Sparse Autoencoder Features

Reinforcement learning (RL) is widely utilized in large language model training to improve targeted capabilities, yet how RL reshapes a model remains poorly understood. Prior attempts to explain how RL works largely offer behavioral perspectives, leaving open what RL gives a model at the representation level: can RL create genuinely novel features, and which existing features does it enhance or suppress? Recent developments in mechanistic interpretability suggest sparse autoencoders (SAEs) as a promising lens to decompose internal activations into human-interpretable features; however, they cannot be directly applied to tracking change across training. In this work, we introduce Fixed-SAE Track, a framework that trains one shared SAE per considered layer on activations pooled across the base model and all RL checkpoints, holding every feature direction fixed so that representation shifts are rigorously defined through the activations of interpretable SAE latents, including the detection of emerging novel features. Validated across multiple datasets and RL algorithms, we find that RL-induced drift is small, gradual, concept specific, and concentrated in late layers, mainly enhancing the sampling rates of a small set of ladder tokens, formatting scaffolding such as step breaks and answer delimiters, rather than reshaping problem content. Steering these features into the base model recovers around 80% of RL's performance gain, suggesting that RL primarily elicits capabilities the model already possesses, much as steering does. We further design a synthetic benchmark with features known by construction to test whether RL can instill genuinely novel features. We believe Fixed-SAE Track provides a principled approach to tracking representation shifts and offers representational evidence for understanding how reinforcement learning changes the inner representation of LLMs.

Foundation models are increasingly adapted through fine-tuning, model editing, and alignment procedures while retaining previously acquired capabilities. Understanding the internal computations that support these adaptations is therefore becoming increasingly important for continual model evolution. Sparse autoencoders (SAEs) provide interpretable feature dictionaries for residual-stream activations and sublayer outputs, but it remains unclear how state features and update features interact to produce downstream residual features. In this work, we focus on MLP updates as a first test case. We construct a transition atlas of triples $s_k + u_j \rightarrow t_\ell$, where a residual-state feature and an MLP-update feature jointly predict a target residual feature, and validate candidate triples by ablating the decoded update feature. In a 20M-token Pythia-160M $L_7 \rightarrow L_8$ run, we find 38,125 strong ablation-effect transitions, but 88.0% have both state-target and update-target decoder cosine similarity below 0.7. As a preliminary cross-model check, a run of 20M-token Gemma-3-4B $L_{21} \rightarrow L_{22}$ causally validates only the top 30,000 ranked candidate triples by ablating the decoded update feature, and 53.6% of strong-effect triples have both state-target and update-target decoder cosine similarity below 0.7. The Gemma result is directionally consistent with Pythia, but weaker, since update-target cosine recovers many of the strongest Gemma effects and the run is not a full-atlas causal validation. Ultimately, our results suggest that feature flow atlases can serve as diagnostics of representation-update mechanisms and thereby inform tools for steering model updates. Future work will validate more complex patterns across layers, models, and SAE families.

Sparse autoencoder (SAE)-based steering has been widely used to address knowledge conflicts by guiding LLMs to be more faithful to the contextual knowledge. Existing methods usually perform mass steering, which modifies a large batch of SAE features identified via correlation-based methods. However, due to the inaccurate correlation and the neglected feature interactions, mass steering methods fail to precisely identify the features that play the key roles in steering and introduce a large number of redundant ones, which add noise and weaken the steering effects. Our empirical studies reveal that steering only a small subset of the identified features can achieve comparable or even better performance. Motivated by this finding, we propose Key Path Identification (KPI), a novel method that identifies key steering features characterized by strong causal dependencies with both upstream and downstream features. From these features, KPI constructs key paths and steers through less feature modifications. In this way, KPI advances SAE-based steering from quantity-driven to quality-focused, offering a perspective for more precise and interpretable model editing. Experiments in RAG tasks with knowledge conflicts show that our method improves the accuracy by 18% on average compared to the best baseline of mass steering, effectively filtering redundant features, alleviating side effects and demonstrating the core role of key paths in steering.

