RICA replaces ICA's global generative model with local Riemannian geometry, introducing a disentanglement tensor based on the Hessian of the log-likelihood and Ricci curvature to measure pointwise disentanglement, which recovers sources across manifolds in controlled tests.
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Open Problems in Mechanistic Interpretability
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abstract
Mechanistic interpretability aims to understand the computational mechanisms underlying neural networks' capabilities in order to accomplish concrete scientific and engineering goals. Progress in this field thus promises to provide greater assurance over AI system behavior and shed light on exciting scientific questions about the nature of intelligence. Despite recent progress toward these goals, there are many open problems in the field that require solutions before many scientific and practical benefits can be realized: Our methods require both conceptual and practical improvements to reveal deeper insights; we must figure out how best to apply our methods in pursuit of specific goals; and the field must grapple with socio-technical challenges that influence and are influenced by our work. This forward-facing review discusses the current frontier of mechanistic interpretability and the open problems that the field may benefit from prioritizing.
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representative citing papers
Persona vectors form within the first 0.22% of LLM pretraining and remain effective for steering post-trained models, with continued refinement and transfer to other models.
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.
GAE reduces the faithfulness gap in dictionary-based explainers under distribution shift by geometrically realigning the ID dictionary to the OOD-active subspace, with a quadratic excess-loss bound.
fmxcoders improve cross-layer feature recovery in transformers via factorized weights and layer masking, delivering 10-30 point probing F1 gains, 25-50% lower MSE, doubled functional coherence, and 3-13x more coherent latents than standard crosscoders on GPT2-Small, Pythia, and Gemma2 models.
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.
Manifold steering along activation geometry induces behavioral trajectories matching the natural manifold of outputs, while linear steering produces off-manifold unnatural behaviors.
Linear readouts incur an Omega(d^{-1/2}) crosstalk floor that caps the Hanni template at d^{3/2} capacity, while threshold recovery succeeds at quadratic loads for s = O(d/log d) sparsity, resolving the apparent contradiction via distinct readout invariants.
Llama-3.1-8B computes sums for cyclic concepts using base-10 addition via task-agnostic Fourier features with periods 2, 5, and 10 rather than modular arithmetic in the concept period.
Diverse dictionary learning identifies intersections, complements, and dependency structures of latent variables from data X = g(Z) up to indeterminacies, and full identifiability when structural diversity is sufficient.
The Linear Centroids Hypothesis reframes network features as directions in centroid spaces of local affine experts, unifying interpretability methods and yielding sparser, more faithful dictionaries, circuits, and saliency maps.
Defines Decision Potential Surface (DPS) whose zero isohypse equals an LLM decision boundary and supplies a K-sample approximation algorithm with derived upper bounds on absolute, expected, and concentration errors.
Harder classification tasks produce neural representations whose accuracy collapses under binarization and shuffling while easier tasks remain robust, defining task complexity via the performance gap between full-precision and perturbed networks.
A vision transformer for runway keypoint regression is decomposed via K-SVD into content and style atoms; the model relies primarily on content atoms, enabling out-of-model-scope detection for runtime assurance in aviation.
LLMs perform in-context learning as trajectories through a structured low-dimensional conceptual belief space, with the structure visible in both behavior and internal representations and causally manipulable via interventions.
Bilinear autoencoders decompose neural activations into low-rank quadratic forms to discover interpretable multi-dimensional manifolds, improving reconstruction in language models and challenging linear representation assumptions.
In LLM agents, memory routing circuits emerge at 0.6B scale while content circuits appear only at 4B, and write/read operations recruit a pre-existing late-layer context hub instead of creating a new one, enabling a 76% accurate unsupervised failure diagnostic.
Counterfactual prompting effects on LLMs are often indistinguishable from those caused by meaning-preserving paraphrases, causing most previously reported demographic sensitivities to disappear under proper statistical comparison.
A small set of sparse autoencoder features in LLMs drives shifts between generous and selfish allocations in dictator games, with causal patching and steering confirming their role and generalization to other social games.
Stylistic rewrites of harmful prompts raise attack success rates from 3.84% to 36.8-65% across 31 frontier models, indicating weak generalization in safety refusals.
