arXiv:2606. 18538v1 Announce Type: new Abstract: One of the major difficulties in the mechanistic interpretability of neural networks is the occurrence of polysemanticity, which suggests that each neuron is typically responsible for multiple different tasks, impeding a clean interpretation of their function.
arXiv:2609.06862v1 Announce Type: new Abstract: Superposition refers to neural networks representing more features than they have dimensions. It offers a possible explanation for polysemantic neurons...
The paper introduces a pointwise generalization theory for fully connected deep neural networks, using a pointwise Riemannian Dimension derived from eigenvalues of learned feature representations across layers. This framework provides hypothesis-dependent, representation-aware generalization bounds that are significantly tighter than traditional size- or norm-based approaches, both theoretically and experimentally. The authors analytically identify structural properties that explain deep networks’ tractability and empirically show that the pointwise Riemannian Dimension captures feature compression, over‑parameterization effects, and optimizer bias.
The paper develops a mathematical theory of superposition in neural networks using frame theory and compressed sensing. It shows that a sparse binary vector of active features can be encoded by an overcomplete dictionary and recovered via a ReLU operation with a suitable bias. The authors prove recovery theorems for both random-support and worst-case support settings, providing high-probability guarantees for low-coherence dictionaries and a sharp criterion for sparsity levels, with explicit results for Gaussian random matrices and equiangular tight frames.
arXiv:2503. 07325v2 Announce Type: replace Abstract: Understanding and certifying the behavior of modern deep neural networks remains a fundamental challenge in reliable machine learning.
The paper argues that the linear representation hypothesis—where neural activations encode concepts as linear mixtures—breaks down under superposition, causing linear decision boundaries to lose linearity after projection. Classical sparse coding with per‑sample inference can recover latent factors, but sparse autoencoders (SAEs) amortise this inference into a fixed encoder, creating a systematic gap that persists across training sizes, latent dimensions, and sparsity levels. Experiments show that the failure of SAEs under out‑of‑distribution compositional shifts stems from poor dictionary learning rather than inference, and that a good dictionary can solve the problem at all tested scales, highlighting scalable dictionary learning as the key open challenge.
arXiv:2510. 04500v3 Announce Type: replace Abstract: This work demonstrates how increasing the number of neurons in a network without increasing its total number of non-zero parameters improves performance.
arXiv:2511. 09432v2 Announce Type: replace Abstract: Machine learning (ML) models achieve remarkable performance but remain hard to interpret due to their scale and complexity.
arXiv:2608.20812v1 Announce Type: new Abstract: We develop constructive approximation and learning guarantees for shallow neural models with infinite-dimensional inputs observed through finitely many...
arXiv:2606. 02385v1 Announce Type: cross Abstract: Sparse Autoencoders (SAEs) have found success parsing neural representations into interpretable concepts, providing a basis for understanding and control.
The paper investigates how neural representations that use superposition can encode more features than their dimensionality. It derives sharp dimension thresholds for computing Boolean gates with a single threshold layer, distinguishing between two error criteria: a vanishing expected error count and high‑probability correctness of every output. The study reveals that the expected‑count threshold follows a ball geometry, while joint reliability follows a box geometry, and provides explicit thresholds for conjunction, disjunction, and majority gates, including a transition analysis for pairwise conjunction.
arXiv:2609. 19077v1 Announce Type: cross Abstract: Formal explainability provides mathematically grounded justifications for individual predictions.