Sparse autoencoders (SAEs) are proposed to extract numerous features from large language model (LLM) representations, yet explaining these features still relies primarily on external observation. This reliance leads to superficial explanations inferred from observed model behavior and computational inefficiency from collecting such behavioral evidence at scale. We introduce SAEVerbalizer, a framework that injects SAE decoder directions into an LLM's representations and fine-tunes the LLM's downstream layers to generate natural-language explanations of the injected features. Once trained, the resulting verbalizer explains SAE features directly from decoder directions, addressing both limitations. Our experiments show that the learned verbalization capability generalizes to unseen features, transfers across separately trained SAE dictionaries, and, with a lightweight adapter, extends to SAE features from different LLMs. Intervention experiments show that injecting multiple directions yields an explanation combining their meanings, while reversing individual directions produces corresponding meaning shifts.

Sparse autoencoders (SAEs) have helped uncover mechanistic explanations for LLM behaviours such as reasoning, jailbreaking etc., via understanding the corresponding task-relevant and causally effective features. To evaluate such mechanistic explanations, downstream studies must distinguish surface lexical features from genuinely high-level ones. However, neither an autointerp-based semantic description nor causal steering utility fully resolves the abstraction level of a feature. To this end, we introduce \emph{Feature Nonlocality} (FNL), defined as the entropy of the normalized per-position influence on an SAE feature's activation. We report that FNL correlates with existing LLM-based proxy metrics of feature semantic abstractness, and successfully distinguishes context-dependent reasoning features from token-driven ones, correctly assigning the higher FNL to the contextual feature in $73$--$84\%$ of randomly drawn pairs that consist of one contextual and one token-level feature. We demonstrate two downstream applications. We audit SAE-based features used for jailbreak mitigation and find surprisingly that most effective features are positional features with low FNL rather than genuinely recognizing harmful intents. We report that steering high-FNL features in DeepSeek-R1-Distill-Llama-8B improves MATH-500 accuracy by $4.6$ points over the unsteered model and outperforms steering low-FNL features, though the gains are model-specific. We conclude that FNL provides an LLM-independent, label-free, correlational witness of the abstraction level of an SAE feature, with applications in evaluating mechanistic explanations as well as selecting features for downstream interventions.

Controlling the behavior of large language models (LLMs) remains a critical challenge for AI alignment. Existing steering methods, such as Contrastive Activation Addition (CAA), typically rely on fixed single-layer interventions derived from aggregate activation differences. These methods impose a single intervention across semantically diverse inputs and often fail to sustain consistent behavioral changes across layers, limiting the effectiveness of the steering. In this work, we introduce CircuitSteer, a novel framework that leverages Sparse Autoencoders (SAEs) to identify and manipulate coherent semantic circuits distributed across multiple layers. By constructing a feature flow circuit based on feature co-activation and the geometric alignment of decoder directions, we isolate the specific multi-layer subcircuits responsible for a target behavior. We then synthesize dense steering vectors from these sparse features and apply multi-point interventions to guide the model's internal semantic trajectory. We evaluate CircuitSteer using contrastive examples across a diverse set of tasks, including toxicity, emotion-intensity, sycophancy, and refusal, spanning two model families. Across all models and datasets, CircuitSteer is the only method to consistently produce fluency-preserving interventions; competing methods either sacrifice text quality or lack coverage, failing entirely on complex behaviors like sycophancy and refusal. These results demonstrate that multi-layer circuit steering, enabled by enforcing geometric alignment among selected features, yields strictly more robust and effective behavioral control than static single-point interventions. Code is available at https://github.com/mehrshad-sdtn/CircuitSteer.

