The  Price of Amortized inference in Sparse Autoencoders
Authors: Wenjie Sun
Di Wang
Lijie Hu
Venue: ICLR 2026 Poster (2026)
Keywords: Mechanistic Interpretability
Polysemanticity
Sparse Autoencoders
Amortization Inference
Primary area: interpretability and explainable AI
TL;DR: Amortized encoding's global optimality conflicts with monosemantic instance-level optimality. We advocate reducing investment in purely amortization-based methods.

Abstract: Polysemy has long been a major challenge in Mechanistic Interpretability (MI), with Sparse Autoencoders (SAEs) emerging as a promising solution. SAEs employ a shared encoder to map inputs to sparse codes, thereby amortizing inference costs across all instances. However, this parameter-sharing paradigm inherently conflicts with the MI community’s emphasis on instance-level optimality, including the consistency and stitchability of monosemantic features. We first reveal the trade-off relationships among various pathological phenomena, including feature absorption, feature splitting, dead latents, and dense latents under global reconstruction-sparsity constraints from the perspective of training dynamics, finding that increased sparsity typically exacerbates multiple pathological phenomena, and attribute this trade-off relationship to amortized inference. By reducing reliance on amortized inference through the introduction of semi-amortized and non-amortized approaches, we observed that various pathological indicators were significantly mitigated, thereby validating our hypothesis. As the first step in this direction, we propose Local Amortized SAE (LocA-SAE), a method that groups polysemantically close latents based on the angular variance. This method is designed to balance the computational cost
of per-sample optimization with the limitations of amortized inference. Our work provides insights for understanding SAEs and advocates for a paradigm shift in future research on polysemy disentanglement. The code is available \url{https://github.com/wenjie1835/Local_Amotized_SAEs}.

Published as a conference paper at ICLR 2026
THE PRICE OF AMORTIZED INFERENCE IN SPARSE AUTOENCODERS
Wenjie Sun', Di Wang", Lijie Hu
Moohaeed bin Zayed University of Artificial Intelligence (MBZUAI) "King Abdullah University of Science and Technology (KAUST) (wenjie. sun, lijie. hu (mmbzuua awaaaaa.cc..... ac.ae, di. edu.a..ttedu.....
ABSTRACT
Polysemy has long been major challenge in Mechanistic Interpretability (MI, with Sparse Autoencoders (SAEs) emerging as a promising solution. SAEs em- ploy shared encoder map inputs to sparse codes, thereby amortizing infer- ence costs across all instances. However, this parameter-sharing paradigm in- herently conflicts with the MI community's 's emphasis on instance-level optimal- ity, including the consistency and stitchability of monosemantic features. We first reveal the trade-off relationships among various pathological phenomena, including feature absorption, feature splitting, dead latents, and dense latents under global reconstruction-spaaitty constraints from the perspective training dynamics, finding that increased sparsity typically exacerbates multiple patho- logical phenomena, and attribute this trade-off relationship to amortized infer- ence. By reducing reliance on amortized inference through the introduction of semi-amortized and non-amortized approaches, we observed that various patho- logical indicators esis. As the first step in this direction, we propose Local Amortized SAE (LocA-SAE), method that groups polysemantically close latents based on the angular variance. This method is designed to balance the computational cost of per-sample optimization with the limitations of amortized inference. Our work provides insights for understanding SAEs and advocates for paradigm shift in future research on polysemy disentanglement. The code is available https:/ /ttpbbbggttub...// com hwomm//ejiieeeee 835/Loca A
significantly mitigated, thereby validating hypoth-
Amoti izd SAEs
INTRODUCTION
Mechanistic Interpretability (MI) has emerged critical subfield in artificial intelligence, aiming to open the 'black box' through reverse-engineering the internal computational processes of neural networks understand how models process information and make decisions (Bereska & Gavves 2024). Unlike traditional black-box analysis, MI focuses on the specific mechanisms inside models, such as the roles of attention heads or activation patterns. However, the polysemy phenomenon presents challenges in understanding the mechanisms of components (Saphra & Wiegreffe 2024). This manifests itself as single neuron activating for multiple unrelated concepts, making hard to attribute the neurons precisely (Bricken et al. 2023).
To tackle this challenge, researchers have introduced Sparse Autoencoders (SAEs), a tool to decom- pose activation vectors, aiming to extract complete set of fundamental units that faithfully represent independent concepts, known as monosemantic features (Cunningham et al. 2023 Templeton et al.) 2024). As neural network implementation of sparse dictionary learning, unlike traditional sparse coding, which solves a regularized iterative optimization problem instance-wise (Fel et al. 2025] Tibshirani 2013), SAEs employ encoder to parameterize inference network. This network leamss a deterministic mapping function from input data to sparse codes through global training, thereby amortizing the optimization cost across all samples, process known amortized infer-
*Correspondence Lijie Hu (Email Address: hum..hummbzua ac.ae)

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ence (O'Neill et al. 2024). This approach pursues global optimum by end-to-end minimizing reconstruction error and sparsity penalty (Kissane et al. 2024).
Although efficient, amortized inference often sacrifices instance-level optimality for global con- straints (O'Neill et al. 2024; Costa et al., 2025). In contrast, the monosemantic features desired by the MI community emphasize "instance- optimality." where each sparse code robustly and ac- curately reflects a single concept (Bricken et al. 2023), which is similar to the instance- -wis optimal solutions obtained through sample-by-sample iterative optimization in classical sparse coding like matching pursuit. The performance gap between the sparse codes derived from amortized inference- based SAEs and the ideal sparse codes expected for each sample is referred as the amortization gap (O Neilll et al.) 20044 'Song et al., (2025). This gap represents key price of amortized inference, as it introduces systematic suboptimality that conflicts with the instance- wise precision required for monosemantic features.
To understand the price of amortized inference, we first examine how the amortization gap manifests in various pathological phenomena observed in SAEs. These issues include feature absorption, whereby the shared encoder represents multiple concepts with a single latent to meet global spar- sity budget, and feature splitting, where complex concept is approximated by multiple redundant latents to minimize average reconstruction error (Chanin et al. 2024). Another related issue is the prevalence of dense latents, which indicates overfitting to figg-ffreuency activation patterns the expense of per-sample sparsity (Bussmann et al., 2024a). The last phenomenon is feature incon- sistency. It is the representation of a single concept by different latents under minor distribution shifts, which stems from the encoder's failure to find a stable optimum, instead converging to diver- gent local minima (Song et al. 2025 Leask al., 2025). Collectively, these pathologies highlight core trade-off: amortized inference achieves global efficiency by sacrificing the per-sample fidelity essential for faithful mechanistic interpretation.
Given the problems introduced by amortized inference in the task of disentangling polysemantic features, this paper argues against over-investment in fully-amortized paradigms, such as improve- ments to activation functions and gating mechanisms. Accordingly, we propose locally amortized SAE variant, aimed at finding a trade-off between the computational cost of per-sample optimization and amortized inference. Our contributions can be summarized as follows.
1. We argue that the inherent misalignment between the global optimality emphasized by amortized enference-basee SAEs and the instance-level optimality required for monose- mantic features indirectly leads to numerous pathological phenomena in SAES. From the perspective of training dynamics, we reveal that pursuing the global reconstruction-sparriyy Pareto frontier does not yield improvements in monosemanticity. This issue stems from an architectural trade-off induced by the parameter sharing of amortized inference under global sparsity/reconntrrction constraints. Specifically, this tradc-off means that increas- ing the sparsity penalty not only fails to improve monosemanticity but instead exacerbates pathological phenomena such as dead latents, feature splitting, and feature absorption.
2. To verify the relationship between amortized inference and these pathological phenomena, we introduce amortized and non-amortized methods as intervention and ablation ex- periments, respectively, to reduce reliance on amortized inference. Results show that these alternative approaches significantly reduce reconstruction errors and alleviate the dead la- tent problem. Furthermore, the extracted features exhibit superior performance in targeted concept removal tasks and enhanced controllability in model intervention tasks.
3. As the first step in this direction, we introduce Local Amortized Sparse Autoencoders (LocA-SAE). This method groups latent variables based on their angular variance and assigns an independent encoder and sparsity penalty to each group. This design aims to mitigate the unreasonable trade-offs caused by varying degrees of latent polysemanticity, while balancing the computational cost of instance- optimization against the limita- tions of amortized inference. Results indicate that LocA-SAE alleviates multiple patholog- ical phenomena and even eradicates dead latents entirely, with only marginal sacrifice in reconstruction performance.
