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.
SASA replaces single-vector decoders in SAEs with learned subspaces plus block sparsity and nuclear-norm regularization, proving that a single group becomes the global minimizer once block size meets intrinsic dimension and yielding polynomial rather than exponential sample complexity.
SAEs used for layer selection with raw task vectors outperform subspace projection and raise math reasoning accuracy on Gemma-3-4B-IT.
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.
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.
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