Sparse Autoencoders

We report a small, reproducible audit of which sparse-autoencoder (SAE) features of GPT-2 small fire differently on failed versus successful trials of the Indirect Object Identification (IOI) task. On 300 prompts, GPT-2 small reaches 79.7% accuracy; 146 of the 24,576 features in the layer-8 residual-stream SAE release of Bloom (2024) clear a Holm-corrected significance threshold and 105 reach a large effect size (|Cohen's d| > 0.8). The strongest single correlate of failure -- feature 17,491, d=+2.93, Neuronpedia label 'cryptographic keys' -- is essentially silent except when the prompt's transferred object is 'the keys,' on which GPT-2 small fails 93.3% of the time vs. 7.5% on the other seven objects (Fisher exact p = 8.79 x 10^-33). We put this correlate through three controls that a mechanistic claim should pass. (i) A causal ablation: zeroing feature 17,491 in the residual stream across all token positions of the 45 keys prompts does not restore accuracy (6.7% -> 4.4%); the feature is a correlate, not a sufficient cause at this layer. (ii) A representation baseline: a logistic regression on the raw 768-dimensional residual stream reaches 5-fold ROC AUC = 0.929, matching the top-100 SAE features (0.927); the SAE basis adds interpretability, not predictive power. (iii) A seed-robustness check: across five random seeds the keys-subset failure rate stays in 75.0--93.3% (the behavioural effect is real), but feature 17,491 is the top-|d| feature in only 1 of 5 runs. The methodological contribution is therefore the audit pipeline (cheap, model-agnostic, surfaces named correlates) rather than any single feature found through it. We release the code, the 300-prompt corpus, the 300x24,576 activation matrix, the ablation and baseline scripts, and the figures. The full pipeline runs on a laptop (Apple M3 Max, no discrete GPU).

Vision-language models learn powerful multimodal embeddings, yet their internal semantics remain opaque. While sparse autoencoders (SAEs) can extract interpretable features, they rely on expanding the representation dimension, which compromises the original geometry and introduces redundancy. We introduce CEDAR (Conceptual Embedding Disentanglement via Adaptive Rotation), a post-hoc method that reveals the compositional structure of pretrained embeddings without increasing dimensionality. By learning an invertible transformation with a top-$k$ sparsity bottleneck, CEDAR concentrates semantic information into axis-aligned disentangled coordinates. In CLIP-like architecture, individual coordinates can be interpreted with textual concepts, while for generative models such as BLIP, they can be decoded into natural language descriptions. Experiments demonstrate that CEDAR achieves a competitive reconstruction-sparsity trade-off while producing explanations that are more interpretable and better aligned with human perception. Our results suggest that the apparent entanglement in vision-language representations can be resolved through a suitable change of basis, eliminating the need for overcomplete expansions.

Sparse autoencoders (SAEs) are one of the main methods to interpret the inner workings of deep neural networks (DNNs), decomposing activations into higher-dimensional features. However, they exhibit critical shortcomings where a large fraction of features are never activated and are unstable. Despite variants of SAEs that attempt to mitigate these issues, they require additional data, resampling, or training. We propose the aligned training, a parameter-free reparameterization of SAEs that simultaneously improves reconstruction quality, eliminates dead features, and significantly enhances stability across training seeds. Our approach is motivated by an overlooked observation that SAE feature quality, measured by the inner product between encoder and decoder directions (which we call the alignment score), follows a bimodal distribution across all modern architectures. The proposed aligned training enforces a geometric constraint between the encoder and decoder such that their inner product equals one for every feature, which removes a source of degeneracy in the SAE training without adding any hyperparameters. Across multiple models, dictionary sizes, and sparsity levels, the aligned training shows Pareto improvements on the SAEBench benchmarks. Beyond improving dead features, stability and reconstruction, our method readily integrates with techniques in mechanical interpretability such as Top/BatchTop-K architectures and p-Annealing. Overall, the aligned training substantially improves feature quality and stability of SAE without computational complexity or cost.