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RELATED WORK
Sparse Autoencoders. SAEs (Bricken et al., 2023), as a neural network implementation of dic- tionary learning, aim to learn sparse representations of input data, particularly useful in MI for
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decomposing polysemantic activations in Large language models (LLMs) Yao et al. (2025) Yang et al. (2024). The core principle involves reconstructing imput activations x E R" using a learned overcomplete dictionary D E Rd and sparse latent codes E RT. where the encoder maps to z and the decoder reconstructs x = Dz, minimizing reconstruction loss plus sparsity penalties to extract monosemantic features that resolve superposition (Elhage al. (022). SAEs' evolution starts with vanilla SAEs, employing L1 penalties but facing dead features and shrinkage bias (Cun-) ningham al. 2023). To mitigate these, TopK SAEs enforce hard sparsity via top-k pre-activations, reducing dead latents and enhancing scaling in models like GPT-4 (Gao et al. 2024). Building on this, BatchTopK SAEs relax constraints batch- wise, alleviating sparsity variance and boosting sta- bility in high dimensions (Bussmann et al. 2024b). For shrinkage, Gated SAEs decouple detection and magnitude estimation via dual paths, yielding gains across hyperparameters' in 7B models (Ra-) jamanoharan et al. 2024a). Further refining To sparsity, JumpRel.U SAFs use discontinuous activa- tions and straight- throughh estimators, achieving top fidelity on Gemma 2 9B (Rajamanoharan et al.) 2024b). Addressing feature splitting. Matryoshka SAEs train nested increasing width SAES for hi- erarchical features and multi-resolltion analysis (Bussmann et al. (024a). Additionally, AdaptiveK SAEs dynamically tune ls for uneven distributions; P-anneal SAES anneal penalties progressively to avoid early dead features ( (Yao & Du 2025). Recent RouteSAEs extend to multi-layers with routers integrating residual activations, capturing cross-layer features for better interpretability (Shi al.,
2025
Additional related work can be found in the Appendix. B
3
PRELIMINARIES
3.1 SPARSE CODING AND AMORTIZATION-BANL BASED SPARSE AUTOENCODERS
Sparse Coding, also known as sparse dictionary learning (Olshausen & Field 1996). aims repre- sent an input signal as a linear combination of a set of overcomplete basis vectors, while constraining the representation coefficients to be as sparse as possible. Formally, given an input vector x TR. and an overcomplete dictionary matrix D IRdc (where k >> d), sparse coding seeks the optimal sparse code z E g that satisfies:
z" arg min |X
Dzl Al|z|lo-
where || ll denotes the to pseudo-norm and À controls the sparsity strength. Since the to opti- mization NP-hard, the ε norm is often employed as a convex surrogate for the sparsity constraint in practice. Inference in this classical formulation is iterative process performed each sample, ensuring instance-specific optimality (Chen et al.) 2001 Mallat & Zhang 1993).
SAE emerges neural network implementation of this dictionary learning framework, designed to overcome the computational bottleneck of per-sample optimization. The core architecture of an SABs consists of an encoder fo and a decoder. The encoder fa is typically linear transformation followed by non-linear activation function, which maps the input to sparse latent code z = (x). The decoder then reconstructs the input using a learned dictionary matrix D Rd * Dz (Braun et al. 2024). The training objective minimizes the reconstruction error plus sparsity penalty:
L= ||x
x12 A||2|11-
(2)
Different from the traditional sparse coding schemes to solve an optimization problem for each in- stance, Crucially, SAES employ an amortized inference approach. A shared encoder network fo learns to approximate the posterior over the entire dataset. This approach amortizes the compu- tational cost of inference across the training process. Consequently, SAEs replace the iterative, sample-specific optimization of classical sparse coding with efficient, global inference via an end- to-end feedforward network, enabling scalable application large-scale scale data.
3.2 PATHOLOGICAL PHENOMENA IN SAES
The pursuit of monosemantic features through the amortized inference of SAEs often lead to several common pathological phenomena. These phenomena represent failures in the desired behavior of the learned dictionary and its latents. We briefly define these pathologies and the metrics used to quantify them, which are crucial for interpreting our subsequent analysis.
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Dead Latents. A significant portion of latent units may rarely never activate, indicating failure to utilize the full capacity of the overcomplete dictionary and reducing the effective model size (Gao et al. 2024).
Dense Latents. Contrary to Dead Latents, some latents activate excessively frequently across inputs.
These latents often correspond common, non-specific directions polysemantic combinations, violating the goal of sparsity and monosemanticity (Sun et al. 2025).
Feature Splitting. A single coherent concept may be represented by the activation of multiple similar or redundant features across different contexts. This fragmentation obscures the intended one-to-one mapping between features and concepts, reducing interpretability (Chanin al., al.] (024)) Feature A Absorption. A rarer concept can be "absorbed" into more frequent one, whereby the encoder opts to represent both using same dominant latent. This results the suppression of rarer concept's unique latent and compromises feature completeness (Chanin et al. 2024).
4 THE MISALIGNMENT OF AMORTIZED SAES FOR POLYSEMY DISENTANGLEMENT
In this section, we argue from two perspectives about the misalignment of amortized inference and the polysemy problem. The first is mismatch in evaluation metrics: the global reconstruction- sparsity trade-off emphasized by amortized inference overlooks the instance-level trade-off high- lighted by monosemanticity and may obscure certain pathological phenomena. The second is that the optimization approach of amortized inference tends to preserve latent variables with high marginal contribution (activation frequency) under global reconstruction-spari// constraints, which conflicts with the instance-level semantic purity emphasized by monosemanticity.
4.1 AMORTIZATION GAP FROM THE PERSPECTIVE OF PARETO FRONTIER
The concept of the Amortization Gap is well-established in variational inference literature, referring to the systematic discrepancy between the approximate posterior learned by amortized inference network and the true posterior (Kim et al., 2018 Marino et al. 2018). SAEs, O'Neill et al. (2024) define this gap the systematic discrepancy between the latent representations predicted by a shared encoder (x) under the amortized inference framework and those obtained by instance- wise optimization.
Mathematically, for given input x, let z, = (x) be the amortized sparse code produced by the SAE encoder, and z, be the optimal sparse code obtained via per-sample optimization:
arg min ||x D21
A||2||1-
The amortization gap can be formalized as the difference in the objective function values:
(xx) (||x Dz, 112 + Al|zal11) (llx - -2 2 Al|zol111)
(4)
This gap Axx) 2 0 quantifies the suboptimality per sample, with the average gap over dataset providing global metric: A = Σ. A(x:).
Á reflects fundamental trade-off between efficiency and precision, O'Neill al. (024 proves that there is theoretical minimum from the compressed sensing theory, and attributes it to their linear- nonlinear structure. Here, we describe the A as the "distance" between the reconstraction/ppariiy Pareto frontier of SAEs (their optimal trade-off curve between reconstruction error and sparsity) and the optimal frontier defined by sparse codes from unconstrained sparse inference algorithms (e.g., sparse coding, which solves Eq. 3 per sample). Therefore, the A can serve as metric to quantify the global Pareto improvement reconstruction//saarity. This exactly the goal of improvements in most current SAE variants: to minimize reconstruction error while simultancously maximizing sparsity.
However, minimizing Á to pursue the global reconstruction-spariii Pareto frontier may incur an overlooked cost: it evaluates the trade-off at the level of the entire dataset, whereas monosemanticity emphasizes this trade-off at the instance level. Consequently, the convergence of Á does not nec- essarily imply an improvement monosemanticity and may instead mask the inherent trade-offs among pathological phenomena, thereby misleading researchers.
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4.2 THE PARADOX BETWEEN GLOBAL OPTIMALITY AND MONOSEMY
Amortization-base encoder are trained minimize an expected econstruction-sparsee tradeoff, the shared encoder is encouraged to learn
cross-domain reusable" directions to reduce overall error (Kim et al. 2018 Cremer et al. 2018). However, the evaluation standard for monosemantic features emphasizes per-example semantic purity, robustness, and stitchability (Kar- vonen et a 2025). This inherent tension indirectly leads to many pathological phenomena in SAEs. For instance, when the data distribution is long-tailed multimodal, minimizing expected error and preserving per-example semantic atomicity often cannot be achieved simultaneously. In such cases, the optimizer compromises by sacrificing semantic consistency and trigger completeness for some samples to favor reconstruction accuracy. This mechanism underlies phenomena such as feature splitting and feature absorption, which not only waste dictionary capacity but also reduce inter- pretability (Chanin et al. (2244).
Furthermore, if the goal to discover "canonical units," current SAEs still fail to converge a unigue and stitchable set of features. Through stitching and meta-SAE experiments, [Leask et al. (2025) demonstrated that latent variables learned by different SAEs on the same dataset do not form unified atomic set, reinforcing the conclusion that "global mean optimality * per-sample and cross- setup optimality."" Mechanistically, neural networks encode unrelated semantics in nearly orthogonal directions to accommodate more sparse features within limited dimensions, resulting in neuron-level polysemy and "space sharing." This makes the exact way in which rare concepts are absorbed or split highly sensitive to initialization and mild distribution shifts, so the resulting features are difficult to stitch across runs into a run- unn-invriaant basis. In contrast, the instance-wise optimum 2, (x) depends only on the dictionary and sparsity penalty and therefore defines more stable target. Based on such premises, a monosemantic objective that stresses instance-wise atomicity is intrinsically in tension with a global objective that optimizes average reconstruction (Elhage al. 2022).
We therefore hypothesize that this fundamental misalignment does not merely introduce a perfor- mance gap but systematically distorts the feature learning process, forcing the model into a regime of unreasonable trade-offs among several pathological phenomena. Specifically, when the data distri- bution long-taine or multimodal, minimizing expected error and preserving per-example seman- tic atomicity often cannot be achieved simultaneously. In such cases, the optimizer compromises by sacrificing semantic consistency and trigger completeness for some samples to favor reconstruction accuracy. This mechanism underlies phenomena such as feature splitting and feature absorption, which not only waste dictionary capacity but also reduce interpretability (Chanin et al. 2024). Dead latents may emerge the global constraint prunes low-frequency directions, while dense latents persist due to overfitting to common patterns, further exacerbating the misalignment.
4.3 EVIDENCE FROM TRAINING DYNAMICS
To empirically validate our hypothesis that these pathologies stem from this paradox, examine the training dynamics of SAES. By tracking the evolution of key metrics under varying sparsity constraints, aim understand the trade-offs among these phenomena, demonstrating how the global amortized objective fails to enhance monosemanticityy
Experimental Setup. We use SAEBench's 's open-source implementation, which includes both Stan- dard SAE and Top-k SAE models trained on the resid _post of the 12th layer of Gemma-2-20 over the Pile-uncopyrighted dataset (Karvonen et al. 2025). Each variant incorporates six differ- ent sparsity strengths and checkpoints from seven distinct training steps. The evaluation metrics for these pathological phenomena are detailed in Section 3.2 Notably, for the calculation of the amortization gap, the optimal sparse code 2,is obtained via 200 iterations of the ISTA (Iterative Algorithm).