Multilingual large language models exhibit substantial performance differences across languages, while existing adaptation methods often require parameter updates and considerable multilingual training data. We propose an inference-time multilingual steering method that uses pretrained sparse autoencoders to identify and strengthen target-language-related features. Using multilingual parallel sentences, we compare SAE activations across languages and select a small number of layer-specific features associated with each target language. These features are decoded into steering signals and injected into the model's hidden states without additional training. Experiments with Gemma-3-12B-it show average accuracy improvements of 10.9 percentage points on XCOPA, 5.3 points on XNLI, and 1.9 points on MGSM.

The wide-scale use of sparse autoencoders (SAEs) as interpretability tools is limited by inconsistent links between SAE features and model behavior. Features with clear activation descriptions may have weak or unexpected causal effects; steering can vary across prompts or oppose the intended direction; and activation-based feature selection can miss features that produce the desired output change. Prior work has studied feature geometry inside the model, where features are computed. We instead study the geometry of changes in model logits caused by feature interventions. We introduce Feature-Effect Geometry Analysis (FEGA), an unsupervised framework that removes the same active SAE feature across contexts and analyzes the resulting cloud of logit changes. Across SAE variants, consistent one-dimensional effects are rare: few features behave like reusable directions. To interpret this variation, we distinguish value-like features, tied to static information such as factual attributes, from pointer-like features, associated with context-dependent operations. Value-like features more often exhibit structured, low-dimensional effects, although these effects typically span several directions. Pointer-like features, by contrast, predominantly exhibit diffuse effects. Our results show that a feature can be interpretable and causally relevant without providing a stable direction for steering.

Sparse autoencoder (SAE) features are used to interpret and steer large language models, yet whether a feature's causal role is stable across SAE families remains untested. Single-token features that activate on one vocabulary item provide the diagnostic case where ground truth permits direct comparison. We analyze 3.9M features across six models and three SAE families using zero-ablation at full layer depth. Single-token features cluster 4.7x tighter in decoder space and concentrate in early layers (Layer 0 in GPT2-Small; L0-L4 in Gemma). Ablating them yields Benjamini-Hochberg-significant logit reductions in 178 of 208 full-layer conditions, with depth controlling whether damage cascades downstream or shapes the output directly. Cross-family causal differences exceed within-family scale effects: on the same base model, GemmaScope and BatchTopK features remain causally anchored, while LlamaScope features are locally redundant. The target token's rank recovers to within 2x baseline 96-98% of the time after the same ablation, and a controlled activation-function comparison reverses sign within the same model, leaving training recipe as the residual candidate. Cross-family interpretability claims are therefore sensitive to training methodology, not just activation function or scale.

Sparse autoencoders (SAEs) are the standard for decomposing superposed neural representations into interpretable features, and evaluation relies predominantly on correlational recovery metrics -- cosine similarity between ground-truth directions and decoder atoms. We show this conflates two distinct claims: decoder-geometry alignment and encoder-activation behavior. We reproduce the superposition phase diagram of Elhage et al. (2022), identifying a convergence artifact at high sparsity and an under-described diffuse sharing regime at extreme overcompleteness. We reproduce the TopK-versus-L1 comparison of Gao et al. (2024), with direct evidence of L1 shrinkage. Our central result is causal: subjecting every recovered feature to ablation and steering, we find up to 77% of features passing a recovery bar (cosine >= 0.90) in a degraded SAE -- and 9% in a well-trained one -- are causally inert: the matched atom never fires when the feature is present, including matches at cosine ~1.000. We package the method as sae-causal-audit, a model-agnostic instrument with a deterministic pipeline. Re-auditing refines the finding: inertness decomposes by cause into structural inertness (antipodal-pair geometry, present in good SAEs) and competitive inertness (a TopK pathology of degraded SAEs), and by direction into read- and write-inertness, which five antipodal pairs dissociate completely -- unmonitorable yet steerable through the same atom, with steering specificities of 143-310 attached to zero ablation effects. We document why byte-exact reproducibility is unavailable by construction, and propose reporting it as a stack of claims with explicit scopes. Applying the instrument to a production SAE reproduces the pattern at small scale (14% inert) and surfaces an atom-collision signal: a handful of atoms recur as the nearest match for dozens of unrelated concepts, replicated across three batches.