Sparse autoencoders (SAEs) are a core interpretability tool for large language models, and progress on SAE architectures depends on benchmarks that reliably distinguish better SAEs from worse ones. We audit the SAE quality metrics in SAEBench, the de-facto standard SAE evaluation suite, through three complementary lenses: reseed noise on a fixed SAE, ground-truth correlation on synthetic SAEs, and discriminability across training trajectories. We find that two of these metrics, Targeted Probe Perturbation (TPP) and Spurious Correlation Removal (SCR), fail multiple lenses at their canonical settings and should not be used to evaluate SAEs. The other metrics show higher reseed noise and lower discriminability than the field assumes. The sae-probes variant of $k$-sparse probing is the most reliable metric we tested, but even sae-probes struggles to separate variants of the same SAE architecture. Our results show the field needs better SAE benchmarks.

Deep learning weather prediction models achieve remarkable predictive skill yet remain largely opaque: we know little about how they represent physical climate phenomena internally. Mechanistic interpretability through Sparse Autoencoders (SAEs) offers a principled route to decomposing these representations, but existing SAEs assume strictly linear feature superposition - a constraint ill-suited for the highly nonlinear atmospheric dynamics encoded in modern transformers. We introduce KAN-SAE, a sparse autoencoder whose encoder replaces the standard ReLU with learnable per-feature B-spline activations drawn from Kolmogorov-Arnold Networks (KANs), allowing each latent dimension to develop its own nonlinear gating profile. Applied to Sonny, KAN-SAE discovers 975 alive features (vs. 566 for a linear baseline, a 72% improvement) with 20% lower inter-feature redundancy and comparable reconstruction fidelity. Without any climate supervision, KAN-SAE identifies an interpretable European heatwave feature spatially concentrated over western Europe, and a western Pacific typhoon tracker confirmed by causal steering experiments. Our results demonstrate that nonlinear activations are essential for mechanistic interpretability of deep learning weather prediction models, recovering climate features that remain invisible to linear baselines.

Vision-Language-Action (VLA) policies translate language and visual inputs into robot actions, where their hidden representations directly shape closed-loop behavior. However, mechanistic interpretability tools from language and vision-language models do not transfer cleanly to VLAs: outputs are robot actions rather than human-readable tokens, and interventions can only be tested via expensive closed-loop rollouts. We propose an event-grounded interpretability pipeline that anchors SAE feature analysis to behavioral events rather than text contexts. End-effector keyframes are clustered within each task using visual, state, and temporal cues, linking SAE features to behaviorally salient events and, via optional VLM annotations, to semantic context. To our knowledge, our pipeline is among the first to ground SAE-based VLA analysis in closed-loop behavioral events. Across two simulation architectures and a real-robot study, event-grounded ranking yields the strongest causal effects on OpenVLA and transfers to the continuous action chunks of $π_{0.5}$. SAE is a sparse but imperfect intervention basis: usability varies with architecture and intervention site, and aggressive intervention reveals safety and interpretability limits. Overall, event-grounded SAE analysis emerges as a practical starting point for behavior-anchored VLA interpretability, motivating future work on SAE features beyond action-aligned coordinates, finer-grained closed-loop evaluation, and safe interventions for high-stakes VLA deployments. Code is available at https://github.com/xc-j/Event-SAE.

Large-scale pre-trained vision-language models like CLIP demonstrate remarkable zero-shot performance across diverse tasks. However, fine-tuning these models to improve downstream performance often degrades robustness against distribution shifts. Recent approaches have attempted to mitigate this trade-off, but often rely on computationally expensive text-guidance. We propose a novel method for robust fine-tuning, SAE-FT, which operates only on the model's visual representations. SAE-FT regularizes changes to these representations by penalizing the addition and removal of semantically meaningful features identified by a Sparse Autoencoder trained on the pre-trained model. This constraint prevents catastrophic forgetting and makes the fine-tuning process interpretable, enabling direct analysis of semantic changes. SAE-FT is both mechanistically transparent and computationally efficient, matching or exceeding state-of-the-art performance on ImageNet and its associated distribution shift benchmarks. Code is publicly available at: https://github.com/Fabian-Mor/sae-ft.

Sparse Autoencoders (SAEs) that can accurately reconstruct their input (minimizing distortion) by making efficient use of few features (minimizing the rate) often fail to learn monosemantic representations (highly interpretable), limiting their usefulness for mechanistic interpretability. In this paper, we characterise this tension in learning faithful, efficient, and interpretable explanations, introducing the Rate-Distortion-Polysemanticity tradeoff in SAEs. Under toy-modeling assumptions, we theoretically and empirically show that restricting the SAE to be monosemantic necessarily comes with an increase in rate and distortion. Assuming a generative model behind the input observations, we further demonstrate that the degree of polysemanticity of optimal SAEs is determined by the training data distribution, especially by the probability of features to co-occur. Finally, we extend the analysis to real-world settings by deriving necessary conditions that a polysemanticity measure should satisfy when the data-generating process is unknown, and we benchmark existing proxy metrics on SAEs trained on Large Language Models. Taken together, our findings show that polysemanticity is a data problem that should be accounted for when addressing it at the architectural and optimization level.

