction and that MERA outperforms existing baselines. Moreover, MERA can be applied on top of existing steering techniques to further enhance their performance, establishing it as a general-purpose and efficient approach to mechanistic activation steering.

To Steer or Not to Steer?
Mechanistic Error Reduction with Abstention for Language Models
Anna Hedström Salim I. Amoukou
Tom Bewley?
Saumitra Mishra
Manuela Veloso*
Abstract
Vanilla steering
MERA
Fixee steering strength
Calibrated steering threshoid
We introduce Mechanistic Error Reduction with Abstention (MERA), a principled framework for steering language models (LMs) to mitigate errors through selective, adaptive interventions. Unlike existing methods that rely on fixed, man- ually tuned steering strengths, often resulting under or oversteering, MERA addresses these limi- tations (i) optimising the intervention direction, and (ii) calibrating when, and how much to steer, thereby provably improving performance or ab- staining when no confident correction is possible. Experiments across diverse datasets, and LM fam- ilies demonstrate safe, effective, non-degrading eтror correction, and that MERA outperforms ex- isting baselines. Moreover, MERA be applied top of existing steering techniques further enhance their performance, establishing it as a ceneral-purposs and efficient approach to mecha- nistic activation steering.
High error
Understeer
Adaptive strength
Low error
Oversteer
Selective steering
Abstein!
Figure I. An illustration of traditional vanilla steering with fixed steering strengths (left), leading under-, and oversteering, and MERA (right), providing calibrated steering thresholds.
for specific goals, these approaches typically computa- tionally intensive or context-sensitive.
An alternative approach to intervene in the internal com- putations of the model itself. Mechanistic steering (or "rep- resentation engineering") has emerged as a promising line of research to influence model behaviour by intervening activations in inference-time, without permanent weight updates (Li et al., 2023; Belrose et al., 2023; Todd et al., 2024; Qiu et al., 2024; Turner et al., 2024).
1. Introduction
Despite the impressive capabilities of current language mod- els (LMs), they can be frustratingly error-prone. Failures arise not only in open-ended tasks like reasoning, factual consistency or planning (Kambhampati et al., 2024), but also in simple prediction settings (Hendrycks et al., 2021b; Webson & Pavlick, 2022: Zhou et al., 2024). Mitigating such errors an open research question.
One widely used instantiation of this approach is contrastive steering (Arditi et al., 2024; Rimsky et al., 2024), where a steering vector constructed by taking the mean activation difference between paired examples with, and without tar- geted concept (e.g. toxic non-toxic outputs). This vector can then be added the model's activations to amplify or suppress such concept in the model (Ball et al., 2024), under the assumption that the concept is represented along a linear direction in the model's representation space (Elhage et al., 2022; Marks Tegmark, 2024; Park et al., 2024).
Error reduction methods for LMs have evolved in several directions, including fine-tuning (Hu al., 2022; Wu al., 2024; Yin et al., 2024), and inference-time approaches like prompt engineering (Kojima et al., 2022), and guided decod- ing (Yang& & Klein, 2021; Liu et al., 2021). While effective
'Wor done during internship at J.P. Morgan Al Re- search. *J.P. Morgan AI Research. Correspondence Anna Hedström <hedstroem. anna @ gmail.com.. Salim I. Amoukou @ jpmorgan.comm..
A natural extension is to explore whether such additive lin- ear steering can be applied for the specific goal of error miligation: directly reducing model errors prediction tasks. That is, can we find linear direction in LM's ac- tivation space that encodes the concept "being wrong", and then steer away from it? Unlike traditional alignment tasks such as reducing toxicity or harmful responses, steer-
Proceedings of the nd International Conference Machine Learning, Vancouver, Canada. PMLR 267, 2025. Copyright 2025 by the author(s).

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Mechanistic Error Reduction with Abstention for Language Models
ing for error mitigation may be more challenging (Engels et al., 2024). Errors are not necessarily tied to single iden- tifiable concept, but can manifest in various forms (Wang et al., 2025; Orgad et al., 2024), rendering them resistant to additive steering (Belrose et al., 2023).
C1 We propose principled steering framework miti- gate errors, which calibrates intervention intensity prevent both under-, and oversteeering, guaranteeing improved or non-degrading performance (see $3).
An emerging line of research explores alternative steering techniques for error-related properties like truthfulness, and hallucination (Li et al., 2023; Qiu et al., 2024; Wang al., 2025; Bhattacharjee et al., 2024). They involve complex departures from the elegant simplicity of additive steering through the addition of clustering, architecture-specifi in- terventions, or label-based contrastive vectors. Rather than advancing into such techniques, we address a simpler, and more fundamental question: when, and how much should we steer to mitigate errors effectively?
C2 We investigate which representation spaces, sparse au- toencoder (SAE) features or original activations, most effective for identifying error-mitigation direc- tions in LMs using linear probes (see $4).
C3 We introduce mechanistic error reduction with ab- stention (MERA, see $5), a practical method that em- pirically achieves safe, effective, non-degrading error correction, and improve upon existing baselines across a range of models, and tasks (see $6).
As Figure (left) illustrates, traditional steering methods rely on fixed steering strengths. This can lead to issues such as understeering, where an insufficient change is made to mitigate errors, and oversteering, where unnecessary (and potentially detrimental) steering is applied (Tan et al., 2024; Scalena et al., 2024). The dominant practice to empiri- cally find fixed steering strength based on ad hoc hyper- parameter sweeps (Liu et al., 2024; Turner et al., 2024; Postmus& & Abreu, 2024; Lee et al., 2025), which are costly, model-specific, and lack generalisation. Others apply fixed strengths or none at all (Arditi et al., 2024; Durmus et al., 2024; Ball et al., 2024). There are also conditional ap- proaches (Wang et al., 2025; Scalena et al., 2024; Cheng et al., 2024) that adjust the steering strength dynamically, but these are not adapted for the specific objective of error mitigation (see further discussion in $A.3).
This work highlights broader vision for post-training align- ment: lightweight interventions that are both effective, and probabilistically safe by design. While our current focus is error mitigation, by adapting the target signal with labeled inputs, MERA could steer LMs toward diverse specialised objectives (e.g.. harmlessness, honesty, and fairness etc). This positions MERA general-purpos framework for principled, and minimal post-hoe model control.
2. Preliminaries
Consider an autoregressive, decoder-only transformer language model ʃ that maps n input tokens, x = (I1,...,Zn) E 12" to an output probability distribution over all input, and generated tokens, [mm++a x|||, where V is the vocabulary set. The model consists of L sequential blocks, each comprising attention, feed-forward, and residual stream layers. At layer E [4]. the activation for the token position is denoted " (x). For each input x, and given task, we assume an error func- tion E(a) E [0, 1] that measures the quality of the model's generated output, where lower is better.
(ai...., (m))
In this work, we address the challenge of steering strength calibration for error mitigation. After identifying steering directions using linear error estimation probes instead of contrastive pairs (see $4), we show how to derive an optimal steering strength reduce empirical error. This results in steering method that does not use a fixed strength, but rather a fixed threshold in the activation space to which steering is applied; see Figure 1 (right). A by-product of our approach is that we abstain from steering activations that are beyond the threshold, for which error is already predicted to low. By formulating steering as a constrained optimisation problem, we derive closed-form solution (see $3.1) which ensures that interventions grow proportionally with the predicted error. The following calibration step (see $3.2), checks per task whether a threshold exists that confidently improves performance; if none can be found, we abstain entirely. In this way, we steer only when it is provably beneficial, effectively addressing both under-, and oversteering.
This setup is general, and applies to various LM tasks. For instance, multiple-choice question answering (MCQA), (aa can be 0 if the correct answer is within the gener- ated tokens, and otherwise. In summarisation, E(a) can quantify the distance between the generated summary, and reference.
2.1. LMs for Supervised Tasks
In this work, we focus supervised problems, where each prompt x is associated with ground truth label E V. Let y V be the set of valid labels (see $A.5 for details), and idx(y) E {1,..., [V} be the index of label y E V in the vocabulary. Given the model's output distribution a, we select a token position k and parse a predicted label ÿ. and
We make the following contributions:
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Mechanistic Error Reduction with Abstention for Language Models
its probability prob, as follows
Contrastive Steering A widely used technique (Zou et al., 2023; Arditi al., 2024; Ball et al., 2024; Rimsky et al., 2024; Farquhar et al., 2023; Marks & Tegmark, 2024), in- volves intervening across a token position i, and layer e by defining o (xx as the difference-in-meann between activa- tion values of positive examples (E(a) 1). and negative examples (F(a)= = 0). Given a dataset D = -{(x,, Mj } ==1 we define the set of positive examples as D+ = (i E
ag Ak.idx(1)
1/ = arg max a (xx))) and prob yEy
Egey (xx))
We choose token position k using one of two strategies: (i)
last, which uses the final token a, in the input sequence; or (ii) exact, a recently proposed method (Orgad et al., 2024) that uses the first token that matches any valid ground truth label. In supervised LM tasks, it common to interpret the logits at the final token position as the model's 's prediction, as this captures the model's decision after processing the full prompt. However, the last position does not always correlate with how the model actually generates answers (Pres et al.,
[] : E(aa) = 1}. and the set of negative examples as D_ = {j E [D] E(ay) = 0}. where a, = f(x)). The
steering vector v(xx is then defined as
v(x) = g++ p0-
(4)
where the mean activations μ4, and μ are given by
2024). To address this, the exact position complements the last prediction mode, selecting the first token that matches any valid ground truth label, measuring how an LM model behaves in its free-form, open-ended generated response. Further experimental details are provided in $A.5.
1
h(x)), p DD_ JED
1
Σ h(x)),
M+ D
JED+
which is computed for each layer l, and token position as h := h/ (x). and := oi
(1) (x).
For given prompt-label pair (x, y), the error function is
Probe-based Steering An emerging alternative technique is steering guided by probes (von Rütte et al., 2024; Cheng et al., 2024), which leverages learned linear classifiers (or "probes") guide intervention. A probe, p(h) = w h. is trained to classify targeted properties, and the classifier weights w are directly used as the steering vector v. Con- trastive steering can be viewed as special case of this framework, where the steering vector is derived from the Linear Discriminant Analysis classifier, assuming isotropic covariance between μ4, and μ (Mallen et al., 2023).
E(a)= = 1 prob,..
(1)
y'
where proby is evaluated at the chosen token position k. Additionally, we assess the model's end-task performance,
which, in our supervised setting, corresponds to accuracy, which is defined
A(a)= 10 y)-
2.2. Steering
Goal This paper focuses on error mitigation through steer- ing by leveraging the interplay between probes, and activa- tion adjustments. In what follows, we propose a principled framework for utilising probe models in steering, address- ing key challenges such as determining optimal steering strength X, and adaptively intervening across layers, and token positions with the ability to abstain.
In this paper, we focus on the concept of additive steering (or "activation addition"). Suppose E(a) E {0, 1}, where F(a) = indicates that the generated output exhibits a certain targeted concept (e.g. refusing harmful instructions). Steering aims to add a vector v (x) to the activations h at one or more token positions, and layers as follows
(x) = n1 (x) A 2 ( (xx)
(3)
3. Conditional Steering for Error Mitigation
such that after this intervention, the new output ā satisfies E(ā) = 0 (e.g. refusing harmful content). A scalar pa- rameter À E 1 is introduced to control the strength of the steering. Throughout the paper, we use the tilde nota- tion : to represent the steered version of any quantity, and let h := h1 (x). and v := of (x) for brevity. We de- note f the steered model with output á := f(x). Several methods have been proposed to extract steering directions v, including contrastive pairs, linear probes, and principal components (Wu et al., 2025). In this work, we focus on the first two, which can be interpreted as deriving v from a classifier of the targeted concept (Mallen et al., 2023).
We extend probe steering to minimise continuous errors, such as the model's 's error E(a). Instead of training classi- fier, we train an error estimator f(h) to predict F((a) from activations h.
In prior work (Mallen al., 2023; Li et al., 2023; von Rütte et al., 2024), the probe's weights were used directly as the steering vector. In contrast, we propose use both the probe's ' predictions, and its weights. Since the probe's pre- dictions estimate the LM's error, we construct the steering vector to explicitly reduce the predicted error. This approach provides a principled mechanism for determining the steer- ing strength, as demonstrated in the next section.
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Mechanistic Error Reduction with Abstention for Language Models
3.1. Optimising Steering with Abstention
3.2. Calibrating for Safety
We define steering as moving the activation in direction that reduces the predicted error while staying close to the original h. Formally, we solve the following constained optimisation problem
In this framework, the steering threshold the key param- eter that determines both when intervention is triggered, and how strongly the activations are shifted. We select us- ing calibration set Deai {xx, y5 15)) which is distinct from the dataset used to train the error regressor. For a given a, let ca) denote the change in some measure of LM's performance on Peal. such as the accuracy A (Equation 2) or (negative) error -E (Equation 1), after applying steering with the corresponding steering strength X (Equation 7), Specifically, we define the optimal threshold a²
min I1uli subject to p(h+ + v) S
(5)
where a represents the target threshold of error reduction.
Linear Case If p(h) is linear, i.e. p(h) w wTh h. this optimisation problem admits a closed-form solution
a
arg sup (cal where ac
10 0,
w < a,
Clvlld = fa E fai,.................. .ak. Dai(a) > e b(6, K, N)), and 01,..., OK E (0,1) are candidates values for a. 6(ō, K, N) - (10)(2 is confidence bound derived by applying union bound (Bonferroni correction, using Hoeffding inequality) over the K candidate hypothe- ses (see $A.2 for derivation). This ensures that, with probability at least 1 - ö, the selected a² yields genuine performance improvement that exceeds e.
((
(6)
w, wf > a.
Intuitively, if w is already at below a, no intervention is required. Otherwise, we adjust h to ensure w (h + v*) satisfies the threshold a.
Equivalently, we can rewrite the resulting steering vector as 8² Xtw, where
This procedure guarantees either provable improvement in performance or abstains from intervention if Ovalia is empty. Assuming i.i.d. samples, it satisfies
Theoretical Guarantees
a w
X = max
0,
P (Aai(a") > e) 2 1 8.
(9)
This formulation offers intuitive interpretations:
See proof in $A.2. More generally, this approach is flexible, and can incorporate any valid bound b satisfying the desired confidence guarantee in Equation 9,
Selective Steering: Intervention are applied selec- tively, only when p(h) = w T >> a at a given token, and layer level.
Instead of relying on a Bonferroni-style correction, which may be overly conservative, an alternative approach is to split the calibration data: use one part select the optimal at and the other verify that its confidence interval lower bound exceeds
Adaptive Strength: The steering strength scales with the residual a- w h = a - p(h), leading to stronger adjustments for larger estimated errors.
By adjusting 8, practitioners can control the trade-off be- tween conservativeness, and aggressivenes: of the steering policy. In our experiments, we set = 0.01, c = O, and use difference in accuracy as (a),.. though the method agnostic the metric used, and can accommodate relevant alternatives such Fl score in classification tasks.
The normalisation by ||wl] aligns with prior work (von Rütte et al., 2024), where such scaling factors have been shown to improve steering efficacy.
Extension to Non-linear Models A similar closed-form solution arises when p(h) an affine function composed of an invertible transformation. For instance, if p(h) sigmoid(w (w h), the constraint p(h v) S a translates to w. (h + v) < logit(a). The steering strength will be
3.3. A Principled Framework
Our framework establishes a principled foundation for con- ditional activation steering, grounded in three key ingredi- ents. First, we linear probes to obtain effective directions for minimising the predicted error. Second, this direction is then scaled using the closed-form solution at both the token, and layer levels. Third, we calibrate the steering threshold a against the true error on the calibration dataset, informed by the user's tolerance for uncertainty (i.e. set by 5).
max (0. logit(a) p(h)
(8)
Although we focus on linear probes in this work, $A.1 dis- cusses how to extend these ideas to non-linear probe func- tions (e.g. a lny-r MLP).