Sparse autoencoders (SAEs) have become a useful tool for extracting interpretable features in language models. However, standard SAE architectures operate on individual token activations, meaning that the number of active features scales linearly with context length, and studying long model transcripts becomes difficult. We introduce turn-averaged SAEs, which represent a single Human or Assistant turn with a fixed number of features by learning to reconstruct the average model activation across the turn. We find that turn-averaged features describe a single turn's high-level characteristics more completely than per-token features when judged by an LLM. We also demonstrate that turn-averaged SAEs greatly simplify common downstream uses of SAEs like attribution graphs. Broadly, turn-averaged SAEs make interpretability techniques practical at long context lengths.

Sparse autoencoders (SAEs) provide useful decompositions of Transformer residual streams, but their learned features are usually named post hoc rather than directly connected to the Transformer's token vocabulary. We introduce Vocabulary-Aligned Sparse Autoencoder (VASAE), a method that trains SAE features under vocabulary-aligned anchoring and assigns each feature an intrinsic token name: the token string whose embedding is nearest to that feature. Without reducing reconstruction quality compared with a standard SAE, VASAE produces dictionaries with vocabulary-aligned features. Using a 0.8 cutoff on the nearest-token alignment score, dictionaries trained on GPT-2-small post-residual streams align about 90% of features in layers 0--10. In Llama-3.1-8B, representative shallow and middle-layer dictionaries contain strongly aligned features, including 92.8% in the shallow layer, while the representative final-layer dictionary shows limited alignment. After subtracting the sentence-level mean sparse code, case studies show that many remaining intrinsic token names are relevant to nearby input tokens. These results suggest that vocabulary-aligned anchoring can connect learned features to intrinsic token names during training, complementing post hoc interpretation of learned dictionaries.

Pre-trained transformers have demonstrated remarkable generalization abilities, at times extending beyond the scope of their training data. Yet, real-world deployments often face unexpected or adversarial data that diverges from training data distributions. Without explicit mechanisms for handling such shifts, model reliability and safety degrade, urging more disciplined study of out-of-distribution (OOD) settings for transformers. By systematic experiments, we present a mechanistic framework for delineating the precise contours of transformer model robustness. We find that OOD inputs, including subtle typos and jailbreak prompts, drive language models to operate on an increased number of fallacious concepts in their internals. We leverage this device to quantify and understand the degree of distributional shift in prompts, enabling a mechanistically grounded fine-tuning strategy to robustify LLMs. Expanding the very notion of OOD from input data to a model's private computational processes, a new transformer diagnostic at inference time is a critical step toward making AI systems safe for deployment across science, business, and government.

Sparse autoencoder (SAE) features are increasingly used to steer language models, but feature steering is rarely clean: the same intervention can behave inconsistently across contexts and perturb unrelated features. We introduce a pre-intervention screening framework for forecasting SAE steering side effects from feature statistics computed before steering. We operationalize side effects along two axes of steering modularity, effect stability and collateral spread, and evaluate GPT-2-small, Pythia-70M-deduped, Gemma-2-2B, and Llama-3.1-8B across ReLU, JumpReLU, and TopK SAE dictionaries. Across these settings, decoder geometry, activation statistics, co-activation structure, and direct-logit footprint predict steering modularity better than frequency-only and activation-magnitude baselines. The signal is strongest in GPT-2-small, Pythia-70M, and Llama-3.1-8B, where it survives residualization against magnitude-related confounds, and weaker in Gemma-2-2B. Held-out screening shows that ranking unseen features by predicted cleanliness can select features that steer more cleanly on fresh contexts, but the successful axis varies by setting: GPT-2 improves most cleanly, Pythia improves mainly on stability, Llama mainly on collateral, and Gemma only partially. A controlled Llama Scope width comparison shows that the predictive signal persists under a 32K-to-128K dictionary-width change, although the screening payoff becomes less stable. Overall, SAE steering side effects are predictable in advance, but the useful predictor signature and transferred modularity axis are model- and dictionary-setting dependent.