EEG foundation models achieve state-of-the-art clinical performance, yet the internal computations driving their predictions remain opaque: a barrier to clinical trust. We apply TopK Sparse Autoencoders (SAEs) across three architecturally distinct EEG transformers: SleepFM, REVE, and LaBraM to extract sparse feature dictionaries from their embeddings. By grounding these features in a clinical taxonomy (abnormality, age, sex, and medication), we benchmark monosemanticity and entanglement across architectures. A single hyperparameter procedure, driven by an intrinsic dictionary health audit, transfers robustly across all three architectures. Via concept steering, we introduce a "target vs. off-target" probe area metric to quantify steering selectivity and reveal three operational regimes: selectively steerable, encoded but entangled, and non-encoded. This framework exposes critical representational failures: "wrecking-ball" interventions that collapse global model performance, and clinical entanglements, such as age-pathology confounding, where it is impossible to suppress one concept without corrupting the other. Finally, a spectral decoder maps these interventions back to the amplitude spectrum, translating latent manipulations into physiologically interpretable frequency signatures, such as pathological slow-wave suppression and $α$-band restoration.

Sparse autoencoders (SAEs) are now standard tools for decomposing language model activations into interpretable features, and automated interpretability pipelines routinely assign each feature a short natural-language explanation. Existing critiques of this practice focus on polysemanticity -- one feature with many meanings -- or on whether explanations predict activations. We identify a complementary, structurally distinct problem we call descriptive collision: many distinct SAE features admit the same explanation. Reanalyzing the largest publicly-available dataset of human-annotated SAE features (Marks et al., 2025), comprising 722 annotated features across Gemma 2 2B and Pythia 70M, we find that the mean annotation string is reused across 3.07 features; 82.1% of features share their annotation with at least one other feature; and the single most common annotation string ("plural nouns") labels 101 distinct features spanning 18 layers and four model components. Information-theoretically, the average annotation resolves only 70% of feature identity. We formalize a property called discrimination, prove that current detection-style auto-interpretability scoring is invariant to collision, and propose two complementary corrective metrics -- collision-adjusted detection and discrimination scoring -- that explicitly penalize explanations that fail to distinguish a feature from its neighbors. The collision problem is independent of, and additive with, previously identified failure modes of auto-interpretability; ignoring it inflates reported feature interpretability by a quantity equal to roughly one-third of the bits required to identify a feature.

We introduce WriteSAE, a sparse autoencoder for the matrix updates written into recurrent language-model state. In Gated DeltaNet, Mamba-2, and RWKV-7, each token writes a matrix-shaped update to a recurrent cache; a residual-stream SAE has vector-shaped atoms and cannot replace that update directly. WriteSAE learns rank-1 matrix atoms with the same shape as the model's own write. This lets us test a direct replacement: at positions where the SAE activates an atom, we remove the model's write, insert the atom scaled by its SAE activation, and continue the forward pass. The atom gives a closer final token distribution than deleting the write on 92.4% of evaluated positions; averaged per atom, the rate is 89.8%. For Gated DeltaNet, a formula using the forget gate, read query, and output embedding predicts the resulting logit change with $R^2 = 0.98$. The same replacement test transfers to Mamba-2-370M at 88.1%. In generation, the formula chooses a write direction; writing it into three consecutive cache positions at $3\times$ the norm of the model's write makes tokens initially ranked 100--1000 by the unmodified model appear in 100% of continuations, up from 33.3%. To our knowledge this is the first cache-level steering intervention reported in a state-space or hybrid recurrent layer.

Unlearning specific concepts in text-to-image diffusion models has become increasingly important for preventing undesirable content generation. Among prior approaches, sparse autoencoder (SAE)-based methods have attracted attention due to their ability to suppress target concepts through lightweight manipulation of latent features, without modifying model parameters. However, SAEs trained primarily for sparse reconstruction do not explicitly enforce concept-wise separation, allowing semantically related concepts to share latent features. To address this, we propose SAEParate, which explicitly separates semantically overlapping concepts in the SAE latent space through concept-aware contrastive learning, supported by cross-attention-guided spatial aggregation that emphasizes concept-relevant regions. In addition, we enhance the encoder with a nonlinear transformation to increase its expressive capacity under this separation objective, enabling more concept-discriminative latent representations. Experiments on UnlearnCanvas demonstrate state-of-the-art performance, with particularly strong gains in joint style-object unlearning, a challenging setting where existing methods suffer from severe interference between target and non-target concepts.