Mhrinkage-Thresholdee
Evaluation Matrices. We employ suite of metrics including the Dead Rate, Dense Rate, Ab- sorption Rate, and AFI (for feature splitting), alongside standard measures like Normalized Mean Squared Error (NMSE) and the Amortization Gap (Å). The formal definitions and mathematical details of all evaluation metrics are provided in Appendix (Table. 9)
Observations. We compare the dynamic behaviors of various pathological phenomena in two vari- ants of SAEs under different sparsity levels: Standard SAE and Top-k SAE, as illustrated in Figures T and 2 detailed experimental results can be seen in the Table. 4 and in the Appendix F Our
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Figure 1: Variation of Different Pathological Phenomena Corresponding to Standard SAE at Differ- ent Sparsity Levels from the Perspective of Training Dynamics. Sparsity gradually increases from Trainer 0 to Trainer 5.
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Figure 2: Variation of Different Pathological Phenomena Corresponding to Top-k SAE Differ- ent Sparsity Levels from the Perspective of Training Dynamics. Sparsity gradually increases from Trainer to Trainer 0.
analysis reveals that the training process forces an unreasonable balancing of pathologies, driven by the conflict between shared encoder and global sparsity budget.
Sparsity exacerbates dead latent without resolving dense ones. As shown in the subfigure of NMSE and Dead Rate of Figure] T and increasing the sparsity penalty leads to steady rise in

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the NMSE and Dead Rate. This occurs because the global objective prioritizes latents with high marginal gain (activation frequency). Low-free cow-frequency latents are pruned first as sparsity costs in- crease. However, the Dense Latent Rate was only slightly mitigated. Additionally, of training steps increased, the Dead Rate and Dense Rate did not show a complementary trend. Taking Trainers 3-5 of the Top-k SAE ter the initial training phase, these two metrics even demonstrated tendency to be exacerbated simultaneously. indicating that the common, high-utility directions are preserved due the strong reconstruction constraint. This creates a difficult trade-off: increased sparsity fails to clean up overly dense latents while simultaneously killing off more niche features.
the number
example (Figures 2 Rate, Dense Rate@0.2), af-
Feature splitting and absorption emerge as compensatory mechanisms. The global cetptttruuucioosppsssssi objective often finds it advantageous to represent a concept with multiple splintered features (increasing AFI in Fig. [ or to assign the variance of rare feature to a more frequent, absorbing latent (Fig. Absorrppio Rate). For example, in the mid-to-late stages of train- ing for the Standard SAE under high sparsity, observe a significant spike in both Absorption Rate and AFI. This suggests the model is compensating for the tight sparsity budget by making representations less interpretable, not monosemantic.
The opposite trend between monosemanticity and amortization gap. Figure shows that Á decreases consistently during training for all sparsity levels. indicating that the amortized mapping learned by the encoder does lead to better global Pareto improvements. However, this trend does not correlate with improvements in monosemanticity metrics (Dead, Dense, Absorption, AF1). This demonstrates that optimizing the global amortized objective is not sufficient for learning instance- optimal, monosemantic features, and these pathological phenomena are inherent to the paradigm. also points out that the global reconstruction-sparss Pareto frontier pursued by most current SAEs variants directionally biased.
Top-K SAEs alleviate but do not eliminate the trade-off. The Top-K SAE (Fig. 2 with its hard gating mechanism, shows a drastically reduced Dense Rate and avoids the worst of the dead feature problem. However, it still exhibits a trend of increasing with increasing sparsity in Absorption and AF1 during training (Fig. AAF,, Absorption Rate). It suggests that while modifications to activation functions and gating mechanisms may alleviate specific pathological phenomena, the root conflict stemming from amortization remains unresolved.
In conclusion, the pathological phenomena are inextricably linked, they are not independent failures but interrelated symptoms of a shared encoder competing for a limited global budget. Pursuing a better global Pareto frontier reconstruction and sparsity within the amortized paradigm comes the direct expense of monosemanticity. These findings support our hypothesis that the pathologies originate from the fundamental paradox between global and instance-level optimality, providing empirical evidence for the inherent limitations of amortized inference in SAES.
5 Do PATHOLOGICAL PHENOMENA REALLY STEM FROM AMORTIZED INFERENCE?
To further verify this attribution, we conducted intervention and ablation experiments. Specifically, we explores semi-amortized and non-amortized approaches by reducing or eliminating reliance on shared encoders, aiming to demonstrate whether instance-level optimization can mitigate the ob- served pathological phenomena. Finally, we propose an intermediate approach balance computa- tional cost and amortized inference named LocA-SAE variant of SAE that groups latent variables based on angular variance and assigns each group an independent encoder for locally amortized encoding at varying sparsity levels.
5.1 EXPERIMENTAL SETUP
For this purpose, we reproduce part of the work from SAEBench (Karvonen et al. 2025) cally, we train four different SAE architectures. Standard SAE, JumpReLU SAE, Gated SAE, Top-k SAE, BatchTopK SAE and Matryoshka SAE, which use the resid_poss of the 8th layer of the Pythia- 160mmdddduedd model processed on the samooogy/pileuunooyyrii 2b, the 12th layer is used. The same resid post is also used to train LAC-SAE. Detailed config can
Specifi-
dataset, while for Gemma-2-
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be found in the Appendix H and the evaluation metrics remain consistent with 3.2 the first 10,000 tokens from the training data loaded via streaming.
5.2 METHODOLOGY
Standard SAEs force single encoder Wene to approximate instance-optimal codes for all latents simultaneously. inducing pathological trade-offs. We introduce LocA-SAE, which retains a single shared dictionary but replaces the global encoder with small set of group-war wise encoders at varying sparsity levels.
Angular variance based Latent Grouping. We group latent units based angular variance. This metric is defined as AVary = 1 - ||/5||22 l2, which quantifies the diversity of activating samples and thereby indirectly represents the polysemanticity intensity of the latent unit, where Pj denotes the mean direction of all normalized inputs that activate latent unit j. We then sort the latent units by AVar, and partition the index {1...., m] into 8 contiguous groups 91....,9c:
Architecture and Training. The architecture comprises global decoder D Raxm and discrete group encoders W Each Wile) computes pre-activations u(9) from input z, which then sparsi- fied into a group code (0) via group-specific Top-k, operation and ReLUU The budgets are con- figured as (A.,..., ks) (6, 5, 3, 3, 2, 2, 1), aimed at enforcing higher sparsity on low-variance Dz. This design preserves amortized inference efficiency while enabling heterogeneous sparsity. Training is four-stage process: pretraining global SAE; grouping latents by angular variance; initializing group encoders via weight copying; and fine-tuning all parameters under group-specific hi constraints.
groups. Global reconstruction is given by
5.3 INTERVENTION AND ABLATION
To separate the effects of amortization from architectural choices, we treat the inference method an intervention variable. We compare LocA-SAE against Fully-Amortized baselines and two "intervention" methods defined as follows:
Semi-Amortized: A balanced hybrid method that begins with the quick prediction from the fully- amortized encoder but then fine-tunes it with few steps of sample-specific optimization. Non-Amortized: A complete per-sample optimization starting from scratch, without relying on the shared encoder at all.
Given token activation IRd and dictionary D E [gdx solve the nonnegative sparse coding problem:
Implementation Details:
1 - D21 Al|2|1a, 2 z 0. (xx 2) -
(5)
The amortized encoder computes an initial code (0) max WT T x b, 0), with parameters W and b. For Top-K, we select the top-K K pre-activations before ReLU.
Semi-amortized inference refines 20) over Tsemi ISTA steps:
(t+1) max (a0) aD (Dz A1), 0).
(6)
with step size a 1/ D from power iteration.
Non-amortized inference runs Tisa ISTA steps from zero:
(I+1) max (2(0) -
ax1, 0).
For fair sparsity pattern comparison, calibrate À per method on held-out set to match the amortized baseline's activation density (e.g., Dense@0.1).
5.4
EMPIRICAL ANALYSIS
Table in Appendix F2 presents the pathological phenomenon metrics for various SAE variants under different amortization patterns, evaluated on the Pythia- 160m-deduped (layer 8) and Gemma- 2-2b (layer 12) models. Figures 3 and illustrate the variations in key metrics across these patterns
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NMSEE
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Figure 3: Pathological Phenomenon Indicators Corresponding to SAE Variants Under Different Amortization Models (Pythia- Mertiia-660m--ie 160m-deduped/ Layer8)
and variants. Overall, observe consistent trends: reducing reliance on full amortization via semi-amortized interventions, non-amortized ablations, or the proposed Loc-Amortized approaches generally alleviates multiple pathologies. Specifically, non-amortized ablations and semi-amortized interventions achieve lower NMSE and more stable sparsity control in the majority of cases. In contrary, full-amortized often exhibits higher reconstruction errors and poorer sparsity, as the shared encoder prioritizes global efficiency over instance-level optimality. This gap is evident in variants like JumpReLU and GatedSAE, where non con-amortieed ablations reduce NMSE by up to 80%. Semi- amortized interventions mitigate this partially by refining amortized initializations with per-sample optimization, while non-amortized ablations ensure fully independent solutions, albeit at increased computational cost. The Loc-Amortized pattern in LocÅ-SAE strikes a balance, alleviating numer- ous pathological phenomena of full-amortized without requiring per-sample optimization, demon- strating competitive AF1 and Absorption Rate, even eliminating dead latent completely. These results validate amortization as root cause of pathologies, demonstrating that hybrid or localized approaches can resolve trade-offs like reconstruction-sparsse ics. We additionally perform an ablation over the number of refinement steps in the semi-amortized BatchTopK SAE (Appendix D). We find that increasing the number of steps yields monotonic but quickly saturating gains in NMSE, while the pathological metrics remain essentially unchanged, in- dicating that our conclusions are robust to the specific refinement budget and that moderate number of steps already offers good accuracy-compute trade-off.