PAM, a complex-valued associative memory model, exhibits steeper power-law scaling in loss and perplexity than a matched real-valued baseline when trained on WikiText-103 from 5M to 100M parameters.
A functional similarity metric for ReLU networks uses normalized activation region signatures and MinHash to overcome parametric symmetries like neuron permutation and scaling.
SMDS analysis finds that temporal reasoning features in LLMs form distinct manifolds such as circles, lines, and clusters that reflect semantics, remain stable across models, support reasoning, and reshape with context.
Eigenanalysis of the empirical NTK surfaces feature directions that align with Fourier features in modular addition networks and grammatical features in Gemma-3-270M, outperforming PCA baselines on activations.
citing papers explorer
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Disentanglement Beyond Generative Models with Riemannian ICA
RICA replaces ICA's global generative model with local Riemannian geometry, introducing a disentanglement tensor based on the Hessian of the log-likelihood and Ricci curvature to measure pointwise disentanglement, which recovers sources across manifolds in controlled tests.
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Tracing Persona Vectors Through LLM Pretraining
Persona vectors form within the first 0.22% of LLM pretraining and remain effective for steering post-trained models, with continued refinement and transfer to other models.
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WriteSAE: Sparse Autoencoders for Recurrent State
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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Geometry-Adaptive Explainer for Faithful Dictionary-Based Interpretability under Distribution Shift
GAE reduces the faithfulness gap in dictionary-based explainers under distribution shift by geometrically realigning the ID dictionary to the OOD-active subspace, with a quadratic excess-loss bound.
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fmxcoders: Factorized Masked Crosscoders for Cross-Layer Feature Discovery
fmxcoders improve cross-layer feature recovery in transformers via factorized weights and layer masking, delivering 10-30 point probing F1 gains, 25-50% lower MSE, doubled functional coherence, and 3-13x more coherent latents than standard crosscoders on GPT2-Small, Pythia, and Gemma2 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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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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Linear-Readout Floors and Threshold Recovery in Computation in Superposition
Linear readouts incur an Omega(d^{-1/2}) crosstalk floor that caps the Hanni template at d^{3/2} capacity, while threshold recovery succeeds at quadratic loads for s = O(d/log d) sparsity, resolving the apparent contradiction via distinct readout invariants.
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Arithmetic in the Wild: Llama uses Base-10 Addition to Reason About Cyclic Concepts
Llama-3.1-8B computes sums for cyclic concepts using base-10 addition via task-agnostic Fourier features with periods 2, 5, and 10 rather than modular arithmetic in the concept period.
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Diverse Dictionary Learning
Diverse dictionary learning identifies intersections, complements, and dependency structures of latent variables from data X = g(Z) up to indeterminacies, and full identifiability when structural diversity is sufficient.
-
The Linear Centroids Hypothesis: Features as Directions Learned by Local Experts
The Linear Centroids Hypothesis reframes network features as directions in centroid spaces of local affine experts, unifying interpretability methods and yielding sparser, more faithful dictionaries, circuits, and saliency maps.
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Decision Potential Surface: A Theoretical and Practical Approximation of Large Language Model Decision Boundary
Defines Decision Potential Surface (DPS) whose zero isohypse equals an LLM decision boundary and supplies a K-sample approximation algorithm with derived upper bounds on absolute, expected, and concentration errors.
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Task complexity shapes internal representations and robustness in neural networks
Harder classification tasks produce neural representations whose accuracy collapses under binarization and shuffling while easier tasks remain robust, defining task complexity via the performance gap between full-precision and perturbed networks.
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Mechanistic Interpretability for Learning Assurance of a Vision-Based Landing System
A vision transformer for runway keypoint regression is decomposed via K-SVD into content and style atoms; the model relies primarily on content atoms, enabling out-of-model-scope detection for runtime assurance in aviation.
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Stories in Space: In-Context Learning Trajectories in Conceptual Belief Space
LLMs perform in-context learning as trajectories through a structured low-dimensional conceptual belief space, with the structure visible in both behavior and internal representations and causally manipulable via interventions.
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Bilinear autoencoders find interpretable manifolds
Bilinear autoencoders decompose neural activations into low-rank quadratic forms to discover interpretable multi-dimensional manifolds, improving reconstruction in language models and challenging linear representation assumptions.