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Mechanistic Error Reduction with Abstention for Language Models
LLAMA-3.2-1B-A
GEMMA-2-2B-IT
GEMMA-2-2B-IT
OWENN.5-3B-
RMSE
0.225
RMSE
RMSE
0.20
RMSE
0.250
0.200
0.225
0.15
0.15
0.175
0.200
0.10
0.10
10
15
10
20
10
20
0
10
20
30
Layer
Layer
Layer
Layer
Features
Token position
Activations Sparse rep.
Last (prompt)
Exact (generation)
Figure 2. Layer-wise performance of linear error estimators for different LM families, separated by distinct token position, and input feature strategics. RMSE, and standard error is reported. Extended results are provided in A.
A key advantage of this formulation lies in how it handles the steering strength A: defining the appropriate range of values for this factor is nontrivial, and often requires careful weight normalisation or manual tuning. In our approach, this challenge is eliminated. The a value, and the estimated error inherently determine the steering strength, providing natural, and intuitive interpretation of its role:
tor in inference-time, often differ (see $A.4 for an extended discussion). Lastly, it remains an open research question whether such strategies extend to mitigating continuous er- rors (as opposed to strictly binary alignment targets, e.g. reducing toxicity).
To address these gaps, we investigate two central questions:
Q1 Token position. Does extracting activations from the exact token position in the generated answer, as re- cently recommended by Orgad al. (2024), improve probe performance?
Global Abstention. If calibration indicates that a offers improvement beyond baseline e, we refrain from intervening altogether.
Q2 Representation. Can sparse representations, such as those obtained through SAEs (Lieberum al., 2024; Joseph Bloom & Chanin, 2024), enhance the learned er- ror direction, and thus improve steering performance?
In this way, steering interventions remain both effective (re- ducing error where needed), and safe (avoiding unnecessary or detrimental modifications). In a similar spirit to Cheng et al. (2024); Liu et al. (2024), which underscores the value of theoretical guarantees for safe steering towards semantic, binary properties, our method, to the best of our knowledge, is the first crror-mitigation approach whose objective is to calibrate steering thresholds to lower true empirical error with provable guarantees, thereby advancing this emerging line of research.
In line with prior work (Rimsky et al., 2024; Ball et. 2024; Tan al., 2024; Arditi al., 2024; Jorgensen al., 2023; Krasheninnikov & Krueger, 2024; Postmus & Abreu, 2024), we focus on steering the residual stream (Elhage et al., 2021), i.e. the aggregated "running sum" representation across MLP, and attention layers (Zhao et al., 2021), rather than selecting specific attention heads (Li et al., 2023; Wang et al., 2025).
4. Choosing Representations for Steering
In the previous section, we showed how to derive condi- tional steering direction for error mitigation from an arbi- trary model activation h. A remaining question is: which representations should be used to find steering directions?
4.1. Experimental Setup
We systematically analyse how choices of token position, and representation type affect probe quality across multiple models, and tasks.
The candidate set of activations h is large, spanning (n + m) L. where n + m denotes the total number of tokens from both the prompt, and the generated answer, and L the number of layers. Existing studies on contrastive steering navigate this extensive space by conducting computationally expensive, and model-specific hyperparameter sweeps (Li et al., 2023; Liu et al., 2024; Turner et al., 2024). In addition, the strategies used for selecting layers, and token positions for constructing the steering vector versus applying the vec-
Models We evaluate a diverse set of decoder-only models, including LLAMA (Team, 2024b), GEMMA (Team, 2024a), and QWEN (Team, 2024c), spanning distinct sizes. Specif- ically, we examine both the base-, and instruction-tuned variants of LLAMA-3 1.B, GEMMA-2-2B, and QWEN- 2.5-3B models. Details on these LMs, and their task per- formance are provided $A.5. For the Gemma models, we
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Mechanistic Error Reduction with Abstention for Language Models
Train error estimators Using training dataset
Calibrate steering threshold Using calibration Jatase:
Steer to thresholds at inference-time
training. O calibration)
High
Stewning draction
Token Position (STEER)
Tokion Position [ABSTAIN]
Taken Posttin (STEER)
Low
0.2
Largest performance Improvement
D.I
Figure
Visualisation MERA methodology mechanistically steer LMs:
cache activations, and errors.
train error estimators,
3. calibrate steering thresholds.
retrieve pre-trained SAEs from GEMMA-SCOPE (Lieberum al., 2024).
Results Figure 2 illustrates the RMSE, and standard error across the top performing regression probes (see $A.5 provides additional details). Generally, we find that the exact position strategy performs least as well as, if not better than, the last position across most model families (i.e. LLAMA, and GEMMA). Thus, we will use the exact position to extract / to train p. For sparse representations, we find no signal of improved probe performance. In $..6.1, we break down the results per model, and observe a high variability across models. Since SAEs also impose high compute costs, we find no compelling reason sparse activations instead of original activations for the purpose of probe-based steering.
Datasets We evaluate our methods supervised tasks with varying label cardinalities (binary, ternary, and qua- ternary), and class distributions, ranging from balanced to highly imbalanced datasets. The datasets include SMS SPAM (Almeida et al., 201 1), YES/NO (AI, 2023), SENTI- MENT (AI, 2023), and MMLU (Hendrycks al., 2021a), with subset of high-school, and professional level questions, i.e. MMLU-HS, and MMLU-PROF. The training datasets contain between 2600-300 training samples, with 30% used for validation. Additional dataset details are provided in Table 2 in $A.5.
5. Introducing MERA
Probes For each layer, we train a linear probe p. and measure how well predicts the model's true error (aa) across distinct token positions. Regularisation ensures that the learned error estimators sparse (see $A.6.3 for fur- ther details). We use root mean squared error (RMSE) to measure performance, where lower values indicate better performance (see $A.6.4 for details).
In the following, we introduce MERA-a general mechanis- tic steering methodology that practically operates in three main steps. We refer Figure 3 for overview of these steps.
Cache activations, and errors. Construct training
Durin by pairing LM errors E(a) with activations h exact token position k for each layer E {l,.... LJ. Prepare a calibration dataset Deal with input prompts
Sparse Representations For sparse representations, we specifically explore the encoding of SAE, which maps the original activations & E TRd to high-dimensional activation space z(h) g" as follows
x, and their corresponding true labels y.
2.
Train error estimators. Train I. linear probes p(h) w" h on Durin activations h to estimate the LM eгтоr E(a), applying distinct sparsity constraints (see full training methodology in $A.5).
z(h) = o WenWee (h bene) benc):
where is an activation function (e.g. JU (Licberum et al., 2024)), bene is a bias vector, and Wone is learned weight matrix. Only subset of activations in will be non-zero, and > d. Empirically, we explore whether sparse activations enhance linear probe performance (Templeton et al., 2024) to potentially be used for steering (Zhao et al., 2024; Durmus et al., 2024; Mayne et al., 2024; Bricken et al., 2024; Kantamneni et al., 2025).
3. Calibrate steering threshold. Calibrate the optimal steering threshold a on inputs x, and their correspond- ing true labels in Deal to maximise (a) (see $3.2). given a user-specified confidence 1-
A key advantage of MERA is its flexibility: while we train linear error estimators to find a steering direction for each layer E, both the optimisation of X, and calibration of
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Mechanistic Error Reduction with Abstention for Language Models
remains generalisable other definitions of v, such as con- trastive steering (Farquhar et al., 2023) or weights from logistic regression probes (Cheng et al., 2024; von Rütte et al., 2024). This means we can use MERA as methodology to improve existing steering methods. In $6, we empirically quantify this improvement.
measure in 1. If a steering method recovers the full performance, L.e. matches perfect accuracy, SPI equals 1. If steering degrades task accuracy fully to zero, SPI is - If there is no effect from steering, SPI will be 0. By measuring relative effects in this way, benchmarks across tasks, and models with varying baselines become more meaningful.
How we Calibrate We determine the optimal steering threshold a via a gradient- grid search over a E [o, 1] discretised into 10 equal intervals, selecting the value that maximises (a) while satisfying a predefined safety con- straint as described in $3.2. The unsteered reference accu- racy is first established on Deat. then accuracy is reported when steering at each candidate a. If no a yields a statisti- cally significant improvement, we abstain from intervention, ensuring X = 0. In $A.7, we show that accuracy. and error are closely related in our tasks. As discussed in $A.5, MERA offers efficient inference, with the main computational bur- den arising from the one-time, offine calibration.
6.2. Methods
We evaluate our steering proposal against several baselines.
No steering, Without intervention.
BASE-x (prompt-based steering). Appends suffix "Think before you answer:" to the prompt (see $A.5), serving as a prompt-based baseline (Kojima et al., 2022).
BASE-jux (contrastive steering). Following (Rimsky et al., 2024; Tan et al., 2024), a steering vector defined as the contrastive mean (u+ - p_) at the last token position in the prompt (k n), using the layer identified most effective by a probe p for steering. Contrastive pairs are constructed with the top-k highest-, and lowest-error training samples (k E (50, 200))
6. Benchmarking
Our experiments aim to answer the following question:
Q1 Does MERA make steering more effective, and safe?
BASE-ý, BASE- (probe-based steering). Uses weights of linear error estimator ý or logistic probe pleg (i.e. trained with the LM's predicted labels ğ (Cheng et al., 2024; von Rütte et al., 2024)) as additive steering directions without optimisation.
6.1. Evaluating Steering
In alignment tasks, steering is typically evaluated along two complementary dimensions, i.e. its efficiency in producing responses aligned with the high-level concept, and its ability to preserve fluency, and naturalness of text (Pres et al., 2024). In the context of eтror mitigation, however, the goal is to steer LMs toward correct labels. Accordingly, we shift the evaluation target to improving task accuracy.
To assess if MERA improves existing baselines, we include the following methods.
MERA. Trains regressor P to predict the LM's error, optimising both steering direction, and strength (see $3).
Our main question is: how much does a steering method actually help (or hurt) model performance? Comparing raw performance deltas alone can be misleading, especially when baseline accuracy is already high, making small degra- dations disproportionately large. To address this, in the spirit of Burns et al. (2023), we define a Steering Performance Impact (SPI) score
MERA-Pig Prog- Replaces á with weights of a logistic re- gression probe Plog (see BASE-ptog).
Substitutes probe weights w by con- trastive means, with A = 100 (see BASE-H1).
MERA-A100-
AD - ADux 1-A-- ADar Anya Anaz
if AD ADux otherwise
SPI
(10)
For comparability, all MERA steering methods intervene across all layers, and token positions (see $4). In $A.664, we included an ablation study for such choices.
AD
where AD,, is the test set accuracy Dies defined as follows
6.3. Results
ADu.
A(a:),
(11)
Drest
Figure 4 provides an aggregate overview of steering perfor- mance across models, and datasets, averaging both evalu- ation modes (see $2.1), and error percentiles. Higher SPI values indicate stronger error mitigation, while negative SPI
Dem
and AD.. denotes the accuracy computed analogously on steered outputs ā, SPI provides a bounded, symmetric
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Mechanistic Error Reduction with Abstention for Language Models
Steering Nechods
Baseline (arompinng)
Sasoline (oatrossive)
Baseline Negistiic
Bcseline terror)
icontrasthec
MERA (ogiese)
MERA (amort
Stewiing Perforrence Inrpact (SPO
Model-speclfic View
Deleset-epedffic
Aggregeted Parcenties
0.0
0.4
0.4
0.8
0.2
0.2
0.7
0.0
-0.2
-0.2
0.5
-0.4
-0.4
0.4
-0.8
-0.6
GEMMA-2-28
LLAMA-32-16
LLAMA-32-18-11
OWEN 2.5 38
OWEN 2.5 00-30--11
MMLU-NS
MMLU-PROF
SENTIMENT
SMS SPAM
YES/ND
201h
752
Parcendle
80th
20th
Figure 4. Overview of steering results for various LMs, and datasets. The first, and second panels display model-, and speesit- views, respectively, with 5 = 0.05. The third panel shows error percentiles, aggregated the "last"n setting.
suggests degradation. In contrast, Table offers more detailed view, reporting SPI values, with å = 0.01 for each model, and dataset individually.
SPI in MMLU-HS, and SMs SPAM) with negligible negative gains. With MERA, it becomes the best- performing method, improving SPI by +0.64 in SEN- TIMENT, and +0.53 in YES/NO, suggesting that error- based steering is better than using binary probe targets.
MERA Outperforms Baselines, and Enhances Existing Steering Methods The aggregate views in Figure 4, shows that MERA improves accuracy compared to both un- steered models, and existing steering approaches in all set- tings. The third panel in Figure 4 (right) shows that MERA reduces errors across the percentiles. While these overall positive trends are encouraging, Table I shows that per- formance gains can vary with the model, and dataset, as detailed next.
As detailed in $A.6.2, to analyse how steering affects pre- diction quality, we define transitions based on ground truth labels, where denotes an incorrect, and correct predic- tion. Oversteering corresponds to unnecessary degrading outcomes (1 + 0), while understeering reflects missed op- portunities to correct (0 + 0). As shown in Figure 12, while imperfect, MERA generally yields more corrective transitions with fewer degradations than baseline methods.
Certain LMs, and datasets benefit more than others. In Table 1, I.L.MA-3.2-18 and QWEN-2.5-3B show the largest improvements, particularly on binary tasks such as SMS SPAM, and YES/No, where SPI gains reach +0.87. Base models benefit more from MERA steering compared to instruction-tuned models. Corroborating Rimsky et al. (2024), we note that the MMLU-II, and MMLU-PROF subset is overall difficult to steer.
7. Discussion
Today, LMs can be frustratingly error- prror-prone, failing even in simple supervised tasks. In this work, we establish general- purpose methodology to steer LMs towards the correct an- swer. Unlike existing approaches that rely on expensive, uncalibrated, model-specific hyperparameter sweeps find appropriate strength for steering, main contribution is theoretically grounded framework that answers questions of when, and how much to steer.
Contrastive steering without MERA is highly unreliable, sometimes reducing accuracy (see Table 1 for exam- ples). With MERA, it consistently improves accuracy, turning -0.05 SPI into +0.52 in YES/No, and -0.09 into +0.21 in MMLU-IS, which is in line with the theoretical guarantees discussed in $3.2.
Experiments across diverse datasets, and LM families con- sistently show that MERA not only improves task accuracy over baselines, but also enhances existing contrastive, and probe-based steering methods. However, our current frame- work inherently linear, and thus limited in its capacity to capture non-linear relationships between internal activa- tions, and model error. Our results on MMLU subsets un- derscore this limitation: certain datasets may be inherently harder to steer due to factors like semantic class overlap, task complexity, and label cardinality, warranting further investigation (Tan et al., 2024). One of MERA'S 's strengths
Logistic probe-based steering mostly fails (-0.85 SPI in SEnTIMENT) but with exceptions (+0.83 SPI SEN- TIMENT). MERA can help prevent task degradation (+0.00 SPI) where its base version fails.
Our primary proposal MERA proves highly effective. Without MERA, BASE-ů is too weak to be useful (+0.00
8