Large language models have achieved remarkable capabilities across diverse tasks, yet their internal decision-making processes remain largely opaque, limiting our ability to inspect, control, and systematically improve them. This opacity motivates a growing body of research in mechanistic interpretability, with sparse autoencoders (SAEs) emerging as one of the most promising tools for decomposing model activations into sparse, interpretable feature representations. We introduce Qwen-Scope, an open-source suite of SAEs built on the Qwen model family, comprising 14 groups of SAEs across 7 model variants from the Qwen3 and Qwen3.5 series, covering both dense and mixture-of-expert architectures. Built on top of these SAEs, we show that SAEs can go beyond post-hoc analysis to serve as practical interfaces for model development along four directions: (i) inference-time steering, where SAE feature directions control language, concepts, and preferences without modifying model weights; (ii) evaluation analysis, where activated SAE features provide a representation-level proxy for benchmark redundancy and capability coverage; (iii) data-centric workflows, where SAE features support multilingual toxicity classification and safety-oriented data synthesis; and (iv) post-training optimization, where SAE-derived signals are incorporated into supervised fine-tuning and reinforcement learning objectives to mitigate undesirable behaviors such as code-switching and repetition. Together, these results demonstrate that SAEs can serve not only as post-hoc analysis tools, but also as reusable representation-level interfaces for diagnosing, controlling, evaluating, and improving large language models. By open-sourcing Qwen-Scope, we aim to support mechanistic research and accelerate practical workflows that connect model internals to downstream behavior.

Rare semantic innovations in high-dimensional, mission-critical domains are often obscured by dense background contexts, a challenge we define as feature density conflict. We introduce the Hybrid Hierarchical SAE (HH-SAE) to resolve this by factorizing manifolds into a nested hierarchy of Contextual ($L_0$), Atomic ($f_1$), and Compository ($f_2$) tiers. Evaluating across disparate manifolds, HH-SAE demonstrates superior resolution by ``fracturing'' administrative clinical labels into physiological modes and achieving a peak cross-domain zero-shot AUC of 0.9156 in fraud detection. Path ablation confirms the architecture's structural necessity, revealing a 13.46% utility collapse when contextual subtraction is removed. Finally, knowledge-steered synthesis achieves a +9.9% AUPRC lift over state-of-the-art generators, proving that HH-SAE effectively prioritizes high-order mechanistic innovation over environmental proxies to enable high-precision discovery in high-stakes environments.

Sparse autoencoders (SAEs) operationalise the linear representation hypothesis: they reconstruct model activations as sparse linear combinations of interpretable dictionary atoms, on the implicit assumption that activation space is well approximated by a globally linear structure. Their reconstruction error varies sharply across layers in ways that existing scaling laws, fitted at single layers, do not explain. We argue that this variation is the empirical trace of a geometric mismatch: where the activation manifold is curved and its intrinsic dimension varies across layers, no sparse linear dictionary can match it uniformly, and the SAE's width-sparsity scaling becomes a layer-dependent function of manifold structure rather than a single universal law. We conduct the first cross-layer SAE scaling study, fitting and regressing on 844 residual-stream Gemma Scope SAE checkpoints across 68 layers of Gemma 2 2B and 9B. Stage 1 fits a per-layer scaling-law surface; Stage 2 regresses the fitted parameters and the derived per-layer width exponents on four layerwise geometric summaries. We find that manifold geometry predicts the per-layer width exponent in both models, and that the same regression coefficients learnt on one model predict the other model's per-layer exponents under cross-model transfer, indicating a transferable geometric law. At the showcase layers where richer width grids permit identification of the asymptotic floor, we find that the fitted floor tracks the layerwise geometric ordering: higher curvature and intrinsic dimension correspond to higher floor, consistent with the irreducible second-order residual that any sparse linear approximation of a curved manifold must leave behind. SAEs thus encounter not a finite-resource ceiling but a geometry-dependent wall, set by the manifold they are trying to reconstruct.

