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Vatsal Sharan

29 accepted papers

2026

FoNE: Precise Single-Token Number Embeddings via Fourier Features

ICLR 2026poster

Language models treat numbers in the same way as ordinary word tokens, which introduces two major issues: (1) embeddings of numerical tokens primarily reflect their frequency in text corpora rather than their inherent numerical properties, leading to frequency bias, and (2) numbers are often split i…

Cited by 0SourcecodeScholar
2026

How Muon’s Spectral Design Benefits Generalization: A Study on Imbalanced Data

ICLR 2026poster

The growing adoption of spectrum-aware matrix-valued optimizers such as Muon and Shampoo in deep learning motivates a systematic study of their generalization properties and, in particular, when they might outperform competitive algorithms. We approach this question by introducing appropriate simp…

Cited by 0SourceScholar
2026

Latent Concept Disentanglement in Transformer-based Language Models

ICLR 2026poster

When large language models (LLMs) use in-context learning (ICL) to solve a new task, they must infer latent concepts from demonstration examples. This raises the question of whether and how transformers represent latent structures as part of their computation. Our work experiments with several contr…

Cited by 0SourceScholar
2026

Transformers Provably Learn Algorithmic Solutions for Graph Connectivity, But Only with the Right Data

ICML 2026poster

Transformers often fail to learn generalizable algorithms, instead relying on brittle heuristics. Using graph connectivity as a testbed, we explain this phenomenon both theoretically and empirically. We consider a simplified Transformer architecture, the Disentangled Transformer, and prove that an $…

Cited by 0SourceScholar
2025

Discovering Data Structures: Nearest Neighbor Search and Beyond

NeurIPS 2025poster

We explore if it is possible to learn data structures end-to-end with neural networks, with a focus on the problem of nearest-neighbor (NN) search. We introduce a framework for data structure discovery, which adapts to the underlying data distribution and provides fine-grained control over query and…

Cited by 0SourceScholar
2025

The Rich and the Simple: On the Implicit Bias of Adam and SGD

NeurIPS 2025poster

Adam is the de facto optimization algorithm for several deep learning applications, but an understanding of its implicit bias and how it differs from other algorithms, particularly standard first-order methods such as (stochastic) gradient descent (GD), remains limited. In practice, neural networks…

Cited by 0SourceScholar
2025

Transformers Learn Low Sensitivity Functions: Investigations and Implications

ICLR 2025poster

Transformers achieve state-of-the-art accuracy and robustness across many tasks, but an understanding of their inductive biases and how those biases differ from other neural network architectures remains elusive. In this work, we identify the sensitivity of the model to token-wise random perturbatio…

Cited by 0SourcePDFScholar
2024

Fast Test Error Rates for Gradient-Based Algorithms on Separable Data

ICASSP 2024accepted

In recent research aimed at understanding the strong generalization performance of simple gradient-based methods on overparameterized models, it has been demonstrated that when training a linear predictor on separable data with an exponentially-tailed loss function, the predictor converges towards t…

Cited by 0SourceScholar
2024

Pre-trained Large Language Models Use Fourier Features to Compute Addition

NeurIPS 2024poster

Pre-trained large language models (LLMs) exhibit impressive mathematical reasoning capabilities, yet how they compute basic arithmetic, such as addition, remains unclear. This paper shows that pre-trained LLMs add numbers using Fourier features---dimensions in the hidden state that represent number…

Cited by 5SourcePDFScholar
2024

Stability and Multigroup Fairness in Ranking with Uncertain Predictions

ICML 2024poster

Rankings are ubiquitous across many applications, from search engines to hiring committees. In practice, many rankings are derived from the output of predictors. However, when predictors trained for classification tasks have intrinsic uncertainty, it is not obvious how this uncertainty should be rep…

Cited by 4SourcePDFScholar
2024

Transductive Learning is Compact

NeurIPS 2024poster

We demonstrate a compactness result holding broadly across supervised learning with a general class of loss functions: Any hypothesis class $\mathcal{H}$ is learnable with transductive sample complexity $m$ precisely when all of its finite projections are learnable with sample complexity $m$. We pro…

Cited by 2SourcePDFScholar
2024

Transformers Learn to Achieve Second-Order Convergence Rates for In-Context Linear Regression

NeurIPS 2024poster

Transformers excel at *in-context learning* (ICL)---learning from demonstrations without parameter updates---but how they do so remains a mystery. Recent work suggests that Transformers may internally run Gradient Descent (GD), a first-order optimization method, to perform ICL. In this paper, we ins…

2024

When is Multicalibration Post-Processing Necessary?

NeurIPS 2024poster

Calibration is a well-studied property of predictors which guarantees meaningful uncertainty estimates. Multicalibration is a related notion --- originating in algorithmic fairness --- which requires predictors to be simultaneously calibrated over a potentially complex and overlapping collection of…

Cited by 5SourcePDFScholar
2023

Efficient Convex Optimization Requires Superlinear Memory (Extended Abstract)

IJCAI 2023poster

Minimizing a convex function with access to a first order oracle---that returns the function evaluation and (sub)gradient at a query point---is a canonical optimization problem and a fundamental primitive in machine learning. Gradient-based methods are the most popular approaches used for solving t…

Cited by 0SourcePDFScholar
2021

One Network Fits All? Modular versus Monolithic Task Formulations in Neural Networks

ICLR 2021poster

Can deep learning solve multiple, very different tasks simultaneously? We investigate how the representations of the underlying tasks affect the ability of a single neural network to learn them jointly. We present theoretical and empirical findings that a single neural network is capable of simultan…

Cited by 18SourcePDFScholar
2020

Sample Amplification: Increasing Dataset Size even when Learning is Impossible

ICML 2020poster

Given data drawn from an unknown distribution, D, to what extent is it possible to “amplify” this dataset and faithfully output an even larger set of samples that appear to have been drawn from D? We formalize this question as follows: an (n,m) amplification procedure takes as input n independent dr…

Cited by 17SourcePDFScholar
2019

Compressed Factorization: Fast and Accurate Low-Rank Factorization of Compressively-Sensed Data

ICML 2019oral

What learning algorithms can be run directly on compressively-sensed data? In this work, we consider the question of accurately and efficiently computing low-rank matrix or tensor factorizations given data compressed via random projections. We examine the approach of first performing factorization i…

Cited by 19SourcePDFScholar
2019

PIDForest: Anomaly Detection via Partial Identification

NeurIPS 2019spotlight

We consider the problem of detecting anomalies in a large dataset. We propose a framework called Partial Identification which captures the intuition that anomalies are easy to distinguish from the overwhelming majority of points by relatively few attribute values. Formalizing this intuition, we prop…

2019

Recovery Guarantees For Quadratic Tensors With Sparse Observations

AISTATS 2019poster

We consider the tensor completion problem of predicting the missing entries of a tensor. The commonly used CP model has a triple product form, but an alternate family of quadratic models which are the sum of pairwise products instead of a triple product have emerged from applications such as recomme…

Cited by 3SourcePDFScholar
2017

Orthogonalized ALS: A Theoretically Principled Tensor Decomposition Algorithm for Practical Use

ICML 2017poster

The popular Alternating Least Squares (ALS) algorithm for tensor decomposition is efficient and easy to implement, but often converges to poor local optima—particularly when the weights of the factors are non-uniform. We propose a modification of the ALS approach that is as efficient as standard ALS…

Cited by 57SourcePDFScholar