conflicts observed in training dynam-
Among the seven SAE architectures, GatedSAE consistently exhibits high dense rates and near-zero dead rates, indicating efficient feature utilization but at the expense of sparsity, which may compro- mise monosemanticity. JumpReLU and TopK, conversely, enforce stronger sparsity but suffer from elevated NMSE and absorption in full-amortized settings. BatchTopp and Matryoshka show promis- ing behaviors: BatchTopK achieves low NMSE in semi-amortized interventions and non-amortized ablations with zero dead latents, suggesting improved stability through batch-wise sparsity relax- ation. Matryoshka, designed for hicrarchical features, NMSE decreases significantly as reliance on full-amortized on diminishes. and also exhibited lower Absorption Rate and AFL. LocA-SAE, our proposed Loc-Amortized variant, outperforms many baselines by eliminating dead latents entirely while maintaining low AFI and absorption, demonstrating that group- encoders with angular variance based partitioning enable heterogeneous sparsity without sacrificing monosemanticity. As novel methodological framework, LocÅ-SAE bridges the efficiency of global amortization with the precision of instance-level optimization by grouping inputs into localized encoders, which is particularly effective in long tailed data distributions as it allows rare patterns to be captured in- dependently in dedicated sub-encoders, thereby enhancing feature monosemanticity. Compared to the full-amortized baselines. LocA-SAE completely eliminates dead latents and substantially re- duces absorption and splitting, at the cost of modest increase in NMSE. Relative to the non- amortized ISTA baseline, LocA-SAE achieves similar improvements in pathological metrics while avoiding any per-sample iterative optimization. This places LocA-SAE a favorable point of the fidelity-come doeepty- trade-off curve. These architectural comparisons reinforce that while tweaks like gating or hierarchy mitigate specific issues under full amortization, broader reductions in parame- ter sharing via semi-an aomi-amortized interventions, non non-amortieed ablations, or local amortizaaon yield consistent improvements across variants, highlighting shared encoding the primary bottleneck.
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NMSEE
Dead Rate
Dense Rate@0.1
Dense Ratego.2
0.25
0.20
66
0.55
9.3
00
090
1.0
Absorption
0.2
1.0
0.35
0:35
Figure 4: Pathological Phenomenon Indicators Corresponding to SAE Variants Under Different Amortization Models (Gemma-2-205 Layer12)
Additionally, several outliers deserve attention. For instance, Genuma-2-2b/LI2. JumpReLU, Full- Amortization shows an abnormally high Absorption; switching to Semi/Non immediately drives it to O, indicating primary-detector under-firing induced by single-step amortization. A few per-example optimization steps correct this mismatch (Fig- ALAbsorption Rate). Furthermore, GatedSAE un- der full amortization shows very high NMSE (> 1.5), suggesting issues like over-regularization or encoder underfitting, which are mitigated in the semi- and non-amortized patterns. These out- liers serve direct evidence of amortization's 's problems, highlighting the advantages of semi- and non-amortization in instance-level optimization and further confirming that amortization leads to pathologies that can be alleviated by reducing parameter sharing. However, in a few cases, the duced reliance on full amortization has also been accompanied by some negative results. This might be attributed the inherent conflict between TopK hard constraints and ISTA soft-thresholding combined with the loss of cross-sample semantic consistency resulting from the lack of global shar- ing, which subsequently triggers the absorption splitting rare features.
CONCLUSION AND DISCUSSION
Numerous recent variants of SAEs have emerged to mitigate pathological phenomena in polyseman- tic feature disentanglement, primarily targeting the reconstruction-sppaee sparrsst trade-off. However, most of them have overlooked the trade-off between monosemanticity and this acconstrccioonssaaiiii balance. In this study, we demonstrate that within amortization-basee encoding frameworks, im- provements along the aeconstruction-sparsiii Pareto Frontier not lead to better monosemantic- ity. On the contrary, it comes at the expense of dictionary capacity and monosemanticity, while also inducing several pathological phenomenon. Furthermore, our intervention and ablation studies demonstrate that reducing reliance full amortization not only consistently improves reconstruc- tion performance and mitigates the dead latent problem but also yields features that are superior in targeted concept removal tasks and offer enhanced controllability model interventions. However, since per-sample optimization exacerbates the scalability issues of SAEs, we propose LocA-SAE, method that employs local amortization by grouping latents based on their angular variance, thereby balancing the computational cost of instance- wise optimization against the limitations of full amor- tization. Experimental results show that LocA-SAE not only completely eliminates dead latents but also significantly alleviates feature splitting and feature absorption. Based on this, we contend that various pathologies observed SAEs stem not only from their unsupervised learning paradigm but also from the fully amortized inference inherent in their architecture. While modifications to gating mechanisms or activation functions may mitigate specific issues, they fail to resolve the fun- damental conflict between parameter-shane encoding and the instance-level optimality required for monosemantic features.
ACKNOWLEDGMENT
Lijie Hu and Wenjie Sun is supported by the funding BF0100 from Mohamed bin Zayed University of Artificial Intelligence (MBZUAI). Di Wang if supported in part by the funding BAS/1/1689-01-
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O1.RGC/3/112500100 FCC/1/5940-20-05 FCC/1/5940-06-02, and King Abdullah University of Science and Technology (KAUST) Center of Excellence for Generative AI, under award number 5940 and gift from Google.
ETHICS STATEMENT
This work explores theoretical and empirical limitations of amortized inference in sparse autoen- coders for mechanistic interpretability. advocating for alternative encoding paradigms. We anticipate no direct negative societal impacts from this research, as it focuses on improving the transparency and controllability of Al models. Enhanced monosemantic features could contribute to safer Al systems by facilitating better detection of biases, errors, or unintended behaviors in large language models. However, we acknowledge that advancements in interpretability tools might be dual-use; for instance, they could potentially aid in reverse- engineeing models for malicious purposes, such crafting adversarial attacks. To mitigate this, emphasize ethical deployment and encourage open discussions on responsible Al research. All experiments use publicly available, uncopyrighted datasets, and human subjects sensitive data were involved.
REPRODUCIBILITY STATEMENT
To ensure reproducibility, provide detailed descriptions of our experimental setup in Sections and 4, including hyperparameters, training procedures, and evaluation metrics. We utilize the open- source SAEBench framework for training Standard SAE and Top-k SAE variants on the 12th-layer residual post activations of Gemma-2-2B, using the Pile-uncopyrighted dataset. Checkpoints from seven training steps across six sparsity levels are analyzed. For semi-amortized and non-amortized methods, employ ISTA with 200 iterations for optimal sparse codes. Code for experiments, including custom metries (c.g.. Dead Rate, Dense Rate, Absorption Rate, and Á FF1), based on SAEBench and will be released anonymously upon submission via public repository, All results can be replicated with standard hardware (a single NVIDIA 5090D GPU for training).
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Appendices
Appendices
15
LLMS USAGE IN THE PAPER
16
Related Work
16
B. Mechanistic Interpretability and Superposition Hypothesis
16
B.2 Amortized Inference
16
Performance of Different Amortization Patterns in Downstream Tasks
17
Targeted Probe Perturbation (TPP)
17
Generative Intervention Scoring (GIS)
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Dynamies of the Semi-Amortized Pattern
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Limitations
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Experimental Results
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Experimental Results of Section 4.3
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Experimental Results of Section 5
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Experimental Details
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Experimental Details of Section
23
Configuration Information
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Evaluation Metrics
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A LLMS USAGE IN THE PAPER
LLMs were used only occasionally to help polish the writing (propose new words, grammar and spelling correction). All technical ideas, experimental designs, analyses, conclusions, writing were developed and carried out entirely by the authors. The authors have full responsibillig for the final text.
B RELATED WORK
B.1 MECHANISTIC INTERPRETABILITY AND SUPERPOSITION HYPOTHESIS
MI aims to understand how neural networks process and store information by reverse-engineering their internal computational processes (Bereska & Gavves 2024 Wang et al. 2025b Yang al.
2025a Zhang et al. (0255)) The rise of this research field marks shift from traditional behaviorist, black- box analysis methods toward an exploration of internal mechanisms akin to cognitive neuro- science (Sharkey et al.) 2025). Unlike functional explanations that focus on the overall behavior of models, MI focuses on parsing the specific computational mechanisms inside neural networks, in- cluding the specific functions of components such as attention heads, feedforward neural networks, and activation patterns (Saphra & Wiegreffe [2024; Yang et al.] 2025b; Zhang et al., 2025a Dong et al. 2025: Su et al. 2025; ZZhng al.. 2024). However, the existence of polysemantic features poses a major challenge to component attribution, where a single neuron responds to multiple unre- lated concepts simultaneously. Inspired by the linear representation hypothesis (Arora et al. (016)) the Superposition hypothesis proposes that polysemantic features are composed of linear combina- tions of multiple independent concepts (Elhage et al. (2022), thereby initiating research disentan-
gling polysemantic features based on SAEs (Bricken et al. 2023 Gao et al. 2024: Karvonen et al.,
2025
B.2 AMORTIZED INFERENCE
Amortized Inference is a method that uses a learned parameterized function to approximate the posterior distribution of latent variables (Shu et al. 2018). Its core idea is to "amortize" the compu- tational cost of inference across multiple data instances, thereby avoiding computationally expensive iterative optimization for each sample. This paradigm has become relatively mature in variational autoencoders (VAEs) (Margossian & Blei (023). However, this gain in efficiency comes at the cost of compromised representation quality, known as the amortization gap. Zhang et al. (2022a) demonstrated that amortized inference leads to degradation in approximation quality, i.c., sys- tematic discrepancy between the learned posterior distribution and the true posterior. This gap is particularly pronounced in complex models and large-scale datasets, manifesting as reduced gen- eralization ability of the learned encoder, especially when faced with out-of-distribution samples. Similarly, O Neill et al.] (2024) proved the inherent suboptimality of SAFS and demonstrated that this amortization gap stems from their nonliner encoder structure based on compressed sens- ing theory. Current methods to mitigate the amortization gap can be broadly categorized into five types: (1) Demi-amortizatiin
which starts from the encoder's 's code and applies a few per-sample op-
timization steps without abandoning end-to-end training (Kim et al. 2018 Marino et al.) (0188); (2)
Encoder-side structure, which increases expressivity to better approximate the per-sample solution map: (3) Amortized sampling, which distills MCMC into fast inference networks balance fidelity and cost (Li al. 7); (4) Regularization design, which reduces mismatch and L1-shrinkage via loss/constraint choices (Shu et al. 2018 Burda et al. 2015):: and (5) Local amortization, which shifts shared inference from the global level to sub-distribution levels to avoid global dependencies (Wu) al., 2020. Liu Liu, 2020). However, these mitigations that directly adapted SAES for poly- semy disentanglement are still limited. This stems from the fact that VAEs are primarily applied to image generation tasks, where the latent space emphasizes smoothness and continuity to ensure sam- pling quality and generalization capability, prioritizing distribution-level optimality (Zhang et al.) 20226). In contrast, the latent space of SAES serves the purpose of interpretability, emphasizing sparsity, atomicity, and discreteness, prioritizing instance-level optimality. While amortized infer- ence emphasizes global optimality, which aligns well with the distribution-level optimality needed for VAEs, but unsuitable for the instance-level optimality required by SAFs.