Many features in pretrained Transformers span multiple layers: they emerge through stages of inference, persist in the residual stream, or are built jointly by parallel MLPs. Crosscoders (namely, sparse dictionaries trained jointly across layers) aim to recover these cross-layer features in a single shared latent space. We show that standard crosscoders largely fail at this purpose. Although their decoder weight norms spread evenly across layers, a functional coherence metric we introduce reveals that each latent's activation is effectively driven by only one or two layers on average. While functionally coherent latents act as human-interpretable concept detectors (e.g., US states and cities), the layer-localized latents that crosscoders predominantly learn collapse onto surface-level patterns such as digit detectors. We trace this failure to two structural limitations: unconstrained cross-layer parameterization and unregularized cross-layer dependence. We address both by introducing fmxcoders, which (i) replace the encoder and decoder with low-rank tensor factorizations that draw every latent's per-layer weights from a shared cross-layer basis, and (ii) apply stochastic layer masking, a denoising regularizer along the layer axis that penalizes latents whose contribution collapses when a single layer is masked. Across GPT2-Small, Pythia-410M, Pythia-1.4B, and Gemma2-2B, fmxcoders lift mean probing F1 by 10-30 points, surpassing per-layer SAE baselines that standard crosscoders fail to reach, reduce reconstruction MSE by 25-50%, and roughly double mean functional coherence. An LLM-as-a-judge evaluation further shows that fmxcoders recover 3-13$\times$ more semantically coherent latents than standard crosscoders across all four base LLMs.

Sparse autoencoders (SAEs) have been used widely to decompose and interpret neural network activations, especially those of transformer language models. One key issue with SAEs is their inability to directly model multidimensional features. Instead, SAEs may tile such features by a set of independent directions that must be grouped together after the SAE training phase, impeding discoverability and interpretation of learned feature representations. We begin to address this issue by introducing the Sparse MIXture of Autoencoders (SMIXAE) architecture. Empirically, we provide evidence that SMIXAE models have success both in directly learning previously identified manifold structures, as well as finding novel structures, within the open source Gemma 2 2B and 9B models. Finally, we discuss several limitations and point towards areas for future work.

Sparse autoencoders (SAEs) decompose transformer residual streams into interpretable feature dictionaries, yet the relationship between SAE width and causal influence on model output has not been systematically characterised. We introduce causal dimensionality kappa(L, M, T), defined as the effective rank of the expected Jacobian outer product at layer L, and show it can be estimated via the SAE width sweep paired with attribution patching. Across seven SAE widths from 16,384 to 1,048,576 features on Gemma-2-2B layer 12, representational capacity grows 15.6x while causal capacity grows only 4.35x: a robust separation we term the representational-causal wedge. A saturating fit yields kappa-hat approximately 1,990 with kappa-hat / d_model = 0.86 and participation-ratio lower bound kappa_PR approximately 280. Crucially, kappa is invariant to model scaling: Gemma-2-9B and Gemma-2-2B yield identical N_causal = 328 at the same SAE width despite a 3.46x parameter increase (the count is forced to 2% of SAE width by calibration; the substantive empirical claim is shape invariance of the AtP score distribution under matched seq=512 conditions). Across eight network depths kappa is constant while the absolute attribution threshold drops 20x from layer 1 to layer 23. Five controls (architecture invariance, threshold robustness, geometric privilege, synthetic ground-truth recovery, and a four-cell encoder/decoder ablation) pin down what kappa measures and what it does not. Our findings establish kappa as a measurable, model-intrinsic property of transformer layers: sub-linearly recoverable by SAE width, invariant to model scaling, and structured across network depth.

Learning hierarchical features in Sparse Autoencoders (SAEs) is essential for capturing the structured nature of real-world data and mitigating issues like feature absorption or splitting. Existing works attempt to identify hierarchical relationships within independent feature sets by relying on activation coverage, the assumption that child feature should only activate when its parent feature activates. However, we demonstrate that this condition alone is insufficient; that is, it often produces false positives where parent and child concepts are semantically unrelated. To address this, we introduce a novel reconstruction condition that enforces a deeper functional link between hierarchical levels. By combining both activation and reconstruction constraints, we propose the Tree SAE, a model designed to learn hierarchical structures directly from within the feature set. Our results demonstrate that Tree SAEs significantly surpass the existing SAEs at learning hierarchical pairs while maintaining competitive performance to the state-of-the-art on several key benchmarks. Finally, we demonstrate the practical utility of our Tree SAE in mapping the geometry of child feature subspaces and uncovering the complex hierarchical concept structures encoded within large language models.

