10 papers · 1 filter
Sharp Capacity Scaling of Spectral Optimizers in Learning Associative Memory
Juno Kim, Eshaan Nichani, Denny Wu +2
Spectral optimizers such as Muon have recently shown strong empirical performance in large-scale language model training, but the source and extent of their advantage remain poorly…
Emergence and scaling laws in SGD learning of shallow neural networks
Yunwei Ren, Eshaan Nichani, Denny Wu +1
We study the complexity of online stochastic gradient descent (SGD) for learning a two-layer neural network with neurons on isotropic Gaussian data: $f_*(\boldsymbol{x}) = \sum…
Quantitative Bounds for Length Generalization in Transformers
Zachary Izzo, Eshaan Nichani, Jason D. Lee
We study the problem of length generalization (LG) in transformers: the ability of a model trained on shorter sequences to maintain performance when evaluated on much longer, previ…
On the Statistical Query Complexity of Learning Semiautomata: a Random Walk Approach
George Giapitzakis, Kimon Fountoulakis, Eshaan Nichani +1
Semiautomata form a rich class of sequence-processing algorithms with applications in natural language processing, robotics, computational biology, and data mining. We establish th…
Learning Compositional Functions with Transformers from Easy-to-Hard Data
Zixuan Wang, Eshaan Nichani, Alberto Bietti +4
Transformer-based language models have demonstrated impressive capabilities across a range of complex reasoning tasks. Prior theoretical work exploring the expressive power of tran…
Neural network learns low-dimensional polynomials with SGD near the information-theoretic limit
Jason D. Lee, Kazusato Oko, Taiji Suzuki +1
We study the problem of gradient descent learning of a single-index target function un…