arXiv subjects

Alan Oursland

Publications and source records attributed to Alan Oursland.

5 recordsLinked to original sources

arXiv2026

Deriving Decoder-Free Sparse Autoencoders from First Principles

Gradient descent on log-sum-exp (LSE) objectives performs implicit expectation--maximization (EM): the gradient with respect to each component output equals its responsibility. The same theory predicts collapse without volume control analogous to the log-determinant in Gaussian mixture models. We instantiate the theory in a single-layer encoder with an LSE objective and InfoMax regularization for volume control. Experiments confirm the theory's predictions. The gradient--responsibility identity holds exactly; LSE alone collapses; variance prevents dead components; decorrelation prevents redundancy. The model exhibits EM-like optimization dynamics in which lower loss does not correspond to better features and adaptive optimizers offer no advantage. The resulting decoder-free model learns interpretable mixture components, confirming that implicit EM theory can prescribe architectures.

cs.LG↗

arXiv2025

Gradient Descent as Implicit EM in Distance-Based Neural Models

Neural networks trained with standard objectives exhibit behaviors characteristic of probabilistic inference: soft clustering, prototype specialization, and Bayesian uncertainty tracking. These phenomena appear across architectures -- in attention mechanisms, classification heads, and energy-based models -- yet existing explanations often rely on loose analogies to mixture models or post-hoc architectural interpretation. We provide a direct explanation. For any objective with log-sum-exp structure over distances or energies, the gradient with respect to each distance is exactly the negative posterior responsibility of the corresponding component: $\partial L / \partial d_j = -r_j$. The identity is algebraic, requiring only differentiability; it is a specialization of Fisher's identity, and its significance here is its address: standard neural objectives instantiate it without modification. The consequence is that gradient descent on such objectives performs generalized expectation-maximization implicitly, with responsibilities arising as gradients to be applied rather than auxiliary variables to be computed. This result unifies three regimes of learning: unsupervised mixture modeling, where responsibilities are fully latent; attention, where responsibilities are conditioned on queries; and cross-entropy classification, where supervision clamps responsibilities to targets. Our claims live at training time: the responsibility-weighted gradient dynamics recently documented in transformers follow from the objective's geometry. The in-context Bayesian computation that trained transformers perform at inference time is the endpoint of these dynamics, not their per-step content.

cs.LG↗

arXiv2025

Neural Networks Learn Distance Metrics

Neural networks may naturally favor distance-based representations, where smaller activations indicate closer proximity to learned prototypes. This contrasts with intensity-based approaches, which rely on activation magnitudes. To test this hypothesis, we conducted experiments with six MNIST architectural variants constrained to learn either distance or intensity representations. Our results reveal that the underlying representation affects model performance. We develop a novel geometric framework that explains these findings and introduce OffsetL2, a new architecture based on Mahalanobis distance equations, to further validate this framework. This work highlights the importance of considering distance-based learning in neural network design.

cs.LG↗

arXiv2024

Neural Networks Use Distance Metrics

We present empirical evidence that neural networks with ReLU and Absolute Value activations learn distance-based representations. We independently manipulate both distance and intensity properties of internal activations in trained models, finding that both architectures are highly sensitive to small distance-based perturbations while maintaining robust performance under large intensity-based perturbations. These findings challenge the prevailing intensity-based interpretation of neural network activations and offer new insights into their learning and decision-making processes.

cs.LG↗

arXiv2024

Interpreting Neural Networks through Mahalanobis Distance

This paper introduces a theoretical framework that connects neural network linear layers with the Mahalanobis distance, offering a new perspective on neural network interpretability. While previous studies have explored activation functions primarily for performance optimization, our work interprets these functions through statistical distance measures, a less explored area in neural network research. By establishing this connection, we provide a foundation for developing more interpretable neural network models, which is crucial for applications requiring transparency. Although this work is theoretical and does not include empirical data, the proposed distance-based interpretation has the potential to enhance model robustness, improve generalization, and provide more intuitive explanations of neural network decisions.

cs.LG↗