Vision-language models (VLMs) have advanced rapidly and are increasingly deployed in real-world applications, especially with the rise of agent-based systems. However, their safety has received relatively limited attention. Even the latest proprietary and open-weight VLMs remain highly vulnerable to adversarial attacks, leaving downstream applications exposed to significant risks. In this work, we propose a novel and lightweight adversarial attack detection framework based on sparse autoencoders (SAEs), termed SAEgis. By inserting an SAE module into a pretrained VLM and training it with standard reconstruction objectives, we find that the learned sparse latent features naturally capture attack-relevant signals. These features enable reliable classification of whether an input image has been adversarially perturbed, even for previously unseen samples. Extensive experiments show that SAEgis achieves strong performance across in-domain, cross-domain, and cross-attack settings, with particularly large improvements in cross-domain generalization compared to existing baselines. In addition, combining signals from multiple layers further improves robustness and stability. To the best of our knowledge, this is the first work to explore SAE as a plug-and-play mechanism for adversarial attack detection in VLMs. Our method requires no additional adversarial training, introduces minimal overhead, and provides a practical approach for improving the safety of real-world VLM systems.

Backdoor attacks on language models pose a significant threat to AI safety, where models behave normally on most inputs but exhibit harmful behavior when triggered by specific patterns. Detecting such backdoors through mechanistic interpretability remains an open challenge. We investigate two sparse autoencoder architectures -- Crosscoders and Differential SAEs (Diff-SAE) -- for isolating backdoor-related features in fine-tuned models. Using a controlled SQL injection backdoor triggered by year-based context ("2024" triggers vulnerable code, "2023" triggers safe code), we evaluate both approaches across LoRA and full-rank fine-tuning regimes on SmolLM2-360M. We find that Diff-SAE consistently and substantially outperforms Crosscoders for backdoor isolation. Diff-SAE achieves a Backdoor Isolation Score (BIS) of 0.40 with perfect precision (1.0) and zero false positive rate across most experimental conditions, while Crosscoders fail almost entirely with BIS below 0.02 in most cases. This performance gap holds across multiple transformer layers (14, 18, 22, 26) and both fine-tuning regimes, with full-rank fine-tuning producing particularly clean backdoor signals. Our results suggest that backdoors manifest as directional activation shifts rather than sparse feature activations, making difference-based representations fundamentally more effective for detection. These findings have important implications for AI safety monitoring and the development of interpretability tools for detecting model manipulation.

Sparse Autoencoders (SAEs) have become an important tool in mechanistic interpretability, helping to analyze internal representations in both Large Language Models (LLMs) and Vision Transformers (ViTs). By decomposing polysemantic activations into sparse sets of monosemantic features, SAEs aim to translate neural network computations into human-understandable concepts. However, common architectures such as TopK SAEs rely on a fixed sparsity level. They enforce the same number of active features (K) across all inputs, ignoring the varying complexity of real-world data. Natural data often lies on manifolds with varying local intrinsic dimensionality, meaning the number of relevant factors can change significantly across samples. This suggests that a fixed sparsity level is not optimal. Simple inputs may require only a few features, while more complex ones need more expressive representations. Using a constant K can therefore introduce noise in simple cases or miss important structure in more complex ones. To address this issue, we propose SoftSAE, a sparse autoencoder with a Dynamic Top-K selection mechanism. Our method uses a differentiable Soft Top-K operator to learn an input-dependent sparsity level k. This allows the model to adjust the number of active features based on the complexity of each input. As a result, the representation better matches the structure of the data, and the explanation length reflects the amount of information in the input. Experimental results confirm that SoftSAE not only finds meaningful features, but also selects the right number of features for each concept. The source code is available at: https://github.com/St0pien/SoftSAE.

Preference learning in large language models relies on reward models as proxies for human judgment. However, these models frequently exhibit preference instability, producing contradictory preference assignments in response to subtle, meaning-preserving input variations. We analyze this instability at the representation level under three semantic-preserving perturbation types: paraphrasing, pattern injection, and backdoor triggers. We attribute this instability to over-reliance on predictive yet brittle features, which we term unstable features, and isolate them via Sparse Autoencoders (SAEs) in a sparse latent space where benign and perturbed inputs activate distinctly separable patterns. Building on this separability, we propose two SAE-based instability mitigation strategies: SAE Feature Steering, which identifies and suppresses anomalously activated features at inference, and SAE Residual Correction, which learns adaptive adjustments over SAE features to restore correct preferences. Our methods substantially reduce incorrect preference assignments on harmlessness and hallucination benchmarks while preserving benign performance and general utility on other tasks, without retraining the reward model.