-
What Happens Inside Agent Memory? Circuit Analysis from Emergence to Diagnosis
In LLM agents, memory routing circuits emerge at 0.6B scale while content circuits appear only at 4B, and write/read operations recruit a pre-existing late-layer context hub instead of creating a new one, enabling a 76% accurate unsupervised failure diagnostic.
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Compared to What? Baselines and Metrics for Counterfactual Prompting
Counterfactual prompting effects on LLMs are often indistinguishable from those caused by meaning-preserving paraphrases, causing most previously reported demographic sensitivities to disappear under proper statistical comparison.
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Understanding the Mechanism of Altruism in Large Language Models
A small set of sparse autoencoder features in LLMs drives shifts between generous and selfish allocations in dictator games, with causal patching and steering confirming their role and generalization to other social games.
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Adversarial Humanities Benchmark: Results on Stylistic Robustness in Frontier Model Safety
Stylistic rewrites of harmful prompts raise attack success rates from 3.84% to 36.8-65% across 31 frontier models, indicating weak generalization in safety refusals.
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Phase-Associative Memory: Sequence Modeling in Complex Hilbert Space
PAM, a complex-valued associative memory model, exhibits steeper power-law scaling in loss and perplexity than a matched real-valued baseline when trained on WikiText-103 from 5M to 100M parameters.
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Functional Similarity Metric for Neural Networks: Overcoming Parametric Ambiguity via Activation Region Analysis
A functional similarity metric for ReLU networks uses normalized activation region signatures and MinHash to overcome parametric symmetries like neuron permutation and scaling.
-
Hypothesis-Driven Feature Manifold Analysis in LLMs via Supervised Multi-Dimensional Scaling
SMDS analysis finds that temporal reasoning features in LLMs form distinct manifolds such as circles, lines, and clusters that reflect semantics, remain stable across models, support reasoning, and reshape with context.
-
Feature Identification via the Empirical NTK
Eigenanalysis of the empirical NTK surfaces feature directions that align with Fourier features in modular addition networks and grammatical features in Gemma-3-270M, outperforming PCA baselines on activations.
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ASGuard: Activation-Scaling Guard to Mitigate Targeted Jailbreaking Attack
ASGuard identifies tense-vulnerable attention heads via circuit analysis, trains precise scaling vectors on those activations, and applies them in preventative fine-tuning to reduce targeted jailbreaking success across four LLMs with minimal impact on utility or over-refusal.
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Explainable AI Isn't Enough! Rethinking Algorithmic Contestability
The paper defines algorithmic contestability as identifying evidence to overturn potentially incorrect decisions and identifies three types of such evidence that make decisions normatively indefensible under the decision maker's standards.
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Metaphor Is Not All Attention Needs
Poetic jailbreaks succeed because they induce distinct attention patterns in LLMs that are independent of harmful-content detection, not because models fail to recognize literary formatting.
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Do Linear Probes Generalize Better in Persona Coordinates?
Persona axes derived from contrastive prompts and PCA yield linear probes that generalize better than raw-activation probes across 10 datasets for deception and sycophancy.
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Do Activation Verbalization Methods Convey Privileged Information?
Activation verbalization methods for LLMs largely reflect the verbalizer model's parametric knowledge rather than privileged information from the target model's activations.
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Qwen-Scope: Turning Sparse Features into Development Tools for Large Language Models
Qwen-Scope provides open-source sparse autoencoders for Qwen models that function as practical interfaces for steering, evaluating, data workflows, and optimizing large language models.
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Internal Deployment in the AI Act
Interpretations of Articles 2(1), 2(6), and 2(8) of the AI Act support applying the regulation to internal AI deployment while allowing for R&D exceptions, with the provisions viewed as complementary.
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Mechanistic Interpretability Needs Philosophy
The paper claims that mechanistic interpretability needs philosophy as a partner to clarify concepts, refine methods, and navigate epistemic and ethical complexities in AI systems.
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There Will Be a Scientific Theory of Deep Learning
A mechanics of the learning process is emerging in deep learning theory, characterized by dynamics, coarse statistics, and falsifiable predictions across idealized settings, limits, laws, hyperparameters, and universal behaviors.
- Relational Linear Properties in Language Models: An Empirical Investigation
- High-Dimensional Statistics: Reflections on Progress and Open Problems