Sequential LLM defense deployment leads to risk exacerbation in 38.9% of cases due to anti-aligned updates in shared critical layers, addressed by conflict-guided layer freezing.
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Toy Models of Superposition
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abstract
Neural networks often pack many unrelated concepts into a single neuron - a puzzling phenomenon known as 'polysemanticity' which makes interpretability much more challenging. This paper provides a toy model where polysemanticity can be fully understood, arising as a result of models storing additional sparse features in "superposition." We demonstrate the existence of a phase change, a surprising connection to the geometry of uniform polytopes, and evidence of a link to adversarial examples. We also discuss potential implications for mechanistic interpretability.
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- abstract Neural networks often pack many unrelated concepts into a single neuron - a puzzling phenomenon known as 'polysemanticity' which makes interpretability much more challenging. This paper provides a toy model where polysemanticity can be fully understood, arising as a result of models storing additional sparse features in "superposition." We demonstrate the existence of a phase change, a surprising connection to the geometry of uniform polytopes, and evidence of a link to adversarial examples. We also discuss potential implications for mechanistic interpretability.
co-cited works
representative citing papers
WriteSAE introduces sparse autoencoders with rank-1 matrix atoms for recurrent state updates, allowing replacement tests that outperform deletion on 92.4% of positions and a formula predicting logit changes with R²=0.98.
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KANs with learnable univariate spline activations on edges achieve better accuracy than MLPs with fewer parameters, faster scaling, and direct visualization for scientific discovery.
Linear representations of high-level concepts in LLMs are formalized via counterfactuals in input and output spaces, unified under a causal inner product that enables consistent probing and steering.
Subliminal learning occurs via compatible auxiliary and class output heads on task-unrelated inputs, even with random hidden layers or architecture changes, with theory and upper bounds on failure.
Event-grounded SAE analysis in VLA policies produces stronger causal effects on robot behavior than standard methods by anchoring features to clustered end-effector keyframes across simulations and real-robot tests.
In two-layer networks, weak-to-strong training elicits the target feature direction from pre-trained subspaces and preserves correlated off-target features, unlike standard fine-tuning.
SLIM decomposes LLM hidden states via sparse autoencoders with learnable gates to enable precise, interpretable steering of molecular properties, yielding up to 42.4-point gains on the MolEditRL benchmark.
A framework using sparse autoencoders decomposes concept-level forgetting in supervised continual learning into apparent deletion, recoverability, and decodability, showing substantial recoverability under linearity and degrading decodability with added tasks.
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Compositional interpretability defines explanations as commuting syntactic-semantic mapping pairs grounded in compositionality and minimum description length, with compressive refinement and a parsimony theorem guaranteeing concise human-aligned decompositions.
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Winner-take-all linear memory capacity scales as d² ~ n log n due to extreme values; listwise retrieval via Tail-Average Margin yields d² ~ n with exact asymptotic theory.
Manifold steering along activation geometry induces behavioral trajectories matching the natural manifold of outputs, while linear steering produces off-manifold unnatural behaviors.
A four-step recipe partitions the input space using interchange intervention behavior to diagnose where causal abstractions hold and to guide improvements, demonstrated by recovering a full hypothesis from scratch in a toy logic task.
CNN classifiers work by holographic superposition and destructive interference in pixel space rather than selecting cleaned features, as proven by a new adjoint inversion framework that also yields a covariance-volume channel selection algorithm.
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Uncertainty and correctness in LLMs are encoded by distinct feature populations, with suppression of confounded features improving accuracy and reducing entropy.
Large language models encode relational bindings via a cell-based representation: a low-dimensional linear subspace in which each cell corresponds to an entity-relation index pair and attributes are retrieved from the matching cell.
Local linearity of LLM layers enables LQR-based closed-loop activation steering with theoretical tracking guarantees.
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citing papers explorer
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Defenses at Odds: Measuring and Explaining Defense Conflicts in Large Language Models
Sequential LLM defense deployment leads to risk exacerbation in 38.9% of cases due to anti-aligned updates in shared critical layers, addressed by conflict-guided layer freezing.
