5 papers
Scaling Laws from Sequential Feature Recovery: A Solvable Hierarchical Model
Arie Wortsman-Zurich, Hugo Tabanelli, Yatin Dandi +2
We propose a simple mechanism by which scaling laws emerge from feature learning in multi-layer networks. We study a high-dimensional hierarchical target that is a globally high-de…
Deep Learning as Neural Low-Degree Filtering: A Spectral Theory of Hierarchical Feature Learning
Yatin Dandi, Matteo Vilucchio, Luca Arnaboldi +2
Understanding how deep neural networks learn useful internal representations from data remains a central open problem in the theory of deep learning. We introduce Neural Low-Degree…
Deep Learning of Compositional Targets with Hierarchical Spectral Methods
Hugo Tabanelli, Yatin Dandi, Luca Pesce +1
Why depth yields a genuine computational advantage over shallow methods remains a central open question in learning theory. We study this question in a controlled high-dimensional…
Computational Thresholds in Multi-Modal Learning via the Spiked Matrix-Tensor Model
Hugo Tabanelli, Pierre Mergny, Lenka Zdeborova +1
We study the recovery of multiple high-dimensional signals from two noisy, correlated modalities: a spiked matrix and a spiked tensor sharing a common low-rank structure. This sett…
Reentrant localisation transitions and anomalous spectral properties in off-diagonal quasiperiodic systems
Hugo Tabanelli, Claudio Castelnovo, Antonio Å trkalj
We investigate the localisation properties of quasiperiodic tight-binding chains with hopping terms modulated by the interpolating Aubry-André-Fibonacci (IAAF) function. This off-…