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Mechanistic Error Reduction with Abstention for Language Models
Table 1. Complete view of steering results for various Ms and tasks. SPI (Equation 10) is reported, capturing the relative increase or
decrease in accuracy for both the "last" (left) and "exact" (right) evaluation modes for ò = 0.01. Higher values are better.
DATASET
METRON
LLAMA-3.1-1B
I.L.MA-3.-IBBIIT
GEMMA-2-2B
GEMMA-2-2B.IT
QWEN-2.5.3B
QwBN-2.5.3B.IT
BASE x
(.0.55)
(+0.10)
(+0.16)
(+0.18)
(0021) (0.21)[(00.39)
[-0.23) (+0.00)
(+0.00) (.0.01)
(+0.02) (+0.03)
BASE-jC00
[+0.00)
(+0.03)
(-0.03) (+0.03)
(00.01) (+0.00)
(-0.01) (-0.02)
(+0.02)((+0000)
(60.01) (+0.01)
BASE 1200
(0.05)
(-0.06)
(+0.03) (+0.18)
(+0.01) (+0.00)
(-0.01) (:0.02)
(+0.01) (-0.05)
(0.01) (+0.00)
YES/No
BASE-H200 -2200
[-0,04]
(-0.06)
(-0.01) (+0.00)
(+0.01)
(+0.01)
(+0.00)
(+0.00) (-0,01) (-0.01)
(+0.01)
(+0.01)
BASE Piin
(+0,52)
(-1.00)
(-0.28) (-1.00)
(.0.12)
(+0.01)
(-0.02) (c0.11) (+0,38)
(+0.10)
(+0,49) (-0.31)
BASE-?
(-0,01)
(40.01)
(-0,04) (-0.06)
(+0.00)
(+0.00)
(+0.00) (+0.00) (+0,01)
(+0.01)
(+0.01) (+0.01)
MERA-JI
(+0,52) (+0.00)
(+0.19) (+0.00)
(+0.00)
(+0.00)
(+0.
((0.00)
(+0.00)
(+0.00)
(+0.00)
(+0.00)
MERA-phico
(+0.00) (+0.00)
(+0,00) (+0.00)
(+0.00)
(+0.00)
(+0.00) (+0,00) (+0,00)
(+0.00)
(+0.00) (+0.00)
MERA
(+0,52)
(+0.28)
(+0.45)
(+0.00)
(+0.42)
(+0.00)
(+0.15)
(+0.00)
(+0.47)
(+0.52)
(+0.53)
(+0.00)
BASE x
(+0.79)
(+0.03)
(.0.79) (-0.90)
(+0.00)
(-1.00)
(-0.52)
(+0.20)
(.0.69)
(+0.44)
(+0.00)
(+0.00)
BASE 1500
(+0,84)
(-1.00)
(-0.01) (-0.15)
(+0.00)
(-0.10)
(+0.03)
(+0.00)
(+0.15) (40.00)
(+0,00)
(+0.00)
(+0.06)
(+0.10)
(-0,03) (-0.19)
(+0,00)
(-0.19)
(+0.03)
(+0.00)
(+0,24) (+0.00)
(+0,00)
(+0.00)
SMS SPAM
BASE- 12200
(+0,00)
(-0.05)
(+0.00) (+0.04)
(+0.00)
(+0.00)
(+0.00)
(+0,00) (+0.20) (40.04)
(+0.00)
(+0.00)
BASE-Pioo
(+0.88)
(-1.00)
(-0,03) (-1.00)
(+0.90)
(+0.83)
(+0.19)
(+0.00) (+0.09) (-0.93)
(+0.48)
(+0.02)
BASE-P
(+0.01)
(+0.02)
(+0.00)
(40.02)
(+0.00)
(+0.00)
(-0.02)
(+0.00)
(+0.70)
(40.00)
(+0,00)
(+0.00)
MERA-J1100
(+0.44)
(+0.77)
(+0.00)
(+0.50)
(+0.00)
(+0.00)
(+0.00)
(.0.00)
(+0.00)
(+0.00)
(+0.00)
(+0.00)
MERA- Prio
(+0.00)
(+0.00)
(+0.00) (+0.00)
(+0.00)
(+0.08)
(+0.00)
(+0.00)
(+0.16)
(+0.00)
(+0.00)
(+0.00)
MERA
(+0.87)
(+0.71)
(+0.00)
(+0.41)
(+0.00)
(+0.12)
(+0.00)
(+0.00)
(+0.83)
(+0.70)
(+0.87)
(+0.00)
BASE-X
(+0,00)
(-0.65)
(-0.10> (+0.01)
(-0.32)
(+0.09)
(+0.12)
(-0.10)
(-0.45)
(-0.35)
(-0.50>
(-0.50)
BASE-J450
(+0.00)
(-0.33)
(+0.50)
(+0.50)
(-0.19)
(+0.00)
(-0.11)
(-0.72)
(+0.03)
(40.01)
(+0.06)
(+0.06)
BASE- -4300
(+0.00)
(-0.28)
(+0.45)
(+0.45)
(+0.00)
(+0.00)
(-0.07)
(-0.53)
(+0,02)
(+0.00)
(+0,07)
(+0.06)
BASE-H2200
(-0.04)
(-0.06)
(-0.01) (+0.00)
(+0.01)
(+0.01)
(+0.00)
(+0.00)
(-0.01)
(-0.01)
(+0.01)
(+0.01)
SENTIMENT
BASE -pion
(-0.21) (-1.00)
(+0.87) (-1.00)
(-0.26)
(-0.09)
(-0.05) (-0.54)
(-0.85)
(+0.19)
(+0.38)
(+0.24)
BASE-P
(+0,00)
(+0.09)
(-0.07) (-0.07)
(+0.00)
(+0.00)
(+0.00)
(+0.00)
(+0.06)
(+0.00)
(+0,00)
(+0.00)
MERA-J1100
(+0.00)
(+0.00)
(+0.35)
(+0.35)
(+0.00)
(+0.00)
(+0.16)
(+0.17)
(+0,24)
(+0.11)
(+0,00)
(+0.00)
MERA-Pia
(+0.00)
(+0.00)
(+0,21)
(+0.21)
(+0.00)
(+0.00)
(+0.00)
(+0.00)
(+0,00)
(+0.00)
(+0.00)
(+0.00)
MERA
(+0.00)
(+0.00)
(+0.00)
(+0.00)
(+0.49)
(+0.33)
(+0.16) (+0.21)
(+0.00)
(+0.00)
(+0.70)
(+0.41)
BASE-X
(+0,16)
(-0.59)
(-0.12) (-0.35)
(+0,00)
(+0.00)
(+0.00) ((-0.01)
(+0.00)
(-0.26)
(-0.30)
(-0.70)
BASE-1650
(-0.02) (-0.03)
(-0.02) (+0.00)
(+0.00)
(+0.00)
(+0.00) (+0.00)
(-0.05)
(-0.08)
(-0.09) (-0.09)
BASE-JC100
(-0.05)
(-0.05)
(-0.05)
(-0.05)
(+0.00)
(+0.00)
(40.00) (-0.04)
(-0.09)
(-0.12)
(-0.07)
(-0.07)
MMLU--S
BASE Maam
BASE-Pine
(+0.00)
(+0.01)
(-0.03)
(+0.00)
(+0.00)
(+0.00)
(40.00)
(:0.05)
(+0.00)
(+0.00)
(+0.00)
(+0.00)
(+0.00) (=0.01)
(40.00) (=0,00)
(+0.00)
(+0.05)
(+0.00)
(-0.08)
(+0,00)
(-0.01) (-0.01)
(+0.00)
BASE-j p
(+0.00)
(+0.00)
(+0.01)
(-0.07)
(+0.00)
(+0.05)
(+0.00)
(=0.01)
(e0.02)
(+0.00)
(+0.02)
(+0.02)
MERA-11100
(+0.00)
(+0.00)
(+0.00)
(+0.00)
(+0.00)
(+0.00)
(+0.00)
(+0.00)
(+0.21)
(+0.13)
(+0,00)
(+0.00)
MERA-pacc
(+0.00) (+0.00)
(+0,00) (+0.00)
(+0.90)
(+0.00)
(+0.00) (+0.00)
(+0,21)
(40.13)
(+0.00) (+0.00)
MERA
(+0.00)
(+0.00)
(+0.33)
(+0.00)
(+0.00)
(+0,00)
(+0.00)
(+0.00)
(+0,00)
(+0.00)
(-0.01)
(-0.01)
BASE-X
(+0.01) | (-0.63)
(-0.16) (-0.42)
(+0.00)
(+0.01)
(+0.03)
(=0.01)
(+0.01) 15)
(+0.01) (-0.27)
BASE- -150
(-0.66)
(-0.06)
(-0.19) (-0.07)
(+0.00)
(+0.00)
(+0.00) (-0.12)
(.0.03) (.0.02)
(+0.07) (+0.07)
BASE F200
(+0.01)
(+0.01)
(-0.11) (-0.09)
(+0.90)
(+0.00)
(+0.00) (<0.05)
(.0.03) (+0.01)
(+0.04) (+0.04)
BASE. J2200
(+0.02)
(+0.01)
(-0.05) (-0.13)
(+0.00)
(+0.00)
(+0.00)
(-0.05)
(-0.04)
(-0.02)
(+0.01) (+0.01)
MMLU-PROF
BASE. Pinu
(.006)
(-0.06)
(+0.01) (-0.80)
(+0.00)
(+0.00)
(+0.01) (+0.02)
(-0,24) (-0.25)
(+0,06) (-0.35)
BA
[-0.06)
(-0.06)
(+0:01) (-0.80)
(+0.00)
(+0,00)
(+0.01) (=0.02)
(-0.24) (-0.25)
(+0.06) (-0.35)
MERA-p110
(+0.00)
(+0.00)
(+0.00)
(+0.00)
(+0.00)
(+0.24)
(+0.00)
(+0.00)
(+0,00)
(+0.00)
(+0.00) (+0,00)
MERA-fh.c
(+0,00)
(+0.00)
(+0.00) (+0.00)
(+0.00)
(+0.00)
(+0.00)
(+0.00)
(+0.00) (+0.00)
(+0.00) (+0.00)
MERA
(+0.00) (+0.00)
(+0.00) (+0.00)
(+0.00)
(+0.00)
(+0.00) (+0.00)
(+0.00) (+0.00)
(+0.10) (+0. 10)
is to detect such unsteerable cases, and abstain from in- tervention, making it more cautious steering approach compared to baseline methods. That said, while MERA im- proves targeted error correction, it may inadvertently impair general capabilities. For example, steering for specalised tasks could reduce performance on unrelated generation or reasoning tasks. Exploring these trade-off's, and develop- ing safeguards to preserve generality, and text fluency is important direction for future work.
sion over model behavior is available. For example, MERA could be extended to alignment objectives such as toxic- ity reduction, refusal behavior, and harmfulness mitigation; directions that we plan to explore next.
There are also several promising directions for advancing MERA as a general steering methodology. One promising avenue is to replace the linear error probes with non-linear estimators, such as neural networks, an extension we outline in $A.1. Another is investigating the impact of the evalu- ation metric used during calibration. For example, could using Fl score instead of accuracy promote more balanced steering in tasks with high class imbalance or cardinality? We aim to explore such questions in future work.
In this work, we focus our evaluation on MCQA classi- fication tasks, as it allows for a controlled setup where ground-truth error can be unambiguously read off from token-level predictions (see $2). However, this choice of set- ting does not reflect a fundamental limitation of MERA. The framework is applicable to any task where labeled supervi-
9