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WriteSAE: Sparse Autoencoders for Recurrent State
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Crafting Reversible SFT Behaviors in Large Language Models
LCDD creates sparse carriers for SFT behaviors that SFT-Eraser can reverse, with ablations showing the sparse structure enables causal control.
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The Linear Representation Hypothesis and the Geometry of Large Language Models
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Learning Through Noise: Why Subliminal Learning Works and When It Fails
Subliminal learning occurs via compatible auxiliary and class output heads on task-unrelated inputs, even with random hidden layers or architecture changes, with theory and upper bounds on failure.
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Event-Grounded Sparse Autoencoders for Vision-Language-Action Policies
Event-grounded SAE analysis in VLA policies produces stronger causal effects on robot behavior than standard methods by anchoring features to clustered end-effector keyframes across simulations and real-robot tests.
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The Mechanism of Weak-to-Strong Generalization: Feature Elicitation from Latent Knowledge
In two-layer networks, weak-to-strong training elicits the target feature direction from pre-trained subspaces and preserves correlated off-target features, unlike standard fine-tuning.
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SLIM: Sparse Latent Steering for Interpretable and Property-Directed LLM-Based Molecular Editing
SLIM decomposes LLM hidden states via sparse autoencoders with learnable gates to enable precise, interpretable steering of molecular properties, yielding up to 42.4-point gains on the MolEditRL benchmark.
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Lost or Hidden? A Concept-Level Forgetting in Supervised Continual Learning
A framework using sparse autoencoders decomposes concept-level forgetting in supervised continual learning into apparent deletion, recoverability, and decodability, showing substantial recoverability under linearity and degrading decodability with added tasks.
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SMIXAE: Towards Unsupervised Manifold Discovery in Language Models
SMIXAE is a new mixture-of-autoencoders architecture that learns multidimensional manifolds directly from transformer activations, recovering known structures and identifying novel ones in Gemma 2 2B and 9B models.
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From Mechanistic to Compositional Interpretability
Compositional interpretability defines explanations as commuting syntactic-semantic mapping pairs grounded in compositionality and minimum description length, with compressive refinement and a parsimony theorem guaranteeing concise human-aligned decompositions.
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What Cohort INRs Encode and Where to Freeze Them
Optimal INR freeze depth matches highest weight stable rank layer; SAEs reveal SIREN atoms are localized while FFMLP atoms trace cohort contours with causal impact on PSNR.
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Sharp Capacity Thresholds in Linear Associative Memory: From Winner-Take-All to Listwise Retrieval
Winner-take-all linear memory capacity scales as d² ~ n log n due to extreme values; listwise retrieval via Tail-Average Margin yields d² ~ n with exact asymptotic theory.
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Manifold Steering Reveals the Shared Geometry of Neural Network Representation and Behavior
Manifold steering along activation geometry induces behavioral trajectories matching the natural manifold of outputs, while linear steering produces off-manifold unnatural behaviors.
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Bucketing the Good Apples: A Method for Diagnosing and Improving Causal Abstraction
A four-step recipe partitions the input space using interchange intervention behavior to diagnose where causal abstractions hold and to guide improvements, demonstrated by recovering a full hypothesis from scratch in a toy logic task.
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Adjoint Inversion Reveals Holographic Superposition and Destructive Interference in CNN Classifiers
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Sparsity as a Key: Unlocking New Insights from Latent Structures for Out-of-Distribution Detection
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Are LLM Uncertainty and Correctness Encoded by the Same Features? A Functional Dissociation via Sparse Autoencoders
Uncertainty and correctness in LLMs are encoded by distinct feature populations, with suppression of confounded features improving accuracy and reducing entropy.
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Cell-Based Representation of Relational Binding in Language Models
Large language models encode relational bindings via a cell-based representation: a low-dimensional linear subspace in which each cell corresponds to an entity-relation index pair and attributes are retrieved from the matching cell.
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Local Linearity of LLMs Enables Activation Steering via Model-Based Linear Optimal Control
Local linearity of LLM layers enables LQR-based closed-loop activation steering with theoretical tracking guarantees.