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SAE Variant
Encoding Pattern
ACCCrage
ACCnon sarget
Selectivity
Top-k
Fully-amortized Non-amortized
0.303
0.058
0.245
Top-k
0.531
0.047
0,484
Top-k
Semi-amortized
0.552
0.044
0,508
Gated
Fully-amortized
0.358
0.066
0.292
Gated
Non-amortizee
0,404
0.051
0.353
Gated
amni-amortized
0.422
0.048
0,374
JumpReLU
Fully-amortized
0.321
0.063
0.258
JumpReLU
Non-amortized
0.374
0.057
0.317
JumpReLU
Semi-amortizer
0.392
0.050
0.342
Standard Fully-amortized
0.283
0.071
0.212
Standard Standard
Non-amortized
0.315
0.062
0.253
remi-amortized
0.336
0.052
0.284
Table 1: Targeted Probe Perturbation (TPP) on Pythia-160M-dcdduped (layer 8, m=16,384, M=100).
C PERFORMANCE OF DIFFERENT AMORTIZATION PATTERNS IN DOWNSTREAM TASKS
C.I TARGETED PROBE PERTURBATION (TPP)
To evaluate the directional controllability of features learned by SAEs under different amortization paradigms, we conduct the TPP experiment. We first train linear probes on fixed model layer's activations identify specific concepts. Subsequently, dictionary latents are ranked via an attribu- tion score, and select subset is ablated from the residual stream. The core evaluation measures the probe's 's performance degradation on the target class while verifying the stability of non-target classes Karvonen et al. 2024).
Model and Data. The experiment is based on the Pythiz--60MMdeeuuped model, using activations E T 768 from the resi i i post of layer 8. We evaluate four SAE variants (Standard, Gated, JumpRelLU, and Top-k) with a dictionary size of m = 16, 384. The TPP experiment utilizes the AG News dataset, for which as the probe's ' input.
the representation of the last non-padding token from each sample
Inference Paradigms, Attribution, and Intervention. The experiment compares three inference paradigms: fully-amortized, semi-amortized, and non-amortized, all sharing common decoder dictionary For targeted intervention, we first compute an attribution score 8j for each latent with respect to a given class probe's 's weight vector w RR.:
$ (D... w) (E[z, yy y= 1] E[z, 0)).
This score jointly considers the alignment of a dictionary atom with the probe's direction and the feature's 's class-conditinall activation difference. We select the top-M latents according to |sy| to form an index set S and perform zero-ablation on the activation vector
x' = x D.,sss,
which subtracts the reconstructed components corresponding only the latents in S.
Metrics. We employ the following metrics: (i) On-target Drop (AAccrageet): The accuracy de-
crease on the target class, AcChase AcCublated- (ii) Off-target Leakage (AAccnon- taageetarre The mean accuracy change across non-target classes, measuring intervention precision. (iii) Top-M Curve: AAcctarget as function of the number of ablated latents M.
Observation As shown in Table. the results of the Targeted Probe Perturbation experiment demonstrate that semi cemi-amortized and non-amortized inference methods consistently outperform the fully-amortized approach across all tested Sparse Autoencoder variants. Specifically, for all four
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SAE architectures- Top-k, Gated, JumpReLU, and Standard Standard- adopting semi- or non-amortized inference leads to a significant increase in the target class accuracy drop and better control over off-target leakage, resulting in marked gains in the selectivity metric.
These results resonate with the core argument in Section. 4.3 of the main text: the global optimality pursued by fully-amortized inference comes the cost of instance-level semantic purity. From the perspective of downstream intervention task, this experiment confirms that reducing reliance on the parameter-shared encoder significantly mitigates the amortization gap and enhances the monose- manticity and intervenability of the learned features, thereby providing strong empirical support for the paper's advocacy of "reducing over-investment in amortization -asedd encoding methods."
C.2 GENERATIVE INTERVENTION SCORING (GIS)
To further assess the interpretability of SAE latents, perform generative interventions. We manip- ulate a targeted set latents during autoregressive generation and evaluate the effect on the model's output using external scoring language model (LM). The intervention strength is rigorously cali- brated to ensure fair comparisons across different amortization paradigms.
Model and Data. We the same setup in the TPP experiment: resid resid.post. layer 8. Latent sets for intervention are selected from the high- sigh-attribution features identified via TPP. To prevent informational leakage, a separate, base LM is employed as scorer. Prompts are designed to elicit interpretable phenomena, such as numeracy and pronoun resolution.
Intervention and Calibration. Interventions can be either zero-ablation or additive. To ensure comparability, the intervention strength, controlled by multiplier a, is calibrated for each setup. Specifically, we use a binary search to find an a such that the mean per-token KL divergence between the clean and intervened next-token distributions matches a predefined target {0.10, 0.33, 1.00).
Metries. The primary metric is the Intervention Score (S), which quantifies the change in log- probability of target hypothesis & as evaluated by the scorer model par:
E log pas (Ó) gr) log (Ø [9)]
where and denote the intervened and clean generations, respectively. We compare S across all SAE variants and inference paradigms at matched KL divergence levels.
Observations The results (Table. i show that semi-amortized and non-amortized inference paradigms consistently achieve higher intervention scores (S) than full-amortized ones across all SAE variants (TopK, Gated, Jump Standard). For example, with TopK SAE KL target = 1.00, semi-amortization yields 1.968, non-amortization 1.781, and full-amortization 1.412. This trend persists across variants and KL levels. Furthermore, aeniiaamrtizattonn slightly outper- forms non-amortized in most cases, indicating that limited per-sample optimization improves feature quality while balancing efficiency.
These findings align with Section where global optimality in aulttzemo inference sacri- fiees instance-level semantic purity, favoring nigh-frequency latents and reducing intervention pre- cision. In contrast, semi- and non-amortized methods mitigate the amortization gap, enhancing monosemanticity and intervenability. summary, the GIS experiment supports reducing reliance on amortized inference for better polysemy disentanglement.
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Published as a conference paper at ICLR 2026
SAE
Encoding Pattern
S @ k=0.10
S @ x=0.33
x=1.00
TopK
Semi-amortized
0.231
0.646
1.975
TopK
Unamortized
0.224
0.653
1.812
TopK
Amortized
0.168
0.472
1,415
Gated
Semi-amortized
0.214
0.599
1.792
Gated
Unamortized
0.206
0.552
1.796
Gated
Amortized
0.153
0,436
1.289
JumpReLU
Semi-amortized
0.194
0.555
1.668
JumpReLU
Unamortized
0.183
0.506
1.523
JumpReLU
Amortized
0.140
0.398
1.193
Standard
Semi-amortized
0.164
0.485
1,432
Standard
Unamortized
0.148
0.437
1.291
Standard
Amortized
0.151
0.344
1.027
Table 2: GIS results on Pythia-160M-deduppel "resid.post layer 8). S is the scorer LM log- probability gain under matched KI. targets k. E {(0.10, 0.33, 1.00}.
D DYNAMICS OF THE SEMI-AMORTIZED PATTERN
We further ablate the semi-amortizer BatchTopK SAE by varying the number of refinement steps T in the inner sparse-coding loop (Table Across both Myyhia-660M-dedug
(layer 8) and Gemma- 2-2B (layer 12), increasing monotonically reduces the reconstruction error (NMSE), while the pathological metrics remain largely stable. For Pythia, NMSE drops from 0.477 T 5 to 0.132
at 7 25 and 0.046 at T = 50, with the majority of the gains already obtained by T 20-30. similar trend holds for Gemma-2-2B, where NMSE decreases from 0.072 T
0.025
at 7 = 25 and 0.014 at 7 = 50. In contrast, the Dead Rate stays at zero for all settings, Dense Rate 1.100.2 only fluctuates within a narrow band, and the FI @ 1/F1 @2 scores are almost flat. The feature-splitting indicator AFI exhibits a mild increase with T on Pythia (from 0.026 at T = 5 to 0.06 around 7 20-40) and then slightly decreases again for very large T, while the Absorption Rate is either nearly constant (Pythia) or decreases slightly (Gemma). Overall, these results suggest that semi-amortized inference robust to the exact choice of refinement budget: moderate number of refinement steps (T' R3 20-30) already recovers most of the reconstruction benefit of iterative inference, without materially changing the profile pathological phenomena, and at a fraction of the cost of the fully aoortiedd solver used to estimate the amortization gap.