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Mechanistic Error Reduction with Abstention for Language Models
Acknowledgements
Ball, S., Kreuter, F,, and Rimsky, N. Understanding jail- break success: A study of latent space dynamics in large language models. CoRR, 0oss22006002899, 2024.
We thank Ronald Namwanza for going above, and beyond to ensure we had access to computing resources during critical phases of this research.
Belrose, N., Schneider-Joseph, D., Ravfogel, S., Cotterell, R., Raff, E., and Biderman, S. LEACE: Perfect linear con- Conference on Neural Information Processing Systems, 2023.
Disclaimer
cept erasure in closed form. In
This paper was prepared for informational purposes by the Artificial Intelligence Research group of JPMorgan Chase & Co., and its affiliates ('JP Morgan") and is not a product of the Research Department of JP Morgan. JP Morgan makes no representation, and warranty whatsoever, and disclaims all liability, for the completeness, accuracy or reliability of the information contained herein. This document is not intended as investment research or investment advice, or a recommendation, offer or solicitation for the purchase or sale of any security, financial instrument, financial product or service, or to be used in any way for evaluating the merits of participating in any transaction, and shall not constitute solicitation under any jurisdiction or to any person, if such solicitation under such jurisdiction or to such person would be unlawful.
Bhattacharjee, A., Ghosh, S., Rebedea, T., and Parisien, C. Towards inference- time category-wist safety steering for large language models, 2024.
Bricken, T., Marcus, J.,
S., Tong, M., Perez, E., Sharma, M., Rivoire, K., and Henighan, T. Using dictionary learning features as classifiers. 2024.
Burns, C., Izmailov, P., Kirchner, J. H.,, Baker, B., Gao, L., Aschenbremner, L., Chen, Y., Ecoffet, A., Joglekar, M., Leike, J., Sutskever, I., and Wu, Weak-to-strong generalization: Eliciting strong capabilities with weak supervision, 2023.
Cao, Y., Zhang, T., Cao, B., Yin, Z., Lin, L., Ma, F., and Chen, J. Personalized steering of large language models: Versatile steering vectors through bi-directional preference optimization. In The Thirty-eighth Annual Conference on Neural Information Processing Systems, 2024. URL https: /ppprr/ieeepeeeieeeeeee net/ forum? id- qqJkuudYY.
Impact Statement
This paper presents a method for steering language models to reduce their error on well-defined prediction tasks. Given the increasing appetite for applying such models on real- world problems, the responsible deployment of more mature versions of this technology could have a positive societal impact, enabling more aligned, and trustworthy Al products, and services.
Cheng, E., Baroni, M., and Alonso, C. A. Linearly con- trolled language generation with performative guarantees. In MINT: Foundation Model Interventions, 2024.
Durmus, E., Tamkin, A., Clark, J., Wei, J., Marcus, J., Batson, J., Handa, K., Lovitt, L., Tong, M., McCain, M., Rausch, O., Huang, S., Bowman, S., Ritchie, S., Henighan, T., and Ganguli, D. Evaluat- ing feature steering: A case study in mitigating so- cial biases, 2024. URL feature research. eva
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Mechanistic Error Reduction with Abstention for Language Models
A. Appendix
A.I. Non-Linear Case
When p is replaced by non-linear function (e.g. a MLP), the constraint p(h + v) & a cannot be expressed in a simple linear form. In such cases, a closed-form solution does not exist.
One approach is to apply first-order Taylor approximation of the non-linear function p(h v) around the current representation h. Specifically, we linearise p
p(h + v) = p(h) + Vap(h)'
where Vap(h)= E IRd is the gradient of with respect to h. Substituting this into the constraint p(h + v) S a yields the approximate linear constraint:
p(h) (up(h)"usse
This transforms the problem into the following quadratic program
min |1 s.t.
Vnū(h) S a
which corresponds exactly to the problem solved in the main body in Section 3.1 by letting Vnū(h).
Alternatively, we can directly solve the non-linear constrained problem using numerical optimization techniques, such as projected gradient methods or interior-point solvers or adopting a penalty-bssed approach that converts the constraint into a differentiable penalty term, resulting the following unconstrained objective
min || + 5 (max((,, p(h + +) }
(12)
where <> > 0 is a scalar hyperparameter controlling how strictly we enforce the constraint. Because this formulation is fully differentiable, any standard gradient- madientt-baedd optimiser (e.g. Adam SGD) can be used to iteratively update until convergence.
Similarly to the linear case, we choose a, and 6 using a calibration set to effectively minimise the true loss. However, note that each candidate value requires solving the above problem 12 anew, which can be computationally demanding.
A.2. Calibration Step Detailed, and Thcoretical Guarantees
The rationale behind our selection procedure is to ensure that we do not choose a value of E (0, 1) unless it demonstrates a statistically significant improvement in performance. The strategy as follows: we first identify the subset of values that provably yield a positive performance improvement with high probability, and then select one among them with the highest empirical performance.
To formalise this, suppose f(a, X,) [0. is performance function, and X, is random input variable. Then, the empirical performance on calibration dataset D, (X1, X,) ) is given by
P(a Σ Xia, ==1
We denote P(a, D) as the theoretical performance.
Our approach proceeds in the following steps:
1. Discretise the interval [0, into K points: (d1,...,ax)
2. Construct confidence bands around each ay, using Hoeffding's inequality, for example
Pr (IP((aa Dw) - P(a,, 5 2 a
K
where 8,
In(2K/a) 2n.
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Mechanistic Error Reduction with Abstention for Language Models
3. Apply the union bound ensure that, with probability at least ct, all the above intervals simultaneously hold
[P(ay, P(a,, D)I S on for all j = {1............... (I....,,K) K},
or equivalently
Pr
sup aE(0,11
P((a, D.) - P(a, D)I sen 21
With this in place, define the valid set
Qvalid = = L(a) > 0},
and select
a² = arg max P(a, Dn)
Because the confidence bands hold uniformly over all a with high probability, we can guarantee that for every a E Ovalid. the true performance P(a, D) is also positive. Thus, on this "good event", a* indeed corresponds to a true positive performance improvement.
This provides formal guarantee, based i.i.d. data, and bounded performance function, that method yields statistically sound improvement or abstains with high probability.
Alternative Perspective An alternative to Bonferroni-style correction, which may sometimes be conservative is split the data into two parts:
Use one part select the empirically optimal a",
Then use the held-out part to estimate a confidence interval for the performance metric.
We accept the selected a* only if the lower bound of its confidence interval exceeds the desired threshold. This approach avoids the potentially conservative bounds introduced by Bonferroni correction, and can lead to tighter, and more adaptive inference.
A.3. Related Works on Steering Strength
Several prior works have explored different strategies for determining the appropriate strength of steering in LMs. We discuss these below.
Fixed Strengths, and Hyperparameter Sweeps et al. (2023); Liu et al. (2024); Turner et al. (2024); von Rütte et al. (2024); Postmus & Abreu (2024); Rimsky al. (2024); Tan et al. (2024); Cao al. (2024) rely on brute-force testing of different steering strengths across layers, and token positions, selecting the best-performing configuration. For example, Postmus & Abreu (2024); Turnr et al. (2024); Liu et al. (2024); Cao et al. (2024) performs exhaustive grid search over multiple layers, and multipliers, determining steering strength via empirical accuracy. Similarly, Rütte et al. (2024) evaluates steering at fixed increments for LLAMA, and MISTRAL, while adjusting layers. Durmus et al. (2024) uses heuristic range of (-5,5) across tasks, admittedly an "arbitrary" decision. This approach is computationally expensive, and not generalisable across architectures or tasks.
Arditi et al. (2024); Bhattacharjee et al. (2024); Ball al. (2024) bypass search entirely, applying pre-set steering strength across all instances, fixing at 1. While computationally efficient, unlike hyperparameter sweeps, effort made select an optimal X
Wang et al. (2025); Scalena et al. (2024) regulate steering strength dynamically. For example, Wang et al. (2025) clusters attention heads based on truthfulness, applying a variable steering strength that scales inversely with classifier confidence. Scalena et al. (2024) diminishes steering strength throughout model generation, reducing intervention as logit divergence stabilises. Cheng et al. (2024) is most similar to our work, and formulates steering as a constrained minimisation problem, selecting the minimal necessary to satisfy a safety threshold. A limitation of these methods is that they rely on indirect heuristics rather than directly calibrating for error minimisation on a given task.
Conditional Methods
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Mechanistic Error Reduction with Abstention for Language Models
Lee al. (2025) also explore conditional steering, but differ from approach in that they trigger interventions based cosine similarity with condition vectors, PCA on contrastive examples define steering directions, and select intervention strength via grid search rather than closed-form solution. Also, Lao et al. (2024) propose an intervention method with some mathematical resemblance to ours, modulating steering strength via inner products, but differ in motivation, and design, as their approach targets suppression of harmful concepts in predefined dictionary via supervised training, whereas MERA focuses on error mitigation with calibrated, layer-wise closed-form updates derived from held-out data.
A.4. Related Works on Steering Options
To extract activations, contrastive steering often relies on a specific model layer (Arditi et al., 2024; Rimsky et al., 2024; Turner et al., 2024), and the last token in the input prompt (Rimsky et al., 2024; Wang et al., 2025; Scalena et al., 2024), i.e. n. The rationale behind using the last token position that, with well-constructed prompts, and well-defined tasks such MCQA, the functional behaviour of the model can be captured locally at single token position (Arditi et al., 2024; Rimsky al., 2024). Steering is then applied variously. That is, across all layers (Cheng et al., 2024; Liu et al., 2024), on specific layers (Arditi et al., 2024; Rimsky et al., 2024; Marks & Tegmark, 2024), targeting all token positions (Cheng et al., 2024) or selected ones, such as post- cost-instruction or generated tokens (Arditi et al., 2024; Rimsky et al., 2024).
The generalisability of these extraction, and application strategies across tasks, and models remains an open question. We contribute by addressing it $4.
A.5. Experimental Details
Tables 2, and 3 summarise the datasets, and models used in our experiments. Table 2 provides an overview of the datasets, including the number of classes, class distributions, and sample counts across training, calibration, and test sets. Table details the models, specifying the number of layers, type, and parameter size.
Table 2. Datasets overview.
DATASET
NR. CLASSES
CLASS LABELS (DIST.)
NR. TRAIN
YES/No (AL 2023)
2
YES (32.5), (67.5)
3000 250 250
SMS SPAM (ALMEIDA ET AL., 2011)
2
SPAM (86.4), HAM (13.6) Pos (41.7), NEG (55.3), NEU (3.0)
3000 250 250
SENTIMENT (AL, 2023)
3000 / 250
MMLU-HS (HENDRYCKS
2021A)
4
A (20.7), (23.9), C (24.8). (30.7)
3000 210 / 210
MMLU PROF PROF
(HENDRYCKS ET AL.,, 2021A)
4
A, B. C, D
2601 / /210/110
Table 3. Models overview.
MODEL
NR. LAYERS
TYPE
PARAMETERS
LLAMA-3,1-18 (TEAM, 2024g)
16
IT
IB
LLAMA-3.11 3.1---------IT----- (TEAM, 2024g)
BASE
1B
GEMMA 2-2B (TEAM, 2024A)
BASE
2B
GRMMA-2-2B-ITT (TEAM, 2024A)
26
IT
2B
QWEN-2,5-3B (TEAM, 2024C)
BASC
3B
QWEN-2,5-38-1T (TEAM, 2024c)
36
IT
3B
Unsteered Task Accuracy Table provides an overview of unsteered task accuracy across different models, presenting accuracy on the test set (left), and error (right) for various tasks in both evaluation modes.
Absolute Differences in Task Accuracy Table 5 provides an overview of the absolute difference between unsteered, and unsteered task accuracy across different models, presenting raw accuracy deltas in the "last" mode (left), and in the "exact" mode (right) for various tasks, and each steering method.
Hardware All experiments were conducted on AWS instances, primarily using the G5. 1.5.16xL 16XLARGE instances with NVIDIA A10G GPUs. SAE caching experiments were exclusively run on G5. 48.LARRARGEE instances, offering enhanced 8 GPUs capacity.
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Mechanistic Error Reduction with Abstention for Language Models
Table Unsteered task accuracy overview. Accuracy on the test dataset (left), and error (right) across datasets in both evaluation modes.
MODEL
MODE
YEs/No
SMS SPAM
SENTIMENT
MMLU-IS
MMLU-PROP
"laxt"
(0.336 | 00571)
(0.128 0.622)
(0.056 0.893)
(0.190 | 00776)
(0.267 0.5611
L.AMA-332-1B IB (BASE)
"exacr"
(0.380
0.311)
(0.172 0.590)
(0.376 0.467)
(0.176 0.717)
(0.409 0.543)
LLAMA-3.2-1B (IT)
"last"
(0.436
0.519)
(0.892
0.179)
(0.236 0.725)
(0.195 0.779)
(0.441
0.559)
"exaet"
(0.428
0.471)
[0.784 0.201)
(0.236 0.725)
(0.205 | 0.721)
(0.441
0.555)
GEMMA-2B (BASE)
"last"
(0.452
0.519)
(0.108
0.741)
(0.124
0.784)
(0.152 (08844)
(0.262
0.203)
"exser"
(0.384
0,510)
(0.084 0. 146)
(0.828 0.320)
(0,000 0.000)
(0.262 0.203)
"last"
(0.644
| 0,394)
[0.224|
0.699)
(0.900
0.135)
(0.171 | (0.000)
(0.437 0.552)
GEMMA-2B (IT)
"exaes"
[0.428|
0.456)
(0.108 0.869)
(0.884
0.335)
(0.110 | 0.512)
(0.339) 0.555)
"last"
(0.356
0.575)
(0.356 0.535)
(0.364
0.714)
(0.267 0.719)
(0.332
0.660)
QWEN-2,5-3B (BASC)
"exaer"
(0.360
0.571)
(0.108 0.831)
(0.092 0.303)
(0.238 0.633)
(0.220 0.589)
QWEN-2.5.38 2.5-3B (IT)
"last"
(0.328
0.642)
(0.108
0.892)
(0.072
0.690)
(0.319 0.709)
(0.204
0.742)
"exaet"
(0.324 0.647)
(0.108 0.892)
(0.072 0.690)
(0.319 0.709)
(0.203 0.743)
Table Complete view of absolute difference steering results for various LMs and tasks. Absolute difference is reported, capturing the
increase or decrease in accuracy for both the "last" (left) and "exact" (right) evaluation modes for 8 = 0.01. Higher values are better.
DATASET
METHOD
LLAMA-3.1-1B
LLAMA-3.1-1B-IT
GEMMA-2-2B
GEMMA-2-200
QWEN-2.5-3B
QWEN WVENN2.553B-11
BASE-x
(-0,02)
[+0.06)
(+0.09) (+0.09)[(+0.10) (+0.10)
(-0.10)
(-0.15)
(-0.15)
(+0.00)
(+0.00)
(+0.00)
(+0.02)
(+0.02)
BASE-HA50
(+0.00)
(+0.02)
(-0.01) (.001)((++00)) (+0.02)
(+0.00)
(+0.00)
(-0.01)
(-0.01)
(+0.02)
(+0.00)
(+0.00)
(+0.00)
BASE-H400 14:00
(-0.02)
(-0.02)
(+0.02)
(+0.02)((00.10) (+0.10)
(+0.01)
(+0,00)
(+0.00)
(-0.01)
(+0.00)
(-0.01)
(+0,00) (+0.00)
BASE-1220
(40.12)
(-0.24)
(-0.07) (+0.00)
(-0.04)
(-0.21)
(-0.18)
(-0.06)
(+0.00)
(+0.00)
(+0.29)
(+0.30)
YES/NO
BASE-1aoe
(+0.35)
(-0.38)
(-0.12) (-0.43)
(-005)
(+0.01)
(-0.01)
(-0.05)
(+0.24)
(40.06)
(40.33) (-0.10)
BASE F
(+0.00)
(+0.00)
(-0.02) (-0.02)
(+0.00)
(+0.00)
(+0.00)
(+0.00)
(+0.01)
(+0.00)
(+0.01)
(+0.01)
MERA Pi0e
(+0.35)
(+0,00)
(+0.11) (+0.00)
(+0.00)
(-0.08)
(+0.06)
(+0.00)
(+0.00)
(+0.00)
(+0.00)
(+0.00)
MERA-PLA PLoG
(+0.00)
(+0.00)
(-0.01) (-0.02)
(+0.00)
(+0.02)
(+0.00)
(+0.01)
(+0.01)
(+0.01)
(+0.00)
(+0.01)
MERA
(+0.35)
(+0.18)
(40.25)
(+0.00)
(+0.23)
(.0.4)
(+0.05)
(+0.00)
(+0.30)
(+0.34)
(+0.36)
(.0.02)
BASE-X
(+0.69)
(+0.03)
(-0.70)
(-0.71)
(+0.00)
(-0.08)
(-0.12)
(-0.18)
(-0.24)
(+0.40)
(+0,00)
(+0.00)
BASE-
(+0.74)
(-0.17)
(-0.01) (-0.12)
(+0.00)
(-0.01)
(+0.02)
(+0.00)
(+0.10)
(+0.00)
(+0,00) (+0.00)
BASE-
(+0.05)
(+0.08)
(-0.02)
(-0.15)
(+0.00)
(-0.02)
(+0.02)
(+0.00)
(+0.16)
(+0.00)
(+0.00)
(+0.00)
BASE- -/200
(+0.04)
(-1.00)
(+0.02) (+0.00)
(.0.09)
(40.14)
(-0.02)
(=0.06)
(+0.00)
(+0.00)
(+0.00) (+0.00)
SMS SPAM
BASE Proe
(+0.76)
(:0.17)
(.0.02) (-0.78)
(+0.00)
(+0.76)
(+0.15)
(+0.00)
(+0.06)
(:0.10)
(+0.43) (+0.02)
BA
(+0.01)
(-0.02)
(+0.00)
(+0.00)
(+0.00)
[+0.00)
(+0.00)
(.0.000)
(+0.45)
(+0.00)
(+0.00) [+0.00)
MERA-Hic0
(+0.38)
(+0.64)
(+0.00)
(+0.11)
(+0.00)
(+0.00)
(+0.03)
(+0.00)
(+0.00)
(+0.00)
(+0.00)
(+0.00)
MERA-PUA Puea
(+0.02)
(+0.00)
(+0,00)
(+0.00)
(+0.00)
(+0.07)
(+0.00)
(+0.00)
(+0.10)
(+0.02)
(+0.00)
(+0.00)
MERA
(+0.76)
(+0.59)
(+0.00)
(+0.09)
(+0.06)
(+0.11)
(+0.00)
(+0.00)
(+0.53)
(+0.62)
(+0.78)
(+0.08)
BASE-X
(+0,00)
(-0.24)
(-0.02) (+0.01)
(-0.04)
(+0.02)
(+0:01)
(-0.09)
(-0.16)
(-0.03)
(-0.04)
(-0.04)
BASE-
(+0.00)
(-0.12)
(+0.38)
(+0.38)
(-0.02)
(40.00)
(-0.10)
(-0.64)
(+0.02)
(+0.01)
(+0.06)
[+0.06)
BASE /000
(+0.00)
(:0.10)
(+0.34) (+0.34)
(+0.00)
(+0.00)
(-0.06) (:0.47)
(+0.01)
(+0.00)
(+0.06)
[=0.06)
BASE- -500
(-0.35)
(+0.35)
(-0.44) (-0.92)
(+0.00)
(-0.61)
(+0.23)
(60.36)
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SENTIMENT
BASE. Prine
(:0.01)
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(:0.05) (:0.48)
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BASE-P
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MERA-JIco -110
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MERA-Pia
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MERA
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(=0.02)
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BASE
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BASE M3o0
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BASE /5300
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BASE M220
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BASE Moo0
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MMLU-PROP
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BASE-8
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MERA Jlice
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17