Sparse autoencoders (SAEs) have become central to mechanistic interpretability, decomposing transformer activations into monosemantic features. Yet existing analyses characterise features almost exclusively through top-activating token lists or decoder weight vectors, leaving the higher-order co-occurrence structure shared across features largely unexamined. We introduce a graph-structured representation in which each SAE feature is modelled as a token co-occurrence graph: nodes are the tokens most frequent near strong activations, and edges connect pairs that co-occur within local context windows. A custom WL-style, frequency-binned graph kernel then provides a similarity measure over this structural space. Applied as a proof of concept to features from a large SAE trained on GPT-2 Small and probed with a synthetic mixed-domain corpus, our clustering recovers heuristic motif families (punctuation-heavy patterns, language and script clusters, and code-like templates) that are not recovered by clustering on decoder cosine similarity. A token-histogram baseline achieves higher overall purity, so the contribution of the graph view is complementary rather than dominant: it surfaces structural relationships that token-frequency and decoder-weight views alone do not capture. Cluster assignments are stable across graph-construction hyperparameters and random seeds.

Sparse autoencoders (SAEs) are used to disentangle the dense, polysemantic internal representations of large language models (LLMs) into interpretable, monosemantic concepts. However, standard $\ell_1$-regularized SAEs suffer from feature starvation (dead neurons) and shrinkage bias, often requiring computationally expensive heuristic resampling and nondifferentiable hard-masking methods to bypass these challenges. We argue that feature starvation is not merely an empirical artifact of poor data diversity, but a fundamental optimization-geometric pathology of overcomplete dictionaries: the $\ell_1$-induced sparse coding map is unstable and fundamentally misaligned with shallow, amortized encoders. To address this structural instability, we introduce adaptive elastic net SAEs (AEN-SAEs), a fully differentiable architecture grounded in classical sparse regression. AEN-SAEs combine an $\ell_2$ structural term that enforces strong convexity and Lipschitz stability with adaptive $\ell_1$ reweighting that eliminates shrinkage bias and suppresses spurious features, thereby jointly controlling the curvature and interaction structure of the induced polyhedral geometry. Theoretically, we show that AEN-SAEs yield a Lipschitz-continuous sparse coding map and recover the global feature support under mild assumptions. Empirically, across synthetic settings and LLMs (Pythia 70M, Llama 3.1 8B), AEN-SAEs mitigate feature starvation without auxiliary heuristics while maintaining competitive reconstruction abilities.

The standard sparse-autoencoder (SAE) interpretability protocol labels each feature from its top-activating contexts and validates by single-feature steering. We propose the pairwise matrix protocol, co-varying steering coefficient with joint condition, and report three findings the standard one-corner protocol misses on Qwen3-1.7B-Instruct, replicated on Gemma-2-2B-it. First, a feature labelled "AI self-disclaimer" from its top contexts produces an inverted U-shape under a coefficient sweep: at c=+500 the model substitutes a fluent contemplative-philosopher voice for the disclaimer. Two further features anchor the criterion (one monotonic, one pure breakdown). Second, three near-orthogonal cluster-specific features that individually steer a philosophy-of-mind register, jointly suppressed at c=-500, damage grounded composition on recipes and engine explanations as well as introspective prompts; single-feature suppression at the same magnitude leaves controls intact. Third, a matched-geometry comparison of single-feature, joint, and random-direction perturbations (norm ~1.55, cosine ~0.64) yields three distinct output regimes: single-feature substitutes strategy filler, random direction substitutes diverse content, joint suppression alone produces placeholder text. Coherence loss is direction-pattern-dependent, not magnitude-dependent. All three findings reproduce on Gemma with model-specific damage signatures; the matched-geometry control is CI-separated by ~10x. The pipeline also locates a top causally responsible feature in Llama-3.1-8B-Instruct.