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Published as a conference paper at ICLR 2026
Table 3: Pathological Phenomena Metrics of BatchTopk SAE under Semi-Amortized Patterns
Different ISTA Iteration Steps
Iteration Step (ISTA)
NMSE
Dead Rate
Dense Rate@0.1
Dense Rate@0.2
@l@1
@1@2 AF1
Absorption Rute
Pythia-160m-deduppee Layer
10
0.388
0,000
0,064
0,049
0,704
0.722
0.017
0.144
15
0.250
0.000
0.060
0.047
0.692
0.746
0.054
0.134
20
0.177
0.000
0.057
0.034
0.689
0.755
0.119
25
0.132
0,000
0,048
0.034
0.688
0.755
0.067
0.121
30
0.102
0,000
0.048
0,034
0.687
0.755
0.068
0,121
35
0.081
0,000
0.046
0.036
0.687
0.756
0.068
0.122
40
0.066
0.000
0.062
0.040
0.687
0.755
0.068
0.122
45
0.055
0.000
0.057
0.039
0.726
0.121
50
0.046
0.000
0.059
0,036
0.687
0.726
0.039
0.121
Gemma-2-2h, Layer 12
0.072
0.000
0.231
0.150
0.647
0.682
0.034
0.014
0.207
0.129
15
0.037
0.000
0,215
0.123
0.648
0.682
0,034
0.007
20
0.029
0.000
0.218
0.167
0.688
0.682
0.034
0.005
25
0.025
0.000
01.223
0.168
0.648
0.682
0.33
0.004
30
0.021
0.000
0.239
0.160
0.648
0.682
0.034
0.003
35
0.019
0.000
0,210
0.135
0.648
0.682
0,034
0.003
40
0.017
0.000
0,226
0.125
0.648
0.681
0.034
0.003
45
0.015
0.000
0,230
0.154
0.647
0.681
0.034
0.003
50
0.014
0.000
0.202
0.142
0.647
0.681
0.033
0.002
E
LIMITATIONS
Although the metrics for many pathological phenomena in SAEs have been significantly allevi- ated by the semi-amortized and non-amortized encoding methods proposed this paper, there are still some anomalies. For instance, in the Topk SAE case corresponding to Demmm-22-2b/ayerrll the non-amortized approach instead exacerbates feature splitting and feature absorption, the rea- sons for which remain worthy of exploration 44. Additionally, since both semi-amortized and non-amortized methods involve per-sample iterative traditional sparse coding, which aligns with the goal of monosemanticity, it exacerbates the existing scalability issues of SAEs. Therefore, how to balance scalability while mitigating the limitations introduced by amortized inference remains area worthy of researchers' exploration. Potential approaches could include meta learning pro- posed in VAES (lakovleva et al., 2020), or gradually updating sparse codes with online dictionary learning (Mairal al. 2009).
F EXPERIMENTAL RESULTS
F.1 EXPERIMENTAL RESULTS SECTION 4.3
F.2 EXPERIMENTAL RESULTS OF SECTION 5
20

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Published as a conference paper at ICLR 2026
Table 4: Variation of Different Pathological Phenomena Corresponding to Standard SAE at Different Sparsity Levels from the Perspective of Training Dynamics.
Trainer
Checkpoint
NMSE
Deud Rate
Dense Rate@0.2
FI@1
F1@2
AFI
Absorption Rate
0
0.9413
0.2587
0.5346
0.7129
0.8051
0.0923
0.0186
25978.81
0.1555
0.2368
0,6643
0.8240
0.0535
0.0694
4350.55
2441
0.0332
0.2300
0.7397
0.4534
0.6164
0.1631
0.4564
855.77
24414
0.1048
0.2214
0,0862
0.6034
0.6383
0.0349
0,2342
1689.17
772
0.0303
0.2313
0.7295
0.6356
0.6864
0.0508
0.2554
880.45
7720
0.0764
0.2285
0.0438
0.5949
0.6509
0.0559
0,2546
1449.20
77203
0.1174
0.2185
0.0890
0.5590
0.7156
0.1566
0.4352
1773.85
0
0.9413
0.2587
0.5346
0.7129
0.8051
0.0923
0.0186
25978.70
0.1550
0.2368
0,6642
0.8240
0.0539
0,0728
4335,57
2441
0.0528
0.2299
0.7250
0.6075
0.6440
0.0366
1.86
1419.51
24414
0.1238
0.2224
0.0502
0.5335
0.6275
0.0940
0,5034
1748.02
772
0.0316
0.2316
0.7287
0.6316
0.6938
0.0622
0.2698
913.97
7720
0.0858
0.2282
0.0206
0.0398
1606.65
77203
0.1430
0.2224
0.0535
0.5746
0.6801
0.1055
0.4900
1996.48
0
0.9413
0.2587
0.5346
0.7129
0.8051
0.0923
0.0186
25978.86
0.1544
0.2368
0.6647
0.7685
0.8239
0.0554
0.0796
4316.75
2441
0.0964
0,2301
0.6917
0.4788
0.5679
0.0891
0.4530
2603,39
24414
0.1318
0.2294
0.0287
0.5129
0.6418
0.1289
0.5222
1325.94
772
0.03488
0.2318
0.7286
0.6250
0.6918
0.0668
0.3008
999.66
7720
0.0963
0.2289
0.0070
0.5082
0.6457
0.1375
0,4992
1763.15
77203
0.1533
0.2361
0.0286
0.5831
0.6342
0.0511
0,3398
1669.68
0
0.9413
0.2587
0.5346
0.7129
0.8051
0.0923
0.0186
25978.76
0.1537
0.2368
0.6655
0.7683
0.8241
0.0557
0.1076
4293.68
2441
0.2042
0.2296
0.6129
0.5224
0.6094
0.0869
0.5208
$528.09
24414
0.1294
0.2595
0.0104
0.5998
0,6313
0.0315
0,2012
306.95
772
0.0427
0.2317
0.7267
0.6108
0.6803
0.0695
0.3520
1203.42
7720
0.2300
0.0044
1638.43
77203
0.1395
0.2686
0.0128
0.5334
0.6350
0.1016
0,3860
212.58
0
0.9413
0.2587
0.5346
0.7129
0,8051
0.0923
0.0186
25978.76
0.1535
0.2367
0,6663
0.7655
0.8212
0.0557
0.1148
4284.31
2441
0.3266
0,2288
0.5286
0.4851
0.6023
0.1171
0,5840
8849.26
24414
0.1402
0.2838
0.0045
0.5075
0.6299
0.1224
0,4498
92,56
772
0.0544
0.2319
0.7234
0. 0.5964
0.6623
0.0659
0.3838
1507.16
7720
0.1255
0,2336
0.0039
0.6635
0.0064
0.0794
1419,27
77203
0.1388
0.3023
0.0074
0.5646
0.6626
0.0980
0.4772
338..1
0
0.9413
0.2587
0.5346
0.7129
0.8051
0.0923
0,0186
25978.77
0.1537
0.2367
0.6669
0.7570
0.7937
0.0367
0.1234
4285.21
2441
0.5447
0,2278
0.4059
0.5490
0.6196
0.0705
0.3480
14650.23
24414
0.1633
0,3221
0.0013
0.5146
0.5589
0.0443
0,1422
-161.76
772
0.0833
0,2319
0.7186
0.6006
0.6431
0.0425
0.2176
2259.97
7720
0.1549
0.2297
0.0034
0.6638
0.6797
0.0160
0.0032
1483.02
77203
0.1537
0.3524
0.0028
0.1998
0.6406
0.5008
0.9164
-782.56
21

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Published as a conference paper at ICLR 2026
Table 5: Variation of Different Pathological Phenomena Corresponding Top-k SAE Different Sparsity Levels from the Perspective of Training Dynamics.
