analiza aiqbench
The Spectral Neuron proposes a novel architecture bridging the gap between interpretable linear models and opaque deep neural networks by leveraging eigenvalues of learned symmetric matrices. This approach retains mathematical transparency regarding coefficient influence while scaling expressive power, offering researchers a new tool for analyzing feature importance in complex functions. The work represents significant theoretical progress in machine learning model interpretability rather than an immediate consumer product or policy shift.
The Spectral Neuron
arXiv:2608.08003v2 Announce Type: replace-cross Abstract: As machine learned models increase in complexity and expressive power, features of simpler models, such as intrinsic coefficient transparency and control over the shape of the modeled function are lost. On the one edge of the spectrum we have simple linear models that possess coefficient transparency, but have a limited expressive power. On the other edge we have neural networks, that have expressive power that improves with scaling, but are mostly opaque. In this work we develop the \emph{spectral neuron} concept: a scalar model given by $f(x)=\lambda_k (A_0 + A_1 x + ... + A_n x_n)$, with learned real symmetric matrices $A_0, ..., A_n$. The input enters the model through an affine matrix function, but the prediction is obtained by reading one of its eigenvalues. Thus, the model is nonlinear, but the source of nonlinearity is still mathematically explicit. This gives us a useful middle ground: the model can become more expressive as the matrix dimension grows, while retaining coefficient transparency through the learned matrices. For example, extremal eigenvalues yield convex or concave functions, semidefinite constraints on the coefficient matrices impose monotonicity, and the associated eigenspaces characterize local feature influence. We study coefficient transparency, feature-influence bounds, and shape-control properties of this model family, and then test whether it can be learned and scaled in practice. We develop a systematic study of this model family, bringing together spectral results from several mathematical literatures to characterize its expressivity, coefficient transparency, feature influence, and shape-control properties. Code available at https://github.com/alexshtf/spectral_neuron_paper.
Abstract:As machine learned models increase in complexity and expressive power, features of simpler models, such as intrinsic coefficient transparency and control over the shape of the modeled function are lost. On the one edge of the spectrum we have simple linear models that possess coefficient transparency, but have a limited expressive power. On the other edge we have neural networks, that have expressive power that improves with scaling, but are mostly opaque. In this work we develop the \emph{spectral neuron} concept: a scalar model given by $f(x)=\lambda_k (A_0 + A_1 x + ... + A_n x_n)$, with learned real symmetric matrices $A_0, ..., A_n$. The input enters the model through an affine matrix function, but the prediction is obtained by reading one of its eigenvalues. Thus, the model is nonlinear, but the source of nonlinearity is still mathematically explicit. This gives us a useful middle ground: the model can become more expressive as the matrix dimension grows, while retaining coefficient transparency through the learned matrices. For example, extremal eigenvalues yield convex or concave functions, semidefinite constraints on the coefficient matrices impose monotonicity, and the associated eigenspaces characterize local feature influence. We study coefficient transparency, feature-influence bounds, and shape-control properties of this model family, and then test whether it can be learned and scaled in practice. We develop a systematic study of this model family, bringing together spectral results from several mathematical literatures to characterize its expressivity, coefficient transparency, feature influence, and shape-control properties. Code available at this https URL.
Machine Learning (stat.ML); Machine Learning (cs.LG)
arXiv:2608.08003 [stat.ML]
(or arXiv:2608.08003v2 [stat.ML] for this version)
https://doi.org/10.48550/arXiv.2608.08003 Focus to learn more arXiv-issued DOI via DataCite
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.
Text integral sub licența deschisă a publicației · 344 cuvinte
Subiecte conexe
Neuromorphic Wireless Split Computing with Resonate-and-Fire Neurons
arXiv · 16 iun. 2026
LILA: Calibration-Free Structured Pruning of Large Language Models via Latent Spectral Geometry
arXiv · 11 sept. 2026
On the Interaction of Compressibility and Adversarial Robustness
arXiv · 30 sept. 2026
Random matrix theory of sparse neuronal networks with heterogeneous timescales
arXiv · 15 sept. 2026