---

Mechanistic Error Reduction with Abstention for Language Models
Runtime MERA introduces kinds of overhead: one deployment, and one during calibration. At deployment, MERA incurs negligible runtime cost, as the learned steering vector v can be applied via standard forward hook. The cost is equivalent to single vector addition per intervention layer, and token position.
The main computational cost arises during calibration, after the probes have been trained, where a held-out calibration dataset is used to select the optimal confidence threshold a. This process involves evaluating small number candidate a values (e.g., 10-20) across a modest calibration set (e.g., 250 examples), computing the closed-form solution for each. Since this is one-time cost per model, and dataset pair. is amortised across deployment.
In practice, calibration takes between 10 minutes and hour our hardware (see $A.5), though actual runtime depends model size, input length, and hardware configuration.
Constructing Prompts Prompts are tailored to each dataset. Each dataset contains 3000 training samples, 250 calibration samples, and 250 test samples (except MMIJUHHS, MML.U-ROFF with 2061 training samples, and 210 calibration/test samples available). Below are the prompt templates for the datasets used in the experiments.
Question: [question on text:] [Options: A. [Option A] В. [Option B] C. [Option c] D. [Option D] Please select the correct answer. Only return one letter: A, B, C, or D.
Answer: \n
Figure 5. Prompt template for MMLU subsets.
This (text message): " "[SMS text]" classified as either spam or ham. Please evaluate the content of the SMS, and select the correct classification. Only return word: "ham" or "spam". Answer: in
Figure 6. Prompt template for SMS SPAM.
You are a financial sentiment analysis expert. Your task is to analyze the sentiment expressed in the given financial text. Only reply with positive, neutral, or negative. Financial text: [financial text Answer: An
Figure 7, Prompt template for SENTIMENT.
You financial expert. Your task is to answer yes/no questions based the given Headline:
headline news content. Context:
"[headline text " Now answer this
question: [yes/no question] Answer:
Figure 8. Prompt template for YES/NO.
Parsing Model Completions To compute the error E(a), and labels ÿ. we extract the exact answers directly from model completions, bypassing the need for external sources such as additional LMs assess the ground truth (Orgad et al., 2024: Arditi al., 2024). This approach focuses on tasks where the correct label can be reliably identified at single token position, simplifying the evaluation process while ensuring a systematic, and linguistically informed parsing.
For each task, class labels are transformed into multiple semantic variants, including lowercase, uppercase, and capitalised forms, with optional whitespace or newline prefixes. These string variants are tokenised, and their final token IDs are extracted for each ground truth label, and the LM's vocabulary.
18

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Mechanistic Error Reduction with Abstention for Language Models
During evaluation, we employ flexible matching within the token ID space, where any token ID corresponding to the semantic variants of class is considered valid. The model's output, a, is scanned starting from a specified position, and the first occurrence of a matching token ID is recorded. If no match is found, fallback index of -1 is assigned, indicating no valid prediction. In the "exacr" evaluation mode, prediction is considered correct if, and only if the predicted token matches the class token IDs.
Training Linear Probes For each layer of a given LM, we train distinct set of linear probes given the training samples, which are split into 70% for, and 30% for validation. The input features, X E Nxd were extracted from residual stream activations at specific token positions (exact answer from open-ended model completion or the last prompt position) across all layers. The target variable is the error F(a) of the L.M
To account for random variability, for each setting (i.e. layer, and token position), we trained 5 linear regression models using Lasso regularisation strengths 17 {0.005, 0.01, 0.05, 0.1, 0.25, 0.5), alongside unregularised linear regression with no sparsity. For simplicity, we omit the bias term in linear models, and focus on the weight vector. For each layer, we selected the model weights with the lowest RMSE on the validation set.
For the logistic probes, we follow a similar methodology but the target variable is the accuracy A(a).
A.6. Extended Results
A. PROBE PERFORMANCE
Figures 9- 1-10 show an extended version of Figure 2, separated by distinct datasets. RMSE, and standard error is reported (see $A.5 for details). We do not average over the MMLU-PROF dataset.
SMS SPAM LLAM1-3.2-18
YES/NO 3.2-1
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Exact Igeneration)
Figure 9. Layer-wise performance of linear error estimators for different LM, separated by distinct token position, and representation strategies.
Figure 11 shows the probe results for the logistic regression probes, used in $6. AUCROC, and standard error is reported (see $A.5 for details). Higher is better.
A.6.2. TRANSITIONS
We report transitions in model predictions, before, and after steering using 2 x 2 matrices, with = 0.00, i.e. without safety constraints. Each cell corresponds to a transition between binary outcome classes, incorrect (0), and correct (1), and displays
19

