36 citations · 62 across the 19 of their papers we have counts for
20 papers
Fine-Tuning Dynamics of In-Context Factual Recall in Transformers
Ruomin Huang, Eshaan Nichani, Jason D. Lee +1
In-context learning \ -- performing tasks based on examples given in the prompt \ -- is an important capability that has emerged in large language models and has received significa…
Sharp Capacity Thresholds in Linear Associative Memory: From Top-1 Retrieval to Tail-Average Learning
Nicholas Barnfield, Juno Kim, Eshaan Nichani +2
How many key-value associations can a linear memory store? The answer depends not only on the degrees of freedom in the memory matrix, but also on the retrieval c…
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…
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…
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…
Understanding Factual Recall in Transformers via Associative Memories
Eshaan Nichani, Jason D. Lee, Alberto Bietti
Large language models have demonstrated an impressive ability to perform factual recall. Prior work has found that transformers trained on factual recall tasks can store informatio…
Learning Hierarchical Polynomials of Multiple Nonlinear Features with Three-Layer Networks
Hengyu Fu, Zihao Wang, Eshaan Nichani +1
In deep learning theory, a critical question is to understand how neural networks learn hierarchical features. In this work, we study the learning of hierarchical polynomials of \t…
How Transformers Learn Causal Structure with Gradient Descent
Eshaan Nichani, Alex Damian, Jason D. Lee
The incredible success of transformers on sequence modeling tasks can be largely attributed to the self-attention mechanism, which allows information to be transferred between diff…
Learning Hierarchical Polynomials with Three-Layer Neural Networks
Zihao Wang, Eshaan Nichani, Jason D. Lee
We study the problem of learning hierarchical polynomials over the standard Gaussian distribution with three-layer neural networks. We specifically consider target functions of the…
Smoothing the Landscape Boosts the Signal for SGD: Optimal Sample Complexity for Learning Single Index Models
Alex Damian, Eshaan Nichani, Rong Ge +1
We focus on the task of learning a single index model with respect to the isotropic Gaussian distribution in dimensions. Prior work has shown that the samp…
Fine-Tuning Language Models with Just Forward Passes
Sadhika Malladi, Tianyu Gao, Eshaan Nichani +4
Fine-tuning language models (LMs) has yielded success on diverse downstream tasks, but as LMs grow in size, backpropagation requires a prohibitively large amount of memory. Zeroth-…
Provable Guarantees for Nonlinear Feature Learning in Three-Layer Neural Networks
Eshaan Nichani, Alex Damian, Jason D. Lee
One of the central questions in the theory of deep learning is to understand how neural networks learn hierarchical features. The ability of deep networks to extract salient featur…
Self-Stabilization: The Implicit Bias of Gradient Descent at the Edge of Stability
Alex Damian, Eshaan Nichani, Jason D. Lee
Traditional analyses of gradient descent show that when the largest eigenvalue of the Hessian, also known as the sharpness , is bounded by , training is "stable" and the…
Metastable Mixing of Markov Chains: Efficiently Sampling Low Temperature Exponential Random Graphs
Guy Bresler, Dheeraj Nagaraj, Eshaan Nichani
In this paper we consider the problem of sampling from the low-temperature exponential random graph model (ERGM). The usual approach is via Markov chain Monte Carlo, but Bhamidi et…
Causal Structure Discovery between Clusters of Nodes Induced by Latent Factors
Chandler Squires, Annie Yun, Eshaan Nichani +2
We consider the problem of learning the structure of a causal directed acyclic graph (DAG) model in the presence of latent variables. We define latent factor causal models (LFCMs)…
Identifying good directions to escape the NTK regime and efficiently learn low-degree plus sparse polynomials
Eshaan Nichani, Yu Bai, Jason D. Lee
A recent goal in the theory of deep learning is to identify how neural networks can escape the "lazy training," or Neural Tangent Kernel (NTK) regime, where the network is coupled…
Increasing Depth Leads to U-Shaped Test Risk in Over-parameterized Convolutional Networks
Eshaan Nichani, Adityanarayanan Radhakrishnan, Caroline Uhler
Recent works have demonstrated that increasing model capacity through width in over-parameterized neural networks leads to a decrease in test risk. For neural networks, however, mo…
On Alignment in Deep Linear Neural Networks
Adityanarayanan Radhakrishnan, Eshaan Nichani, Daniel Bernstein +1
We study the properties of alignment, a form of implicit regularization, in linear neural networks under gradient descent. We define alignment for fully connected networks with mul…