A central goal of cognitive neuroscience is to characterize the features that are represented by human language cortex. Artificial language models (LMs) have emerged as a powerful tool to address this challenge, but studies relating biological and artificial representations are often criticized as relating one black box to another. The present work introduces Augmented Sparse Encoding Models, an encoding framework that replaces dense LM hidden states with hierarchically-organized sparse autoencoder (SAE) features, while explicitly including surprisal as a predictor. Using this approach, we (i) produce interpretations of neural responses and (ii) test whether model-brain alignment reflects primary or idiosyncratic variation in LM representations. Using a high-field 7T fMRI dataset of eight participants listening to 200 linguistically diverse sentences, we first validate our modeling framework by recovering previous interpretations of voxel populations tuned to processing difficulty and meaning abstractness. We then interpret a previously-uncharacterized (but reliable) voxel population and find that it is tuned to people-related content. Next, we show that the fronto-temporal human language network is predicted by a common set of features across its constituent regions, but find that frontal regions are relatively well-explained by surprisal alone, even in the absence of LM-based features. Finally, we show that brain responses during language processing are not merely predictable from an arbitrary set of LM features. Rather, brain responses are best explained by the features that tend to capture the most general information encoded in LM representations, suggesting a nontrivial correspondence between brain and LM language representation.

Sparse autoencoder (SAE) features are increasingly used to interpret language models, with auto-generated natural-language labels serving as the primary interface for understanding what each feature represents. We ask whether these labels generalize: does a feature labeled for a concept actually track that concept across languages and scripts? Using Serbian digraphia as a controlled testbed--the same language written in both Latin and Cyrillic via deterministic transliteration--we first find that SAE feature sets activated by the same content in different languages, scripts, and wordings share substantial overlap (mean Jaccard 0.39 vs. 0.13 random baseline, peaking at 0.57), suggesting genuine cross-lingual semantic features. We then test whether auto-interpretation labels keep pace. They often do not: features whose labels describe semantic content miss the same meaning in Serbian up to 4x more often thanwithin English, and miss Serbian Cyrillic more than Serbian Latin--two scripts that are deterministic transliterations of each other--suggesting the failures align with how well each form is represented in training. The gap grows with network depth, yet the labels give no indication that they fail. These results suggest that auto-interpretation labels may reflect a feature's behavior on well-represented inputs rather than the concept itself.

We demonstrate that sparse autoencoders can extract interpretable features from Claude 3 Sonnet, a production-scale language model, addressing the open question of whether dictionary learning methods scale beyond small transformers. We trained sparse autoencoders with up to 34 million features on the model's middle layer residual stream, using scaling laws to guide hyperparameter selection. The resulting features are multilingual and multimodal (generalizing to images despite text-only training), respond to both concrete instances and abstract discussions of concepts, and can be used to steer model behavior in ways consistent with their interpretations. We find features corresponding to famous entities and locations, as well as more abstract concepts like sarcasm or errors in code. We also identify features relevant to ways in which language models might cause harm--including features representing deception, power-seeking, sycophancy, and bias--and show that these causally influence model outputs when manipulated. Additionally, we conduct analyses of feature interpretability, geometry, and computational function. However, significant limitations remain: our suite of features is incomplete, and we lack rigorous methods for evaluating whether our features faithfully capture model computations.