Trainer
Checkpoint
NMSE
Dead Rate
Dense Rate@0.2
FI@1
F1@2
AFI
Absorption Rate
0
0.9413
0.2587
0.5346
0.7129
0.8051
0.0923
0.0186
25978.81
0.1555
0.2368
0,6643
0.8240
0.0535
0,0694
4350.55
2441
0.0332
0.2300
0.7397
0.4534
0.6164
0.1631
0.4564
855.77
24414
0.1048
0.2214
0,0862
0.6034
0.6383
0.0349
0,2342
1689.17
772
0.0303
0.2313
0.7295
0.6356
0.6864
0.0508
0.2554
880.45
7720
0.0764
0.2285
0.0438
0.5949
0.6509
0.0559
0,2546
1449.20
77203
0.1174
0.2185
0.0890
0.5590
0.7156
0.1566
0.4352
1773.85
0
0.9413
0.2587
0.5346
0.7129
0.8051
0.0923
0.0186
25978.70
0.1550
0.2368
0,6642
0.8240
0.0539
0,0728
4335,57
2441
0.0528
0,2299
0.7250
0.6075
0.6440
0.0366
1.86
1419.51
24414
0.1238
0.2224
0.0502
0.5335
0.6275
0.0940
0,5034
1748.02
772
0.0316
0.2316
0.7287
0.6316
0.6938
0.0622
0.2698
913.97
7720
0.0858
0.2282
0.0206
0.0398
1606.65
77203
0.1430
0.2224
0.0535
0.5746
0.6801
0.1055
0.4900
1996.48
0
0.9413
0.2587
0.5346
0.7129
0.8051
0.0923
0.0186
25978.86
0.1544
0.2368
0.6647
0.7685
0.8239
0.0554
0.0796
4316.75
2441
0.0964
0,2301
0.6917
0.4788
0.5679
0.0891
0.4530
2603,39
24414
0.1318
0.2294
0.0287
0.5129
0.6418
0.1289
0.5222
1325.94
772
0.03488
0.2318
0.7286
0.6250
0.6918
0.0668
0.3008
999.66
7720
0.0963
0.2289
0.0070
0.5082
0.6457
0.1375
0,4992
1763.15
77203
0.1533
0.2361
0.0286
0.5831
0.6342
0.0511
0,3398
1669.68
0
0.9413
0.2587
0.5346
0.7129
0.8051
0.0923
0.0186
25978.76
0.1537
0.2368
0.6655
0.7683
0.8241
0.0557
0.1076
4293.68
2441
0.2042
0.2296
0.6129
0.5224
0.6094
0.0869
0.5208
$528.09
24414
0.1294
0.2595
0.0104
0.5998
0,6313
0.0315
0,2012
306.95
772
0.0427
0.2317
0.7267
0.6108
0.6803
0.0695
0.3520
1203.42
7720
0.2300
0.0044
1638.43
77203
0.1395
0.2686
0.0128
0.5334
0.6350
0.1016
0,3860
212.58
0
0.9413
0.2587
0.5346
0.7129
0,8051
0.0923
0.0186
25978.76
0.1535
0.2367
0,6663
0.7655
0.8212
0.0557
0.1148
4284.31
2441
0.3266
0,2288
0.5286
0.4851
0.6023
0.1171
0,5840
8849.26
24414
0.1402
0.2838
0.0045
0.5075
0.6299
0.1224
0,4498
92,56
772
0.0544
0.2319
0.7234
0. 0.5964
0.6623
0.0659
0.3838
1507.16
7720
0.1255
0,2336
0.0039
0.6635
0.0064
0.0794
1419,27
77203
0.1388
0.3023
0.0074
0.5646
0.6626
0.0980
0.4772
338..1
0
0.9413
0.2587
0.5346
0.7129
0.8051
0.0923
0,0186
25978.77
0.1537
0.2367
0.6669
0.7570
0.7937
0.0367
0.1234
4285.21
2441
0.5447
0,2278
0.4059
0.5490
0.6196
0.0705
0.3480
14650.23
24414
0.1633
0,3221
0.0013
0.5146
0.5589
0.0443
0,1422
-161.76
772
0,0833
0.2319
0.7186
0.6006
0.6431
0.0425
0.2176
2259.97
7720
0.1549
0.2297
0.0034
0.6638
0.6797
0.0160
0.0032
1483.02
77203
0.1537
0.3524
0.0028
0.1998
0.6406
0.5008
0.9164
-782.56
22

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Published as a conference paper at ICLR 2026
Table 6: Pathological Phenomenon Metrics for Different SAE Variants under Various Amortization
Patterns
SAE Variants
Paitern
NMSE
Dead Rate
Dense Rate@#0.1
Dense 0.te@10.2
Fl@1
F1
A/1
Absorption Rate
Pythia-160mm-deduppee Layer
Dull-Amorizeed
0,109
0.295
0.093
0.046
0.606
0.649
0.943
0.144
Standard
Semi-Amoriied
0.078
0.260
0.095
0.600
Non-Amorized
0.107
0.338
0.094
0.045
0.590
0.637
0.047
0.283
Full-Amorized
1.947
0.001
0.612
0,432
0.655
0.692
0.037
0.210
GatedSAE
Somi- Amnorizodd
0.014
0.001
0.615
0.431
0.655
0.690
0.035
0.161
Con-Amoriized
0,000
0.008
0.610
0.467
0.676
0.671
-0.008
0.064
Pull-Amorized
0.755
JumpReto
Semi- Amnotizdrt
0,255
0.321
0.033
0.017
0.670
0.744
0.074
0.143
Non-Amorized
0.113
0.055
0.033
0.009
0.681
0.066
Full-Amorized
1.499
0.307
0.028
0.015
0.626
0.679
0.053
0.225
Topk
Amminim
0.087
0.022
0.029
0.010
0.648
0.683
0.036
0.134
Non- Con-Amorized
0.242
0.012
0.029
0.008
0.535
0.558
0.023
0.452
Full-Amortied
0.537
0.316
0.053
0.040
0.700
0,748
0.047
0.171
BatchTopK
Semi-Amomized
Non- Amoriize
0.017
0.000
0.053
0.043
0.726
0.758
0.031
0.033
Bull-Amonized
0.107
Matryoshka
Semi Amomized
0,033
0.000
0.121
0.055
0.681
0.716
0.035
0.219
Non Amoriizze
0.011
0,007
0.114
0.049
0.677
0.729
0.052
0.172
LocA SAE
Loc-Amatizzed
0.427
0.000
0.079
0.044
0.714
0.728
0.013
0.055
Gemma- 2-2b, Layer 12
Bull-Amortized
0.193
0.221
0.251
0.108
0.722
0.737
0.015
0.010
Standard
Semi-Amortized
0.114
0.212
0.254
0.072
0.716
0,737
0,021
0.007
Non Amorrizze
0.135
0.255
Full-Am Boll-Amotizzed
1,580
0.000
0.950
0.854
0.882
0.882
0.000
0.000
GatedSAE
Semi-Amoriized
0.013
0.951
Non Ammorizrz
0.001
0.000
0.939
0.879
0.851
0.854
0.003
0.000
Full-Amotized
0.341
0.102
0.056
0.018
0.815
0.847
0.032
0.923
JumpRelo
Semi- Aanotianrt
0,236
0.086
0.057
0.020
0.841
0.842
0.001
0.000
Non-Amortized
0.225
0,028
0.059
0.014
0.838
0.848
0.010
0.000
Rull-Amorized
0,882
0.051
Topk
Semi- Aami--Amotized
0,186
0.011
0.052
0.018
0.836
0.839
0.004
0.000
Non-Amoriize
0,274
0.011
0.053
0.013
Pull-Amortized
0.152
0.136
0.231
0.147
0.646
0.708
0.062
0.093
BatchTopK
Aomi-Amm
0.021
0,000
0.230
0.150
0.648
0.682
0.034
0.003
Non-Amoriize
0.005
0.000
0.235
0.154
0.629
0.669
0.040
0.018
Full-Amortized
0,573
0.113
0.077
0.037
0.690
0.681
-0.008
0.732
Matryoshka
Amooizzdd
0.059
Non Amoriizd
0,012
0,000
0.083
0.040
0.613
0.654
0.041
0.020
LocA-SAE
Loc-Amertized
0.017
G EXPERIMENTAL DETAILS
G.1 EXPERIMENTAL DETAILS OF SECTION 5
Algorithm Implementation Flow for the Experiment in Section 6
Require: models M, variants V. corpus C, layer É, token budget 10,0000, encoder (Wency bene). decoder D, base X, target density T-0.1, tolerance
1: for (m, v) E M x V do
2: X + BOOLLECHHDDDESSTTESSSSS C,, C,
first tokens + layer-l activations
3:
gfull + ENChau (X; Wene, bene; v)
4:
+ DENSE @ O. (2
5:
Ssemi +- CALIBRATE( Semmi, E); 8pon +- CALIBRATE t, e)
6:
sema
< PGD(X, XX, D, A8semi init = Jull T = 30)
7:
nnn (STA D, Asmon; init 0, 200)
8:
X DT for E (full, semii non} > NMSE, Dead, DENSE@0.1/0.22 FI01, F102, AF1,
9:
EVALUNTE(( {27})
Absorption
23

---

Published as a conference paper at ICLR 2026
H CONFIGURATION INFORMATION
Table 7: Key hyperparameter configurations for six different SAE architectures. All SAEs were trained on the residual stream of layer 12 of the Gemma-2-2B model, with activation dimension of 2304. Parameter
Gated SAE
JunpRel.tStandard SAE
Top-K SAE
BatchTopkKaarroshhaa
SAE
SAE
SAE
Dictionary Size (dasa)
16384 (2
16384 (2
16384 (2
16384
16384
16384
(2!+)
(214)
(2
Learning Rate (LR)
3 x 10
3 x 10
x 10
3 x 10
3 3 10-
x 4
Aparsity-Related Parameters
L1 Penalty
0.012
0.012
Sparsity Penalty
1.0
Target Lo
20
Top-K Value (k)
20
320
20
Training Strategy Parameters
LR Warmup Steps
1000
N/A
1000
1000
1000
1000
Sparsity Warmup Steps
5000
5000
5000
N/A
N/A
N/A
Table 8: Key hyperparameter configurations for six different SAE architectures trained the EleytherAUppythia- diriiduuo0md model. All SAEs were trained on the residual stream of layer 8. with activation dimension of 768.
Parameter
Gated SAE
JumpRee. Top-K SAE
BotchTopkKaattyshhata
SAE
SAE
SAE
SAE
Dictionary Size (dasa)
16384
16384 (2
16384
16384
16384
16384
(2
(2
(2!4)
(214)
(2
Learning Rate (LR)
3 x 10
3 x 10
x 10
3 x 10
3 3 10
x 4
Sparsity-Relater Parametery
L1 Penalty
0.012
0.012
Sparsity Penalty
1.0
Target Lo
20
Top-K Value (k)
20
20
20
Training Strategy Parameters
LR Warmup Steps
1000
N/A
1000
1000
1000
1000
Sparsity Warmup Steps
5000
5000
5000
N/A
N/A
N/A
I EVALUATION METRICS
24

---

Published as a conference paper at ICLR 2026
Table 9: Evaluation Metrics (Zrehn = max (2, 0); feature ranking uses Z. which z-score normalizes
Zrelu per column).
Variable Name
Meaning
Formula
NMSE
Normalized mean squared reconstruction error.
where e 10-9,
z D
1 M
Dead Rate
Fraction dead latents.
Σ
(freq, S 50), where
M j=1
0 == 10-6
freq, = Pr ((Zretu)is > 0).
M
Dense Rate@O @.2
Fraction latents firing at least 20% of tokens (more frequently active).