Sparse Autoencoders (SAEs) decompose large language model representations into interpretable features, but how these features interact under uncertainty remains poorly understood. We introduce Feature Rivalry -- negatively correlated SAE feature pairs -- and study whether rivalry serves as a mechanistic signature of model uncertainty in Gemma-2-2B using Gemma Scope SAEs. Through a controlled within-domain experiment on PopQA split by response entropy, we find that high-entropy questions produce significantly stronger feature rivalry at layers 0 and 12 relative to low-entropy questions (p=5.3x10^-26 and p=5.8x10^-5 respectively), localizing uncertainty to specific processing stages in the residual stream. We then test whether rivalry is causally upstream of model outputs via activation steering along rivalry axes -- finding that steering along the rivalry direction (vec_A - vec_B) causes more output changes than random directions at low steering multipliers across 15 of 20 rival feature pairs. Finally, a per-prompt rivalry score derived from pairwise cosine similarities of active SAE feature decoder vectors predicts answer correctness (AUROC=0.689), approaching but not matching softmax confidence (AUROC=0.808).

Brain MRI foundation models learn rich representations of anatomy, but interpreting what clinical information they encode remains an open problem. Standard sparse autoencoders (SAEs) suffer from severe feature collapse in deep transformer layers, and in Alzheimer's disease (AD) research, aging confounds nearly every clinical variable, making naive annotation unreliable. We propose GeoSAE, a geometry-guided SAE framework that uses the foundation model's learned manifold structure to prevent feature collapse and annotates each surviving feature via age-deconfounded partial correlations. Applied to ~14k T1-weighted MRI scans from the Alzheimer's Disease Neuroimaging Initiative (ADNI) and the Australian Imaging biomarkers and Lifestyle (AIBL) datasets, GeoSAE identifies a compact, fully interpretable feature set that predicts mild cognitive impairment (MCI)-to-AD conversion (AUC 0.746) using only 2% of the embedding dimensions, while comorbidity-annotated features achieve only chance-level performance. The identified features replicate across cohorts without retraining (r=0.97) and localize to neuroanatomically distinct regions consistent with Braak staging. This shows that geometry-guided SAEs can extract interpretable, biomarkers from frozen brain MRI foundation models.

Sparse autoencoders (SAEs) are widely used to extract interpretable features from neural network representations, often under the implicit assumption that concepts correspond to independent linear directions. However, a growing body of evidence suggests that many concepts are instead organized along low-dimensional manifolds encoding continuous geometric relationships. This raises three basic questions: what does it mean for an SAE to capture a manifold, when do existing SAE architectures do so, and how? We develop a theoretical framework that answers these questions and show that SAEs can capture manifolds in two fundamentally different ways: globally, by allocating a compact group of atoms whose linear span contains the entire manifold, or locally, by distributing it across features that each selectively tile a restricted region of the underlying geometry. Empirically, we find that SAEs suboptimally recover continuous structures, mixing the global subspace and local tiling solutions in a fragmented regime we call dilution. This explains why manifold structure is rarely visible at the level of individual concepts and motivates post-hoc unsupervised discovery methods that search for coherent groups of atoms rather than isolated directions. More broadly, our results suggest that future representation learning methods should treat geometric objects, not just individual directions, as the basic units of interpretability.

Large language models (LLMs) acquire most of their factual knowledge during the pre-training stage, through next token prediction. Subsequent stages of post-training often introduce new facts outwith the parametric knowledge, giving rise to hallucinations. While it has been demonstrated that supervised fine-tuning (SFT) on new knowledge may exacerbate the problem, the underlying mechanisms are still poorly understood. We conduct a controlled fine-tuning experiment, focusing on closed-book QA, and find latent directions that causally contribute to hallucinations. Specifically, we fine-tune Llama 3.1 8B, Gemma 2 9B and Mistral 7B v03 on seven distinct single QA datasets, controlling for the percentage of new knowledge and number of training epochs. By measuring performance on the test set, we validate that incrementally introducing new knowledge increases hallucinations, with the effect being more pronounced with prolonged training. We leverage pre-trained sparse autoencoders (SAEs) to analyze residual stream activations across various checkpoints for each model and propose Monotonic Relationship Feature Identification (MoRFI) for capturing causally relevant latents. MoRFI filters SAE features that respond monotonically to controlled fine-tuning data mixtures of a target property. Our findings show that exposure to unknown facts disrupts the model's ability to retrieve stored knowledge along a set of directions in the residual stream. Our pipeline reliably discovers them across distinct models, recovering knowledge through single-latent interventions.