Sparse autoencoders (SAEs) have become a central tool for interpreting language models. However, two key SAE analyses that remain difficult to scale are (1) matching semantically similar features across multi-layers and (2) compressing large feature circuits into interpretable supernodes. Although these have been treated as separate problems, we show that both are instances of a more fundamental challenge, which we frame as the estimation of semantic distances between SAE features that lie on different activation manifolds. We introduce a distributional framework for this problem, in which each feature is represented not by a single decoder vector like in the literature, but by an activation-weighted distribution over the hidden states that express it. By projecting these distributions into a shared reference space and comparing them with Wasserstein distance, our method provides a unified semantic metric for cross-layer feature comparison. We prove that our representation is invariant to activation rescaling, stable under perturbations, and recovers true matches under finite-sample margin conditions. Empirically, our method outperforms decoder-vector and LLM-based baselines and captures subtle functional distinctions between related features. Notably, our method compresses large feature circuits into interpretable supernodes automatically.

Low-Rank Adaptation (LoRA) has emerged as a widely adopted approach for adapting large language models, yet the internal representational changes induced by LoRA fine-tuning remain insufficiently understood. In this work, we investigate the geometry of LoRA-induced representations using Sparse Autoencoders (SAEs). We introduce a delta activation framework that isolates the adapter-specific contribution to the residual stream. Using Gemma-2-9B with LoRA ranks 4, 8, 16, and 32, we train adapter-specific SAEs across multiple transformer layers and compare their learned feature spaces with pretrained SAE dictionaries. We evaluate representational alignment using cosine similarity between decoder directions, principal-angle analysis of feature subspaces, and Centered Kernel Alignment (CKA) between activation representations. Across layers and ranks, we consistently observe comparatively weak geometric alignment between LoRA-induced feature dictionaries and pretrained SAE features. Adapter-specific SAEs also reconstruct delta activations more effectively than pretrained SAEs, suggesting that LoRA updates occupy partially distinct representational structure within the residual stream. Additionally, feature density increases with rank and depth, while geometric divergence remains relatively stable across ranks. These findings provide empirical evidence that LoRA fine-tuning can induce feature structures that are not fully captured by pretrained interpretability dictionaries, with implications for mechanistic interpretability, adaptation analysis, and safety auditing of fine-tuned language models.

Intermediate layers of large language models (LLMs) best predict human brain responses to language, one of the most robust findings in computational neurolinguistics, yet why remains mechanistically unexplained. We address this gap by bridging sparse autoencoders (SAEs) from mechanistic interpretability with neural encoding models, decomposing GPT-2 XL and Llama-3.1-8B into 16K-32K interpretable features per layer. A human-validated taxonomy ($κ\geq 0.74$) reveals that semantic features alone recover 94% of peak encoding performance ($r=0.285$), substantially exceeding variance-matched baselines ($p<0.001$, $d=1.31$). Beyond this aggregate dominance, we test a novel cortical topography prediction: five semantic subcategories derived a priori from three independent neuroscience programs should map onto distinct brain regions. A formal convergence test confirms this alignment (Spearman $ρ=0.72$, $p<0.001$; hypergeometric $p=0.007$), demonstrating that SAE-discovered features recapitulate known cortical semantic organization at a granularity inaccessible to prior methods. SAE features further predict human reading times beyond lexical controls ($Δ\mathrm{logLik}=38.4$, $p<0.001$), and an exploratory prediction-error analysis provides preliminary evidence that the brain additionally encodes unexpected semantic content. Results generalize across English, Chinese, and French.