I (froqq 2 0.2).
M
j=1
F1
Fl score of linear probe using the top-1 ranked latent (by corr(Z,,-. l)
Fl@l F1 (T... order(0]] + v))
F1@2
Fl score of linear probe using the top-2 ranked latents.
F1@2 F1 F1 orderf:
2] + y)) AF1 F1@2 F1@1.
AF1
Marginal improvement from to features; larger values indicate stronger feature splitting.
Absorption Rate
On positive-label tokens, fraction where the dominant latent is inactive while any of the next top-K latents is active.
Let m = order[o],
A order(1 1+ K] (default
K = 5). Absorb
Σ
I( (Zreta) S
N+
A max Zrelu)as > 20). JEA
Amortization Gap
Suboptimality of amortized codes vs. per-token L1 solution (ISTA-200).
Gap
E
L amort
[(>*)], I(z)
2
D
12 + A||2|11, 2" ~
ISTA
(z:
D)
Notes. (1) Labels y use norm-threshold heuristic unless otherwise stated: 3/: = T([1ar || > median, || l12). (2) Linear probes are trained on Z, with class weight-balanced, ranking uses ccorr( Za. w) J. (3) For Top-K SAEs, selection is applied first, then Z.n. is used for firing-based metrics. (4) When comparing amortizelsemi-aaorrizee//// codes, can be calibrated match target density.
25


Reviews:
[{"review_id": "kYBAhyMg1X", "reviewer": "Reviewer_Ycij", "summary": "The paper considers the potentially overlooked interrelation between mono-semanticity and reconstruction-sparsity tradeoff in the SAE context. Specifically, the (position) paper presents empirical findings including (1) improvement over the reconstruction-sparsity Pareto frontier comes at the expense of dictionary capacity and mono-semanticity, and (2) semi-/non- amortized encoding approaches show benefits in improving reconstruction and features (e.g., concept removal tasks) and in addressing dead latents issue. The paper argues that the conflict between parameter-sharing encoding and instance-level optimality stems from the SAE architecture itself, and cautions against the investment in amortization-based encoding for polysemy disentanglement.", "questions": "- Question/Comment on novelty\n\nThe paper lays out issues (\"pathological phenomena\") identified in previous works, e.g., dead latents (Gao et al., 2024), dense latents (Sun et al., 2025), feature splitting and feature absorption (Chanin et al. 2024), and also reproduces some exps from Karvonen et al. (2025). It would be very helpful if the authors can be more explicit about the unique contribution to address the potential concern on novelty.", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "### Writing\n\nOverall, the paper is relatively easy to follow. The problem setting of interest, the previous approaches and how they fit in the discussion, the purpose of empirical evaluations, the settings of experiments and findings are presented in an organized and clear way.\n\n### Significance\n\nThe paper (or position paper?) aims to present a case/caution against the investment in amortization-based encoding, if the goal includes polysemy disentanglement. This is carried out relatively well, since the arguments are well-structured along with empirical evidence.", "weaknesses": "### Novelty\n\nThe paper strikes me more of a position paper than a regular conference paper (just stating this as a neutral comment). There are potential some concerns on the novelty (detailed in \"Questions\" section).\n\n### Minor Things\n\n- please fix the opening quotation marks in lines 160, 192, 243", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "xbiT3po4mI", "reviewer": "Reviewer_S8RY", "summary": "This paper argues that the amortized inference framework, standard in Sparse Autoencoders (SAEs), is fundamentally misaligned with the goal of discovering monosemantic features for mechanistic interpretability. The authors state that the global optimization objective of a shared encoder inherently conflicts with the need for instance-level optimality, leading to pathological behaviors like feature splitting and absorption. They provide empirical evidence showing that moving towards instance-specific, non-amortized optimization significantly improves reconstruction and mitigates these issues, albeit at a high computational cost. Based on this, the authors advocate for a paradigm shift away from purely amortized methods.", "questions": "Please see the weaknesses section.\n\nIn addition, the non-amortized approach appears to worsen some pathologies (feature splitting and absorption) for TopK SAEs on Gemma-2-2b. How do you reconcile this with your central thesis that amortization is the primary cause of these problems?", "limitations": "", "rating": 4, "confidence": 2, "soundness": 3, "presentation": 2, "contribution": 2, "strengths": "1. The paper clearly articulates a critical, and perhaps under-appreciated, conflict in the SAE literature: the trade-off between the computational efficiency of amortized inference and the instance-level fidelity required for true monosemanticity. This reframing of common SAE pathologies as symptoms of an inference problem, rather than just an architectural one, is a valuable conceptual contribution.\n\n2. The core experiment comparing fully-amortized, semi-amortized, and non-amortized inference using the same trained decoder is convincing. It effectively isolates the inference strategy as the key variable, providing direct and convincing evidence that the amortization gap is a significant source of suboptimality and pathological behavior in SAEs", "weaknesses": "1. The paper's main weakness is that it diagnoses a problem without offering a viable solution. The proposed non-amortized alternative, which relies on per-sample iterative optimization (e.g., 200 ISTA steps), is computationally intractable for the very large-scale applications where SAEs are most needed. To make the call for a paradigm shift convincing, the authors should propose and evaluate at least one hybrid approach that balances instance-level fidelity with computational feasibility.\n\n2. The central concept, the \"amortization gap,\" is a well-established phenomenon extensively studied in the context of Variational Autoencoders and recent work on SAEs (e.g., O'Neill et al. 2024), which substantially detracts from the informativeness of this work. It would be great if the authors could make the ``delta'' more transparent.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "vhoKNFcaSL", "reviewer": "Reviewer_KjC9", "summary": "The paper argues that amortized inference, central to SAE, conflicts with mechanistic interpretability goals. Amortization trades instance-level optimality for global efficiency, creating an amortization gap. This gap causes pathological effects that degrade monosemantic feature discovery. Through theoretical and empirical analysis, the authors show that increasing sparsity worsens these issues and that optimizing reconstruction-sparsity tradeoffs doesn’t improve interpretability. They test semi- and non-amortized methods, finding that these reduce reconstruction errors, dead latents, and improve interpretability and control. The conclusion urges a shift away from full amortization toward hybrid or per-instance inference.", "questions": "1. Can amortization be regularized rather than abandoned, e.g., local amortization?\n\n2. How does the amortization gap quantitatively relate to interpretability scores beyond NMSE and sparsity metrics?\n\n3. Could amortization’s failure modes differ across modalities (e.g., vision vs language)?", "limitations": "", "rating": 4, "confidence": 3, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "1. Clear articulation of the conceptual tension between global efficiency and instance-level fidelity\n\n2. Novel experimental demonstration of semi-/non-amortized methods that improve feature interpretability.\n\n3. Situates itself well in current mechanistic interpretability discourse (SAEBench, monosemantic features).", "weaknesses": "1. The paper argues strongly against amortization but doesn’t fully explore potential middle grounds such as localized amortization, mixture-of-experts encoders, or hierarchical amortization. This makes the recommendation (“reduce investment in amortization”) feel a bit absolute.\n\n2. The broader meaning of “instance-level optimality” for interpretability is underexplored. For example, how does this affect feature alignment across runs, or practical model auditing? The paper hints at these but doesn’t go deep.\n\n3. While the paper demonstrates empirical correlations (e.g., lower amortization gap -> lower NMSE, fewer dead latents), it doesn’t provide causal interventions or ablations proving amortization itself causes the pathologies, rather than merely correlating with them.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "R4PLUJ8IME", "reviewer": "Reviewer_gX9Z", "summary": "This paper investigates fundamental limitations of Sparse Autoencoders (SAEs) for mechanistic interpretability, arguing that the amortized inference paradigm conflicts with the instance-level optimality required for monosemantic features. The authors demonstrate through training dynamics analysis that pathological phenomena (feature absorption, splitting, dead/dense latents) are interconnected trade-offs arising from parameter sharing under global reconstruction-sparsity constraints. They propose semi-amortized and non-amortized encoding methods as alternatives, showing improved reconstruction, reduced dead latents, and better performance on downstream intervention tasks.", "questions": "1. Can you provide theoretical results or additional empirical evidence connecting instance-level reconstruction optimality to monosemanticity? What properties of the data distribution determine whether this connection holds?\n2. For the outlier cases (e.g., Gemma-2-2b/L12 TopK absorption), can you provide analysis of what's happening? Does this suggest limitations of the non-amortized approach?\n3. Have you explored whether better training procedures (e.g., curriculum learning, better initialization) for amortized SAEs could narrow the gap?", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. The paper articulates a fundamental issue that has been under-recognized in the SAE literature - that global optimization objectives may be misaligned with the goals of interpretability\n2. The training dynamics experiments across multiple checkpoints, sparsity levels, and SAE variants provide robust evidence for the claims\n3. The amortization gap perspective from variational inference provides a principled lens for understanding SAE limitations\n4. The downstream task experiments (TPP, GIS) demonstrate that the improvements translate to better interpretability and controllability", "weaknesses": "1. The computational cost of non-amortized inference (200 ISTA iterations × N samples) is mentioned as a limitation but needs more serious treatment. For large-scale interpretability applications, this may be prohibitive. The paper should provide concrete runtime comparisons and discuss when the trade-off is worthwhile.\n\n2. While the paper shows that pathological phenomena are correlated, it doesn't fully explain why instance-level optimality necessarily leads to better monosemanticity. The connection between reconstruction quality and semantic purity is assumed rather than proven.\n3. Semi-amortized inference shows promise but receives less attention than it deserves. More systematic exploration of the trade-off between number of refinement steps and performance could be valuable.\n4. The paper acknowledges some anomalous results (e.g., TopK with Gemma showing worse absorption in non-amortized setting) but doesn't investigate them thoroughly. This suggests the full picture may be more complex.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)