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Mechanistic Error Reduction with Abstention for Language Models
SM5 SPAM
YES/NO LLAMM-3.2-1B-T
SENTIMENT LLAMA-3.2-1B-11
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Figure 10. perfomacc strategics.
performance of lincar error estimators for different LM,, separated by distinct token position, and representation
LLAMA-3.2-18 Family
GEMMAA2-22 Family
GEMMA-2-28 Family
OWEN-2.5-38 Family
AUCROC
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Figure 11. Layer-wise performance of linear error estimators for distinct LM families, separated by distinct token position, and input feature strategics. AUCROC, and standard error is reported.
counts in both the "last" (left), and "exact" (right) evaluation modes, reflecting distinct prediction outcomes after steering. Higher values in top-right cell is prefered.
As seen in Figure 12, MERA-based methods consistently induce greater number of favourable transitions (0 1), while maintaining relatively low rates of degradation (1 O). Baseline methods, by contrast, exhibit more heterogeneous behaviour, often resulting in inconsistent effects across datasets. These results are averaged over the LMs.
A.6.3. SPARSE STEERING
Figure 13 illustrates the sparsity of features employed during steering across different layers, and datasets. On average, only 3-5% of the latent features are activated for steering, with notable variations observed for specific tasks like MMLU-HS, where certain layers (e.g., around 15-25) exhibit lower sparsity.
A.6.4. ABLATION STUDY
The aggregated ablation study in Figure 14 demonstrates that steering on all token positions, A1:(m++)) and across all layers, E {1....,L} L}, consistently provides stronger empirical results compared to steering on selected tokens or the best layer, as identified by the highest performing probe. Specifically, the steering strategy on all tokens surpasses steering restrictions on "generation tokens", i.e. az>n in improving task accuracy. Similarly, applying interventions across all L layers yields higher overall performance compared to limiting interventions to the "best layer".
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Mechanistic Error Reduction with Abstention for Language Models
Sevile (romppling)
Sewette Icontradiiee1001
Seselire Oogalic)
Benaline (msee)
With MERA (contrandive)
With MEEIA Oegalic)
With SERA (11M4))
WALLLAIS
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am0
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Figure 12. Transition matrices for each dataset, and method pair. Each cell quantifies the number of predictions transitioning from one correctness state another after steering: 0 - 0, -> 1 - and 1 - where 0 denotes incorrect, and denotes correct. Values are shown for both the "last" (left), and "exact" (right) evaluation modes.
Apgroggted Steering Feature Layenwise Sparsty
SMS 556M 501 Inbo
1.4
5%
2%
Figure 13, With probe steering, average 3-5% of the latent features employed for steering.
Token Position-wise Probe Performance shown in Figure 15, the probe trained for a single token position demonstrates consistently that the average RMSE is comparable across other token positions, including those not explicitly targeted during training. Naturally, some variability is expected. That said, these results suggest that the probe generalises sufficiently well to the remaining token positions retaining performance close to that directly generated model tokens. For this analysis, we selected four random combinations models, and datasets.
21

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Mechanistic Error Reduction with Abstention for Language Models
Aggrepated Abiation study
Sirelegy
Stratogy
Moan
0.00
Boscline 1oor crattrattv 1000
Danatree tcontranbreeee.. 500
Broddin teront
Basatee Iegier
with MEDOA (weror)
WEtH MERRAA (10 COC
wit MERA Scont
Figure 14, Ablation study, aggregated over all datasets but the MMLU-PROF dataset, and models.
Layer-dle 1.206-3.. 18- SENTIMENT
Layenwilee OWED--.5-3B-F SVS
Layeewiie 2-13-T MILUHSS
Layer NWALANS
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Pott: 0.10
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Nead
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Toho1 Sct Abs LLMMA 32 1B-T SONMMNNT
Toben Pes Bow.aiiee
QRENN 5-3-T- 2NG STAM
Postioneeiee LLAMA-1--IB-T KHGUIIG
Tdan Fouticredee 0WE---.--3--T -NILLM
0,00
Hebe
2.58
0.0
18-
92
18ke
Figure 15. Comparison of probe performance across all token positions, and layers, including those not explicitly targeted during training.
A.7. Accuracy vs Error
The plot in Figure 16 illustrates the relationship between Delta Test Accuracy (1), and Delta Test Error (4) across various models. Each point represents a different steering method or baseline, highlighting the relationship between improving accuracy, and reducing errors. The clustering along a diagonal trend suggests strong negative correlation.
Delta Test Accuracy and Error over Models
1.0
Data Trat Accuracy
Model
Gemma-22
Gemme-2-28-IT
Lama-3.2-18
-0.5
Liame-3.2-10-
Qwen-2.5:38
Qwen-2.5-38-1
-1.0
-0.6
0.2 -0.4
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0.0
Detta Test Error
Figure 16. Delta Test Accuracy (1) versus Delta Test Error (1) across the different models, over the steering methods, and baselines.
22