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Psychological Steering of Large Language Models
Mean-difference residual stream injections outperform personality prompting for OCEAN trait steering in most LLMs, with hybrids performing best and showing approximate linearity but non-human trait covariances.
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Can Cross-Layer Transcoders Replace Vision Transformer Activations? An Interpretable Perspective on Vision
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Beyond Semantics: Disentangling Information Scope in Sparse Autoencoders for CLIP
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Isotropic Activation Functions Enable Deindividuated Neurons and Adaptive Topologies
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Scaling and evaluating sparse autoencoders
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Eliciting Latent Predictions from Transformers with the Tuned Lens
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Structure Retention in Embedding Spaces as a Predictor of Benchmark Performance
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Are Sparse Autoencoder Benchmarks Reliable?
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A Distributional View for Visual Mechanistic Interpretability: KL-Minimal Soft-Constraint Principle
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Domain Restriction via Multi SAE Layer Transitions
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Toward Stable Value Alignment: Introducing Independent Modules for Consistent Value Guidance
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Towards Understanding Continual Factual Knowledge Acquisition of Language Models: From Theory to Algorithm
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Decomposing and Steering Functional Metacognition in Large Language Models
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Architecture, Not Scale: Circuit Localization in Large Language Models
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A Single Neuron Is Sufficient to Bypass Safety Alignment in Large Language Models
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Reason to Play: Behavioral and Brain Alignment Between Frontier LRMs and Human Game Learners
Frontier LRMs match human game-learning behavior and predict fMRI signals an order of magnitude better than RL or Bayesian agents because of their in-context game-state representations.
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The Granularity Axis: A Micro-to-Macro Latent Direction for Social Roles in Language Models
LLMs organize prompted social roles along a dominant, stable, and causally steerable granularity axis in representation space that runs from micro to macro levels.
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When Language Overwrites Vision: Over-Alignment and Geometric Debiasing in Vision-Language Models
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The Override Gap: A Magnitude Account of Knowledge Conflict Failure in Hypernetwork-Based Instant LLM Adaptation
Knowledge conflicts in hypernetwork LLM adaptation stem from constant adapter margins losing to frequency-dependent pretrained margins; selective layer boosting and conflict-aware triggering raise deep-conflict accuracy to 71-72.5% on Gemma-2B and Mistral-7B.
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Harmful Intent as a Geometrically Recoverable Feature of LLM Residual Streams
Harmful intent is linearly separable in LLM residual streams across 12 models and multiple architectures, reaching mean AUROC 0.982 while showing protocol-dependent directions and strong generalization to held-out harm benchmarks.
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Representation-Guided Parameter-Efficient LLM Unlearning
REGLU guides LoRA-based unlearning via representation subspaces and orthogonal regularization to outperform prior methods on forget-retain trade-off in LLM benchmarks.
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Geometric Limits of Knowledge Distillation: A Minimum-Width Theorem via Superposition Theory
Student networks are limited to d_S * g(α) features via superposition, creating a permanent importance-weighted loss floor in distillation that cannot be overcome by training.
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In your own words: computationally identifying interpretable themes in free-text survey data
A computational framework identifies more coherent themes in free-text survey data on race, gender, and sexual orientation than previous methods, with applications for survey design, explaining variation, and detecting identity discordance.
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Emergent Manifold Separability during Reasoning in Large Language Models
Reasoning in LLMs produces a transient geometric pulse in which concept manifolds untangle into linearly separable subspaces immediately before computation and compress afterward.
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L2R: Low-Rank and Lipschitz-Controlled Routing for Mixture-of-Experts
L2R improves MoE performance by routing in a low-rank space with Lipschitz-controlled saturated inner-product scoring and multi-anchor mechanisms.
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Deep sequence models tend to memorize geometrically; it is unclear why
Deep sequence models develop geometric memory in embeddings that encodes novel global relationships, transforming l-fold composition tasks into 1-step navigation via a natural spectral bias connected to Node2Vec.