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 \textbf{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 \textbf{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 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 characterize a compositional architecture of literary primitives in two instruction-tuned large language models (Llama 3.1 8B-Instruct and Gemma 2 9B-IT) via sparse autoencoders on mid-depth residual streams. Four feature classes emerge: naming-gates that promote lexical tokens of a target affect, an eleven-self cluster of first-person register features, stylistic register modulators (show-don't-tell and defamiliarization), and compositional emotions that arise only from multi-feature steering. Under a forced-choice 5-LLM judge panel applied to a 27-category emotion taxonomy (Cowen-Keltner), Llama reaches full 27/27 coverage by combining naming-gates, multi-feature recipes, and single self-feature steering; Gemma reaches 23/27 with adoration as the single residual strict-fail. Under random judging, the per-cell pass probability is on the order of $10^{-3}$ and the expected number of two-seed false-positive cells across the catalog is negligible, so the observed coverage is not consistent with chance. A cross-architectural asymmetry sits in the strict-versus-soft judge contrast: on the same generations, judges agree more often on Llama outputs than on Gemma outputs because Llama outputs name the target affect more directly while Gemma outputs evoke it through scene and imagery. Both architectures contain self-features that serve simultaneously as register markers and as emotion emitters, including a single most-RLHF-loaded self-feature per architecture that intensifies the institutional Helper-AI persona at one operating regime and produces affect-categorizable output at the same calibrated coefficient. Methodologically, the paper presents a three-stage validation pipeline (logit-lens, LLM-rate, 5-LLM judge) with documented anti-patterns; the total compute is single-GPU and about 15 minutes per emotion-feature discovery cycle.

Embodied artificial intelligence is rapidly moving from research into real-world systems such as autonomous vehicles, mobile robots, and industrial machines. As these systems become more capable of perceiving, deciding, and acting in dynamic environments, they also introduce new challenges in safety, trust, governance, and operational reliability. This white paper summarizes key insights from the SAE World Congress 2026 panel session \textit{Embodied AI in Action}, which brought together experts from automotive, robotics, artificial intelligence, and safety engineering. The discussion highlighted the need to treat embodied AI as a systems challenge requiring engineering rigor, lifecycle governance, human-centered design, and evolving standards. The paper provides practical perspectives for executives, policymakers, and technical leaders seeking to adopt embodied AI responsibly. The panel reached broad agreement that long-term success will depend not only on advances in AI capability, but equally on safe and trustworthy deployment.

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.

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) 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).

Sparse autoencoders (SAEs) extract millions of interpretable features from a language model, but flat feature inventories aren't very useful on their own. Domain concepts get mixed with generic and weakly grounded features, while related ideas are scattered across many units, and there's no way to understand relationships between features. We address this by first constructing a strict domain-specific concept universe from a large SAE inventory using contrastive activations and a multi-stage filtering process. Next, we build two aligned graph views on the filtered set: a co-occurrence graph for corpus-level conceptual structure, organized at multiple levels of granularity, and a transcoder-based mechanism graph that links source-layer and target-layer features through sparse latent pathways. Automated edge labeling then turns these graph views into readable knowledge graphs rather than unlabeled layouts. In a case study on a biology textbook, these graphs recover coherent chapter and subchapter-level structure, reveal concepts that bridge neighboring topics, and transform messy sentence-level activity containing thousands of features into compact, readable views that illustrate the model's local activity. Taken together, this reframes a flat SAE inventory as an internal knowledge graph that converts feature-level interpretability into a global map of model knowledge and enables audits of reasoning faithfulness.

Although Sparse Autoencoders (SAEs) have mitigated the opacity of large language models (LLMs) by decomposing dense representations into sparse features, explaining these features still remains a central challenge. Current explanation methods, however, typically operate within an open-loop paradigm, failing to leverage mechanistic feedback for further refinement. In this paper, we propose SAEExplainer, a training framework that utilizes activation scores as an objective reward signal to train the model for self-correction and iterative bootstrapping. By iteratively verifying and correcting foundational explanations through a two-round optimization process, SAEExplainer achieves continuous improvement in its explanatory capabilities. This mechanism significantly reduces explanation hallucinations and reinforces causal triggering patterns. Extensive experiments demonstrate our approach improves upon established baselines across most metrics, especially in causal triggering and discriminative activation. The code is available at https://github.com/he-jingyi/SAEExplainer.