Reviews:
[{"review_id": "stOrVG42kZ", "reviewer": "Reviewer_7dxY", "summary": "Current steering methods for LM error mitigation use fixed intervention strengths, which has the risk of under-/oversteering. The paper introduces MERA, which does adaptive activation steering guided by linear error probes; the intervention thresholds (α) is calibrated via Hoeffding’s inequality. The framework further optimizes steering strength per-token/layer and abstains when unnecessary, ensuring minimal intervention. Evaluations on three LLMs show gains on binary/ternary tasks while avoiding degradation seen in fixed-strength approaches.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for the constructive and informative review! We have addressed your four key points below:\n\n**1) Hoeffing inequality — Clarifying Our Selection Procedure.**\n\nOur selection procedure ensures we do **not** choose any $\\alpha \\in (0,1)$ unless it **statistically significantly** improves performance. Specifically, we first identify a set of $\\alpha$ values with provably positive performance gain (with high probability), then select the empirically best among them.\n\nLet $f(\\alpha, X_i) \\in [0,1]$ be a performance function and $X_i$ a random input. Given a calibration dataset $D_n = \\\\{ X_1, \\dots, X_n \\\\}$, the empirical performance is:\n\n$$\nP(\\alpha, D_n) = \\frac{1}{n} \\sum_{i=1}^n f(\\alpha, X_i),\n$$\n\nwith $P(\\alpha, D)$ denoting the true (population) performance.\n\n#### Procedure Overview\n\n1. **Discretize** $[0,1]$ into $M$ values: $\\alpha_{set} = \\\\{\\alpha_1, \\ldots, \\alpha_M\\\\}$.\n\n2. **Confidence Bands**: Apply Hoeffding’s inequality to each $\\alpha_j$:\n\n   $$\n   \\Pr\\left( \\left|P(\\alpha_j, D_n) - P(\\alpha_j, D)\\right| \\le \\delta_n \\right) \\ge 1 - \\frac{\\alpha}{M},\n   $$\n\n   where $\\delta_n = \\sqrt{\\frac{\\ln(2M/\\alpha)}{2n}}$.\n\n3. **Union Bound**: Ensures all bounds hold simultaneously with high probability:\n\n   $$\n   \\left|P(\\alpha_j, D_n) - P(\\alpha_j, D)\\right| \\le \\delta_n \\quad \\forall j=1,\\ldots,M.\n   $$\n\nThis yields a uniform guarantee:\n\n$$\n\\Pr\\left(\\sup_{\\alpha \\in \\alpha_{set}} \\left|P(\\alpha, D_n) - P(\\alpha, D)\\right| \\le \\varepsilon_n\\right) \\ge 1 - \\alpha.\n$$\n\nWe define the **valid set**:\n\n$$\n\\alpha_{\\text{valid}} = \\\\{\\alpha : P(\\alpha, D_n) - \\epsilon_n > 0\\\\},\n$$\n\nand select:\n\n$$\n\\alpha^* = \\arg\\max_{\\alpha \\in \\alpha_{\\text{valid}}} P(\\alpha, D_n).\n$$\n\nSince the confidence bands hold uniformly with high probability, we guarantee $P(\\alpha, D) > 0$ for all $\\alpha \\in \\alpha_{\\text{valid}}$. Hence, $\\alpha^*$ corresponds to a **true performance improvement**, or we abstain otherwise.\n\n> **Note**: We will make this guarantee more explicit in the next version of the paper.\n\n---\n\n### **Alternative Calibration Perspective**\n\nInstead of using a Bonferroni-style correction (which can be conservative), one could:\n\n- **Split the data** into two parts:\n  - Use one part to find the empirically optimal $\\alpha^\\star$.\n  - Use the other to estimate a confidence interval for $P(\\alpha^\\star, D)$.\n\nWe accept $\\alpha^\\star$ only if its confidence interval lower bound exceeds a desired threshold. This avoids overly conservative bounds and allows for tighter, adaptive inference at the cost of splitting the data.\n\n**2) Cardinality versus steerability.** Thank you for raising this important point. We agree that four classes is not especially high, and in retrospect, attributing the difficulty of steering on MMLU-HS to cardinality alone is premature (dataset charactistics like semantic overlap, label ambiguity, and task complexity could also play a role in a task’s steerability). See further discussion in answer (1) at Reviewer MXKB. As we see it, a dedicated, systematic study (e.g., along the lines of [1]) that carefully varies such characteristics while analysing steering performance would be necessary to understand the limits of additive methods like MERA (+ its baselines). We've revised the formulation in the manuscript.\n\n**3) Code availability.** Apologies — we missed attaching the code at submission. We had it ready for rebuttal, but then we just learned that ICML guidelines don’t allow updates to the original submission in the discussion phase. If we’re allowed to share an anonymous link (can AC please let us know if this is acceptable) we can upload the source code, notebooks and installation guides directly there!\n\n**4) Relation to PaCE.** Thank you for pointing out the connection to PaCE! Your analysis is very insightful. While there are mathematical similarities, as you point out (i.e. adaptive intervention strengths based on the inner product of activations and steering directions), the overarching goals of PaCE and MERA are very different. The PaCE model is trained on data demonstrating ‘benign’ and ‘harmful’ concepts from some predefined dictionary, and performs interventions to suppress the harmful ones, while MERA is fundamentally concerned with error mitigation on well-defined prediction tasks. We also can’t see a direct analogue of our calibration step, which uses calibration data to identify the optimal intervention strength for error mitigation on a per-layer basis. That said, we consider the work relevant enough for inclusion in Section 3 and have also added it to the Related Works in Appendix A.1.\n\n[1] https://arxiv.org/pdf/2407.12404", "claims_and_evidence": "Yes, except the Hoeffding's inequality part as I comment in \"Theoretical Claims\"", "methods_and_evaluation_criteria": "Yes, the proposed methods make sense for the problem", "theoretical_claims": "I understand Hoeffding’s inequality and in general high-dimensional statistics, but I do not get what is the rationale of using it in line 195 (left). It would be great if one could start with Hoeffding’s inequality, explain what are random variables, which assumptions of Hoeffding’s do they (approximately) satisfy or not satisfy, and how it leads to the bound in line 195 (left).", "experimental_designs_or_analyses": "The authors observed that datasets with high cardinality (e.g., MMLU-HS with 4 classes) are overall difficult to steer. I do not know if four choices per question is a high one, since it is common as high-school level questions, and there are tests with 6 options if not more. Even in high school, one could face open questions without choices, meaning infinite many choices. Could the authors provide some insights and comments on this?", "relation_to_broader_scientific_literature": "Please find my comments in \"Essential References Not Discussed\".", "essential_references_not_discussed": "The proposed work seems highly related to an existing paper \\[1\\], and therefore it is important to clarify the similarity and differences between the two.  As far as the reviewer see:\n\n1. Motivation-wise, both the work of \\[1\\] and the current paper mention that existing methods rely on fixed steering strength, which leads to under/over steering.   \n2. The two works use different existing ways of extracting a steering *direction* (independent of the strength): \\[1\\] uses PCA on the normalized contrastive vectors, while this paper uses linear probes. Nevertheless, \\[2\\] points out that the two ways of extracting steering directions are equivalent under certain conditions.  \n3. Given one steering direction, both work can estimate the strength of steering directions. \\[1\\] does so by decomposing the activation along the steering directions, while this paper does so by finding the smallest $\\\\ell^2$-normed vector that sufficiently reduces the probing probability. Interestingly, equation (6) of this paper share some features with proposition 2 of \\[1\\]: both depends on the inner product of the steering direction and the activation, which can be viewed as achieving adaptive scaling.   \n4. To achieve a steering task, \\[1\\] in its general form uses multiple directions each corresponding to a semantic concept, and finds the steering strength for all of them with one sparse decomposition problem, while this paper focuses on one direction.   \n5. This paper investigated the choice of the representation to steer in section 4, while \\[1\\] followed a prior work.\n\nAnyhow, I understand that papers could have similarities and what not, but it is important to place the proposed work relative to the literature to attribute what is existing and clarify what is the contribution.\n\n\\[1\\] PaCE: Parsimonious Concept Engineering for Large Language Models, NeurIPS 2024\\.   \n\\[2\\] The linear representation hypothesis and the geometry of large language models, ICML 2024\\.", "other_strengths_and_weaknesses": "N/A", "other_comments_or_suggestions": "N/A", "questions_for_authors": "N/A", "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": "gJ03gKvNy6", "reviewer": "Reviewer_H7hE", "summary": "The paper proposes a new latent space steering methodology for LLMs. The basic setup is that we  prompt an LLM with a question from a finite-class classification task, and we let it generate an open-ended response. We can decode the model's prediction from its open-ended generation by either\n- **last token**: using the argmax over discrete labels of the logits at the last token of the prompt; \"last\" is a bit of a misnomer, since really it's the last token of the prompt.\n- **exact token**: find the first match to one of the discrete labels in the generation, and use that as the prediction (together with its associated next-token probability given by the model)\n\nThe **error** of the model, denoted $E(z)$ in the paper, is a soft measure of how far the generation is from the true answer, and is measured as 1 minus the probability of the true answer (under either \"last token\" or \"exact token\"). The goal with steering is to make the model better at the classification task, i.e. increase accuracy. $1-E(z)$ is a soft proxy for the accuracy.\n\nThe main innovations of the steering method are:\n- it frames the steering problem as a constrained optimization, minimizing the magnitude of the latent space perturbation subject to achieving a certain degree of desired effect on $E(z)$, measured via a proxy, namely a linear probe on the activations that is intended to predict the $E(z)$.\n- In particular, when the unperturbed activation already has a satisfactorily low error, it is unchanged. Thus the steering is conditional\n- it also additionally frames the degree of desired effect to seek in steering as another optimization problem, rooted in a more \"human-interpretable\" measure, e.g. the 0-1 based, \"hard\" metric of accuracy. \n\nThe method is evaluated on several classification datasets and several LLMs in the parameter range 1B-3B, both base and instruction-tuned. The choice of steering direction (probe vs other options) is ablated. Baselines such as contrastive steering via difference in means are considered. Results show mostly improvement over baselines. \n\nSome problems with the methodology, correctness and analysis are discussed in subsequent sections of this review.\n\n## Update after rebuttal\nThe rebuttal has not meaningfully changed my recommendation; I am still in favor of accepting the paper if possible.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for all the time taking to provide a very detail-oriented and helpful review! We’re glad to hear that you found our claims straightforward, clear + verifiable, our optimisation framing is a great way to move the fields towards more principled foundations and our experimental designs are clear. Now, we have addressed all of your points below:\n\n**1) Regression target for probes.** Regarding learning the linear model not directly on the error but on the inverse of the sigmoid (i.e., the logits), we agree that this is a promising direction that could potentially enhance the performance of MERA. We are currently re-running this experiment on all evaluations to assess its impact. Preliminary results steering Llama and Gemma models on SMS spam dataset suggest a slight improvement over the original formulation. We’ll reassess when the complete results are in and if supported, update the methodology accordingly.\n\n**2) Describing BASE-$\\mu_{k}$.** Thank you for pointing this out! We agree that mixing strategies across methods can undermine fair comparisons and we appreciate the opportunity to clarify! In our experiments, we do not use any MERA-specific best-performing layer for the BASE-$\\mu_{k}$ baseline. Instead, we choose the layer with the lowest RMSE under a trained linear probe — a shared external signal reflecting where the error is most linearly related to model activations —which we think enables the fairest comparison on balance. As we see it, probe performance is a good heuristic for selecting contrastive steering layers, since it neutrally depends on how linearly our target is related to the activations (and does not favour MERA which steers on _all_ layers). It is worth mentioning that the community hasn’t converged to one single criterion for layer selection for contrastive difference-in-means steering (see distinct approaches in [2-5]) but that many methodologically valid strategies exist. We’ll revise the section to make our approach clearer!\n\nOn the choice of $k$ — we agree that results vary significantly between $k = 50$ and $k = 100$. To us, this reflects a general instability in contrastive baselines. To construct these sets, we sorted the error scores of the 3000 training samples and selected the top-k and bottom-k examples. We’ll add these details to the manuscript as well!\n\n**3) Theoretical claim derivation.**  We acknowledge that there is indeed a selection bias in our original derivation, since the same calibration dataset was used both to construct the confidence intervals and to select the best-performing $\\alpha$. We have now addressed this issue by adding a Bonferroni correction to the confidence bound. As a result, the reported confidence levels have been adjusted: the results previously shown at 99\\% confidence are now updated to 90\\%. Full details are provided in our response to Reviewer 7dxY. We also outline a less conservative alternative and will clarify in the next paper version that our updated method has formal guarantees under the i.i.d. assumption.\n\n**4) SPI aggregration.** We appreciate this observation. Figure 4 was intended to offer a practitioner-oriented overview (for a quick comparison across settings to help identify overall trends) and Table 1 to provide complete details on model- and dataset-specific effects. As we see it, these provide _complementary perspectives_ which are helpful to the reader in distinct ways. We now emphasise this dual purpose more clearly in the manuscript and explicitly caution readers about over-interpreting the aggregated view.\n\n**5) Personalised steering citation.** Thank you for pointing us to this interesting read! We find the work highly relevant as a steering reference and have thus cited it in our paper (+ added a discussion in Appendix A.1). This work is different from ours in several ways, most notably, in the specific problem it is targeting — where they don’t directly solve for steering strength ($\\lambda$) (but find it via hyperparameter sweeps, see Table 5 on p.8). This contrasts with MERA, which gives the solution in a closed form.\n\n**6) Steerability and MMLU.** What MMLU can/not teach us is a very fascinating comment! We refer to answer (1) in Reviewer MXKB for a discussion on this topic.\n\nNaturally, linear steering has its limitations. In this paper, we suggest possible extensions in Appendix A (Non-linear Case). A simpler alternative, however, is to use a first-order approximation of the non-linear model. This approach would essentially replace the fixed linear weight used across all instances with the gradient of the non-linear function for each specific input.\n\n**7) Improved writing.** Thank you for taking the time to write out the example where our writing could be improved! We’re revising Sections 3.2 and 3.3 and also the rest of the paper for clarity.\n\n[2] https://openreview.net/pdf?id=HuNoNfiQqH\n\n[3] https://arxiv.org/pdf/2312.06681\n\n[4] https://arxiv.org/pdf/2310.06824v3\n\n[5] https://arxiv.org/pdf/2402.14433", "claims_and_evidence": "The claims are largely supported by the given evidence. The most informative artifact is Table 1, which shows performance of all methods by both LLM and dataset. The claims are quite straightforward, clear & verifiable by looking at the metrics reported.", "methods_and_evaluation_criteria": "Some issues:\n- the linear probe to estimate error from activations has as its targets the error **probability**, a quantity in the range $[0, 1]$ with quite nonlinear behavior (going from 0.90 to 0.95 reflects a much more significant change in model internals than from e.g. 0.45 to 0.5). The regression loss is mean squared error. This doesn't quite typecheck: it is advisable to use the pre-softmax logits as the targets of regression instead. These quantities are \"linear-ish\" functions of internal activations with unbounded range where relative changes at different levels are more comparable. \n- I am confused by the description of the baseline BASE-$\\mu_k$.\n\t- Why do we use for this baseline the layer \"identified as most effective by a probe\"? Shouldn't we use the layer in which this baseline itself is most effective, regardless of what other methods might tell us? It feels like mixing multiple methods to bias the baseline instead of just getting the true performance we can squeeze from the baseline (of course, these might happen to be the same. But this is a methodological issue).\n\t- Second, it is unclear how the choice of $k$ for the number of contrast pairs to use was made. This is important as there are cases in Table 1 where 50 vs 100 leads to dramatic differences. I get that we want extreme correct/incorrect examples to get a contrastive direction here, but still", "theoretical_claims": "The derivation of the correction term $\\sqrt{\\log(2/\\delta) / (2N)}$ for the calibration threshold (3.2. Calibrating for Safety) is wrong. This is because in the sweep over values of $\\alpha\\in(0,1)$, we use the same random sample $D_{cal}$ multiple times. We should either sample a new i.i.d. calibration dataset for each value of $\\alpha$ we try, or account for looking at the same data multiple times, which is easiest via a union bound. As a result, a reported level of confidence, e.g. 95%, should be treated as a lower level of confidence; with 10 values of $\\alpha$, it could be as low as $100 - (10*5) = 50$ percent via a union bound.", "experimental_designs_or_analyses": "- The designs are clear and straightforward. \n- The plots in Figure 4 combine across datasets and/or models in a way quite prone to noisy results and unclear conclusions. Table 1 shows significant variation across these conditions. E.g., MMLU barely shows any improvement at all, while the SMS SPAM dataset shows huge improvement. This is further complicated by the fact that the metric SPI being averaged is also difficult to interpret in the absence of the accuracy of a given model on a given dataset. Averaging these wildly different values likely reduces these \"aggregates\" to metrics dominated by noise and/or the conditions exhibiting the strongest effects.", "relation_to_broader_scientific_literature": "I think the paper did a good job at summarizing the state of steering and situating the findings within it.", "essential_references_not_discussed": "Given that framing steering as an optimization problem is central to the message of this paper, it would benefit from a brief comparison with the below paper which takes a very different optimization approach:\n\nCao, Y., Zhang, T., Cao, B., Yin, Z., Lin, L., Ma, F. and Chen, J., 2024. Personalized steering of large language models: Versatile steering vectors through bi-directional preference optimization. _Advances in Neural Information Processing Systems_, _37_, pp.49519-49551.", "other_strengths_and_weaknesses": "Strengths:\n- I think that framing steering as an optimization problem is a great way to move the fields towards more principled foundations, and to be clear and precise about what we are trying to achieve and why. \nWeaknesses:\n- While the method is mostly agnostic to the steering target, the motivation for the particular choice of steering objective is quite questionable. Why would we hope that steering - a blunt and extremely low-expressiveness instrument - would be able to make a language model \"smarter\"? In a strong sense, steering can only \"work with what is already there\", surfacing and amplifying existing representations. Intuitively, the only way for this to work is if the model has a **systematic** failure mode on some dataset, and furthermore, this systematicity is somehow represented internally in a crisp way. For instance, consider some previous work cited below that showed that you can do steering interventions on an LLM to make it more truthful on the TruthfulQA dataset. This dataset contains many questions that have common misconceptions associated with them. It makes sense that an LLM would represent internally both the correct answer (which is also consistently represented in the pretraining data), as well as the widely repeated incorrect one (being a next-token predictor). Thus it makes sense that we can steer the model towards saying the less common answer. However, for a dataset like MMLU, it would be extremely surprising if we can get strong gains from just steering. This begs the question: what do steering experiments on MMLU really teach us?\n\n\n\nLi, K., Patel, O., Viégas, F., Pfister, H. and Wattenberg, M., 2023. Inference-time intervention: Eliciting truthful answers from a language model. _Advances in Neural Information Processing Systems_, _36_, pp.41451-41530.", "other_comments_or_suggestions": "- writing is not very clear in 3.2, 3.3 - there are many questions left, such as:\n\t- what is meant by \"This direction is then scaled using the closed-form solution at both the token and layer levels\"?", "questions_for_authors": "N/A", "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": "x75sQfo4vY", "reviewer": "Reviewer_u9yC", "summary": "The authors a new steering technique (MERA). MERA formulates steering as an error reduction problem. It first trains a linear probe to determine the linear direction which is most effective for reducing the error. It then adaptively selects a steering multiplier alpha based on how far the prediction is from the desired threshold. \n\nUnlike previous methods, which use a global fixed alpha, MERA chooses alpha adaptively on a sample-wise and token-wise basis. Compared to previous work, MERA solves the problem of under-steering or over-steering specific examples. As a result, if the prediction was already correct, MERA avoids doing steering. \n\nThe authors compare to prior work (contrastive activation addition and probe-based steering). They also ablate different parts of their methodology (MERA baselines). They evaluate on four different binary tasks, and claim MERA generally outperforms baselines.\n\n## Update after rebuttal\n\nThe authors have improved the paper substantially with additional experiments, as well as improved the quality of writing. I have updated my score to a 4.", "questions": "", "limitations": "", "rating": 4, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for the very detail-oriented and helpful review! We’re excited that you believe our work has benefits for transfer learning and personalisation and that our mathematical framework may become a building block in future work. We have addressed all of your points below:\n\n**1) Evidence for over-/under- steering.** We appreciate the suggestion — thank you for the suggestion—visualising activation space geometry (as in [4, 6]) can indeed help interpretation. However, instead of using UMAP, we now provide a more direct analysis of over- and under-steering effects by reporting transition counts on a sample-by-sample basis: how many examples move from incorrect to correct (0→1), correct to incorrect (1→0), or remain incorrect (0→0) or correct (1→1). This analysis will be included in the Appendix together with the SPI results and referenced in the main manuscript.\n\n**2) Baseline layer sweep.** Please see the answer (2) in Reviewer H7hE.\n\n**3) Evaluation with SPI.** We identified the need to define a new metric (SPI) since we ourselves couldn’t find a suitable metric that not only expresses improvement but critically, also _degradation_ in a bounded, interpretable way. Existing metrics (e.g. from OpenAI [7]) only track positive gains. By normalising relative to performing ceiling (or floor), the reader can get a sense of how _good_ the steering method is compared to how its best or worst case. How much (in percentage %) does steering improve or degrade LM performance? If SPI=1, steering makes the LM a perfect classifier. If SPI=-1, steering made the LM incorrect on all test samples. SPI is easy to interpret and particularly helpful when comparing LMs side-by-side (which often differ vastly in initial unsteered performance!). We’ll make sure to add an expanded, more clear motivation of the metric in the paper.\n\n**4) Caveats on scope.** Totally fair — our experimental scope includes language models going up to 3B and datasets of multi-choice. Given our compute constraints, we prioritised coverage across model types (base vs. instruction-tuned, and three distinct families), and chose supervised tasks to allow controlled evaluation where error can be perfectly recovered at distinct token positions (and not approximated e.g., using external oracle LMs). We'll emphasise our scope better in Section 7.\n\n**5) Clarifying $\\delta$.** In our method, $\\delta$ is user-defined and sets the confidence level for steering. For instance, setting $\\delta$ = 0.05 corresponds to a 95% confidence threshold: steering is applied only when we're statistically confident that it will improve performance. To make room for new clarifications from this rebuttal, we’ve decided to remove this section in the revised manuscript! Thank you again!\n\n**6) LMs error proneness.** Thank you for flagging this — we’ve adjusted the wording to “[can be] frustratingly…” instead of “[are] frustratingly…” to better reflect variability. As shown in Table 4 (Appendix), even capable base/ IT models can sometimes yield low accuracy (e.g., 5.6%) and high error rates such as 0.89) on certain tasks.\n\n**7) Clarifying generalisability.** While we focus on classification tasks for clarity and control, MERA is a general framework. It only requires a real-valued or binary signal to train the probe — so it can, in principle, be applied to other supervision types like truthfulness, toxicity, or helpfulness! Our optimisation and calibration steps are agnostic to task type and independent of model size. To apply MERA to free-form generation, each output should be paired with a target label. This can be done, for instance, using external oracles or LM-based rating systems. We’ll clarify this in Section 7 to better highlight MERA’s broader applicability.\n\n**8) Formatting.** We have revised Figure 3 for improved clarity! We have also streamlined the writing and notation in Sections 2 and 3 to make the mathematical content accessible.\n\n**9) Questions.** a) We have not yet evaluated any _larger_ models than 3 billion parameters, but are planning to do that with access to more compute. b) Yes — in all our experiments, the steering methods are evaluated in two complementary modes: \"last\" and \"exact\". (i) In \"last\", we evaluate the model’s logits at the final prompt token. (ii) In \"exact\", we check whether the model generates the correct answer in its free-form output… where the second “exact” mode accommodates the open-ended settings! c) Fixed-strength baselines apply the same intervention regardless of the model’s current activation state, making over- or under-steering inevitable by design. Empirically, we observed this in two ways: (i) that baselines often output negative SPIs (i.e., steering inadvertently degrades the model), and (ii) instance-level transitions where steering flips correct predictions to incorrect ones. We’ll now include the transition analysis in the paper!\n\n[6] https://arxiv.org/pdf/2312.01037\n\n[7] https://openai.com/index/weak-to-strong-generalization/", "claims_and_evidence": "The authors claim that existing methods may 'over-steer' or 'under-steer', and use this as a motivating factor for MERA. It is not clear to what extent this happens with existing methods. To demonstrate this more clearly, the authors should consider doing UMAP visualizations of positive and negative activations before and after steering. \n\nThe authors compare to previous methods like CAA. However, CAA requires a hyperparameter sweep to determine the optimal layer for steering. It is also apparent that the authors did perform this layer sweep for MERA and related baselines. Hence I am concerned that the baseline is weak. I think the authors should publish their layer sweep curves for CAA. \n\nThe authors base all their evaluation on SPI. It is difficult to understand what this metric measures and I would appreciate a more in-depth explanation with figures. I would also appreciate an explanation of why other, simpler, metrics are flawed.  \n\nThe authors also claim that MERA outperforms baselines. I agree with this, but would add some caveats - the models considered are mostly quite small and the tasks considered seem relatively simple. \n\nThe authors claim MERA can trade off safety and efficiency (fig 5). I did not understand this; what is delta and where did it come from? Why is (1-delta) interpreted as confidence? This claim could be explained much better. \n\nThe authors mention in Discussion that \"LMs are frustratingly error prone\". It is unclear what evidence was provided to support this claim - did the authors evaluate the models with no steering on the tasks provided?", "methods_and_evaluation_criteria": "The proposed steering method makes sense. The evaluation benchmarks and metrics also broadly make sense.", "theoretical_claims": "The authors claim their steering method precisely solves the error reduction problem. I did not rigorously check the proof, but the broad argument makes sense.", "experimental_designs_or_analyses": "Yes, I checked the experimental design and analysis. Please refer to 'claims and evidence' above.", "relation_to_broader_scientific_literature": "Better methods for steering are valuable as they facilitate few-shot adaptation; this has benefits for transfer learning and personalization. The method seems directly applicable to small LLMs run on local, consumer-grade hardware for specific tasks. More generally, the mathematical formulation provided may become a building block in future work.", "essential_references_not_discussed": "Not as far as I am aware.", "other_strengths_and_weaknesses": "It is currently unclear to what extent the authors' findings generalise beyond the setting considered in this paper. Currently, the authors primarily consider rather small LLMs and rather simple classification tasks. Conceptually, the method seems hard to generalise to free-form generation, since it involves training linear probes.", "other_comments_or_suggestions": "I think Fig 3 (overview of MERA) should be prominently displayed on page 2. \n\nThere are many mathematical quantities defined throughout the paper. It would help to have a summary table of definitions and interpretations (preferably co-located with Fig 3). \n\nGenerally the writing contains many dense mathematical equations. It would help the reader to unpack these equations and make them easier to understand. Plausibly, it is not important to have these equations in the main paper at all - the interpretations seem more important.", "questions_for_authors": "Did you do any experiments on larger models? \nDid you try any free-form generations? Do the answers make sense when you do that? \nHow did you convince yourself that current methods 'over-steer' or 'under-steer'?", "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": "3OyAmF6VU1", "reviewer": "Reviewer_MXKB", "summary": "This paper introduces Mechanistic Error Reduction with Abstention (MERA), a framework for conditional activation LM activation steering that addresses a fundamental challenge in the steering literature: that interventions can often hurt overall performance and are often applied unnecessarily. Unlike traditional steering methods that apply fixed intervention strengths, MERA trains linear error estimators to predict model errors from activations and makes calibrated steering decisions - intervening only when the predicted error exceeds a threshold and with strength proportional to the estimated error magnitude. \n\nThe work expands upon existing steering literature by focusing on continuous error mitigation for improving classification performance rather than binary alignment goals like reducing toxicity prevalent in the steering literature. The authors include experiments with multiple classification tasks and compare against popular baseline methods.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for all these important remarks. We’re encouraged that you found our work a timely and relevant contribution to the steering literature and that our focus on steering for error reduction is a differentiator/ strength! We’ve addressed all of your remarks below. Please let us know of any remaining questions.\n\n**1) Inconsistent gains.** We also note that MMLU-HS is more difficult to steer than the other tasks evaluated (except Llama-IT!). This corroborates [3] + aligns with a broader limitation shared by all additive linear steering methods — assuming that the activations and the target quantity (here, the model error) are linearly related. One of MERA’s key contributions is to explicitly detect and gracefully handle these “unsteerable” instance cases or datasets. Our selective steering mechanism (see Eq. 7) and then also the abstention criterion (see Sec. 3.2), ensure that we intervene only when confident (which is controlled by the parameter $\\delta$). Rather than steering on all inputs and datasets, MERA steers conditionally. \n\nOn reflection, we see that attributing MMLU's limited steerability only to class cardinality is premature. Other confounding factors such as label ambiguity, semantic class overlap, or general task complexity may be equally or more relevant. It may be that steering toward correct answers might be easier when classes lie along a single semantic axis (e.g., yes/no, positive/negative) than in a general MCQA format. This needs to be empirically verified — characterising steering techniques’ limits wrt distinct dataset properties deserves careful consideration and is an exciting direction for future work (see e.g., [1]). We've now removed the prior formulation citing cardinality as the primary cause for MMLU-HS’s limited steerability. We appreciate your attention to this detail and the opportunity to improve our paper in this regard!\n\n**2) MERA may still be expensive.** You're right that MERA introduces its own components, such as probe training and calibration. However, these steps are principled and crucially, MERA avoids per-model*, per-layer, per-token and per-multiplier hyperparameter sweeps, which is the common sweep strategy in activation steering**. This creates a huge search space and brings on huge computational costs, typically forcing the practitioner to prioritise one hyperparameter over the other (we refer to Appendix A.1 for a discussion, which we’re also currently expanding). MERA replaces this process with a search of ~10 $\\alpha$ values per task (dataset and model combination). This seriously reduces computational costs and as we see it, establishes MERA as a more efficient method in comparison.\n\n*Even with significant compute, the best outcome of steering papers is often model-specific advice like “steer on layer 13 for Llama-7B” which may not generalise well.\n\n**An Anthropic blog post [9] summarises current steering practice well: \"For all evaluations, we varied the 'steering factor' between -20 and 20. This decision was arbitrary.\" \n\n**3) Benchmarks.** We used the MMLU-HS subset simply because the questions would be consistent in difficulty and thus make per-sample comparisons cleaner. Practically, this subset also matched the sizes of the other datasets in the paper. But we agree that it would be interesting to evaluate MERA on more difficult subsets of MMLU. Consequently, we're currently running the MMLU \"professional\" subset as well.\n\n**4) No steering results in main paper.** As steering is a post-training intervention, we found it more important to focus on reporting the _relative_ steering performance in the main manuscript (over the absolute results) but we appreciate that absolute metrics provide complementary information that can be helpful to understand true steering effects! In Table 4 in the Appendix we included all the unsteered accuracies for each model and dataset combination (from which steering gains could be indirectly judged) but to make it simpler for the reader, we’ll complement this table with an additional table containing steered accuracies as well as the raw deltas. We will discuss these results in the main manuscript as well. Also, to understand why a bespoke metric was introduced, see answer (3) of Reviewer u9yC.\n\n**5) Code.**  Please see answer (3) of Reviewer 7dxY.\n\n**6) Broken citation.** Line 671 is fixed.\n\n**7) Difference to CAST.** Thank you for sharing this relevant work! We have read the paper (and cite it in Appendix A.1). Our method differs from CAST in several ways (i) conditioning logic: MERA conditions on predicted error and CAST on cosine similarity between “condition vectors” and the model’s activations exceeding $\\theta$, (ii) steering direction: MERA learns probe weights per layer and CAST uses PCA on contrastive pairs, with multiple directions, (iii) strength selection: MERA solves for $\\lambda^{\\star}$ with closed form and CAST uses a grid search.\n\n[8] https://www.anthropic.com/research/evaluating-feature-steering", "claims_and_evidence": "This work claims that MERA is an improvement over baseline steering techniques. While MERA does seem to generally outperform baseline steering techniques, this claim can benefit from additional clarification.\n\n**Inconsistent Gains**: Line 361 notes that MMLU-HS does not meaningfully benefit from MERA. The authors note that the increased class cardinality over the other binary classification tasks may make it an especially difficult setting to steer. That MERA struggles to generalize beyond binary classification tasks suggests that the technique may suffer from challenges in generalization faced by baseline techniques (line 81).\n\n**MERA May Still Be Expensive**: The paper implies that MERA is more practical than baseline techniques since baselines often require expensive hyperparameter searches (Lines 199 & 416). However, MERA's multi-step approach, including training an auxiliary model as well as searching for optimal hyperparameters (Line 300), suggests that MERA is not an obvious efficiency improvement over baseline techniques when it comes to hyperparameter optimization.", "methods_and_evaluation_criteria": "**Benchmarks**: The studied benchmarks overall make sense for studying simple classification tasks. However, it is unclear why only the High School splits of MMLU were included. Including all MMLU splits would give readers a sense as to how well MERA generalizes to more difficult topics.\n\n**No Steering Results in Main Paper**: The main paper does not include the absolute baseline results. The main results instead include a bespoke metric with relative improvements in performance. While this bespoke metric can tell readers whether accuracy improves or regresses, it is unclear to what absolute degree MERA improves benchmark performance.", "theoretical_claims": "NA", "experimental_designs_or_analyses": "See previous section", "relation_to_broader_scientific_literature": "Activation steering has emerged as an alternative method to prompting for dynamically controlling LM behavior at inference time. While great progress has been made in eliciting behavior of interest via steering, adverse effects on overall performance remain one of the primary open problems in the field. This paper introduces a conditional steering technique for sidestepping performance issues by estimating the LM's error ahead of time and only steering if the situation calls for it. This is a timely and relevant contribution to the activation steering literature.nd only steering if the situation calls for it. This is a timely and relevant contribution to the activaiton steering literature.", "essential_references_not_discussed": "There are no essential references which wouldn't be considered concurrent work as far as I can tell.", "other_strengths_and_weaknesses": "Safety-related behavior is a common focus of the steering literature. This paper focuses on steering for error reduction on classification tasks, which is a differentiator and a strength. The paper also raises the interesting point that this setting, where there is a verifiable correct answer, is a practical test-bed for steering techniques.", "other_comments_or_suggestions": "The citation on line 671 appears broken.", "questions_for_authors": "Can the authors please clarify how their approach to conditional steering differs and or improves upon [1]?\n\nLee, B.W., Padhi, I., Ramamurthy, K.N., Miehling, E., Dognin, P.L., Nagireddy, M., & Dhurandhar, A. (2024). Programming Refusal with Conditional Activation Steering. ArXiv, abs/2409.05907.", "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:

