The current state of the art in AI/ML rests on deep neural architectures, which, in general, suffer from a lack of interpretability. Interpretability is crucial to gleaning insights while analyzing experimental data, where quantitative predictions may not be adequate for a scientist. We present a three layer neural architecture, SAMPAT (Smooth Approximation via Multivariate Polynomials and Analytic Transformations), that can provably learn a continuous, everywhere differentiable function, that can approximate any smooth function arbitrarily closely. SAMPAT's approximant can be expressed as a closed and compact algebraic, analytic expression, providing complete interpretability. Experiments on synthetic and benchmark datasets indicate that SAMPAT yields competitive performance with simpler representations. For many tasks, a two layer SAMPAT suffices. By imposing restrictions on the connectivity between neurons, SAMPAT may be used to provide a range of approximants, including regular and trigonometric polynomials, rational expressions, Gaussians, mixtures of Gaussians, as well as arbitrary combinations of the same; without restrictions, it learns a suitable structure. SAMPAT may be used to factorize polynomials and model nonlinear systems. With the addition of skip connections, a 4 to 6 layer SAMPAT is adequate to represent a substantive range of methods widely used in AI/ML, allowing the choice of a model's family, not just its parameters, to also be optimized as part of the learning process.
A prominent research direction in mechanistic interpretability is learning sparse circuits over LLM components to reveal how they jointly produce model behavior. However, raw neurons are polysemantic, making learned circuits hard to interpret. Sparse autoencoder (SAE) features alleviate this, but their high dimensionality makes existing intervention-based circuit learning methods computationally prohibitive. We propose CircuitLasso, a scalable circuit-learning approach based on sparse linear regression. CircuitLasso recovers circuits whose structural accuracy matches that of state-of-the-art intervention-based methods on the benchmark data, at a fraction of the computational cost. For interpretability, CircuitLasso efficiently uncovers relationships among SAE features, showing how human-interpretable semantic features propagate through the model and influence its predictions. Finally, we validate the utility of our learned circuits by leveraging their insights to achieve comparable performance at substantially lower cost on a domain-generalization task.
Deep networks often exhibit a preference for "simple" solutions, and such a simplicity bias is widely believed to play a key role in generalization. Yet a broadly applicable, quantitative measure of simplicity remains elusive. We introduce polynomial representations as a distribution-aware, low-dimensional surrogate for neural functions: we approximate a network's predictive behavior along data-dependent interpolation paths using orthogonal polynomial bases, yielding a compact functional representation. We show that the effective degree of this representation serves as a practical simplicity metric that is predictive of generalization across tasks and architectures, and consistently outperforms existing generalization proxies such as sharpness. Finally, polynomial representations naturally yield a differentiable simplicity regularizer, which consistently improves generalization in image and text classification, fine-tuning contrastive vision-language models, and reinforcement learning.
Recent advances in generative AI, especially powerful Large Language Models (LLMs) and Large Reasoning Models (LRMs), raise concerns over the interpretability, safety and sustainability of these large and opaque AI models. The power of such architectures is derived not only from the scalability of deep neural networks, but also massively parallel hardware such as GPU clusters. The diffuse nature of deep neural networks gives them great function-approximation capability when provided with sufficient training data but imposes a cost in interpretability and computational efficiency. Observing that localised machine learning (ML) models tend to be more interpretable and computationally efficient than deep neural networks on small datasets, we reason by analogy that similar advantages may apply to specific localised hardware ML architectures. We argue that localised architectures with lower bandwidth but higher expressivity per node have the potential to be fundamentally more interpretable than deep neural networks running on GPU clusters while remaining competitive for smaller datasets. We then evaluate the suitability of various hardware ML paradigms for implementing such localised architectures and evaluate their per-node expressivity, energy efficiency and practical maturity of the technology required.