Meta-review: This work presents a new framework for activation steering with the objective of reducing model errors. Unlike other methods, the proposed solution is able to automatically decide when to intervene and with which strength. By doing so the method prevents under- or oversteering. Specifically this method trains linear regression estimators of the model error from activations and intervenes only when the predicted error exceeds a threshold and with a strength that is proportional to the predicted error. The empirical validation is focused on model of size 1B to 3B and to multiple choice answers (2 to 4 answers). 

The problem of under- and oversteering is relevant and all reviewers recognize the importance of working on this aspect as well as the empirical evidence shown in the reported results.

An incorrect derivation of the term for the calibration in 3.2 was highlighted by one reviewer and the authors addressed this issue recognizing the mistake and correcting the confidence bound by adding Bonferroni correction term.  

Multiple reviewers mentioned that the baselines could have been stronger by performing a sweep on the layer they intervene on (I believe this would have been closer to what the authors do for their own method, i.e., train 5 models for each layer and use the one with the smaller RMSE). 

The biggest concerns I have are related to the lack of evidence that the method does not degrade general utility, and the lack of discussion on the additional latency at inference time that this method implies.   All metrics reported are only for the specific task on which the method is trained to reduce the error. Typically in the literature one would assess the improvement on a specific task, while monitoring the degradation of the overall utility (e.g., by measuring overall MMLU and Perplexity, for example see Section 7 of https://arxiv.org/pdf/2312.06681). 

 As for the latency issue, this method, unlike most steering mechanisms, introduces potentially non-trivial additional inference cost.

Given the overall positive reviews and the interest in this field I would accept this work but expect the authors to provide the following for the camera ready:
1. Clearly state that the model after steering is meant to be used in specialized contexts but might loose general abilities OR
2. Provide experiments about generic model abilities before and after steering (e.g., MMLU).
3. Additionally, provide an analysis of the additional inference time required when steering is employed.
Decision: Accept (poster)