arXiv subjects

Vatsal Sharan

Publications and source records attributed to Vatsal Sharan.

At least 19 recordsLinked to original sources

arXiv2026

Algorithmic Principles For Multiclass Learning Are Hard To Come By: Limits of Regularization and Proper Learning

Two of the most fundamental questions in statistical learning theory are the following: which prediction problems are learnable, and how should they be learned? For the former, elegant answers often take the form of combinatorial dimensions. The latter question, however, has proved considerably more elusive: all known general-purpose multiclass learners rely on intricate orientations of exponentially large one-inclusion structures, and familiar algorithmic principles such as proper learning and regularization remain poorly understood. Motivated by prior work, we ask whether learning reduces to proper learning---possibly over a larger hypothesis class---and whether proper or improper multiclass learning can ultimately be captured by suitable regularizers. Our primary results answer both questions negatively, resolving three open problems from prior work. First, we exhibit a learnable multiclass problem that cannot be embedded in any properly learnable class, meaning learning cannot be reduced to proper learning by enlarging the hypothesis class. Second, we demonstrate that proper learning can require training error and characterize this phenomenon precisely: every properly learnable class admits a proper learner making $o(m)$ errors on samples of size $m$, but every prescribed sublinear scale $a_m=o(m)$ is necessary for some properly learnable problem. Third, regularization is not a general learner: we exhibit a properly learnable class that cannot be learned by any Structural Risk Minimization (SRM) learner, and a learnable class that cannot be learned by any local regularizer. We complement these impossibility results with a positive theory that gives two sufficient conditions for SRM learnability and characterizes SRM representability through integrability of revealed preferences.

cs.LG↗

arXiv2026

Convergent Evolution: How Different Language Models Learn Similar Number Representations

Language models trained on natural text learn to represent numbers using periodic features with dominant periods at $T=2, 5, 10$. In this paper, we identify a two-tiered hierarchy of these features: while Transformers, Linear RNNs, LSTMs, and classical word embeddings trained in different ways all learn features that have period-$T$ spikes in the Fourier domain, only some learn geometrically separable features that can be used to linearly classify a number mod-$T$. To explain this incongruity, we prove that Fourier domain sparsity is necessary but not sufficient for mod-$T$ geometric separability. Empirically, we investigate when model training yields geometrically separable features, finding that the data, architecture, optimizer, and tokenizer all play key roles. In particular, we identify two different routes through which models can acquire geometrically separable features: they can learn them from complementary co-occurrence signals in general language data, including text-number co-occurrence and cross-number interaction, or from multi-token (but not single-token) addition problems. Overall, our results highlight the phenomenon of convergent evolution in feature learning: A diverse range of models learn similar features from different training signals.

cs.CL↗

arXiv2026

Understanding Contextual Recall in Transformers: How Finetuning Enables In-Context Reasoning over Pretraining Knowledge

Transformer-based language models excel at in-context learning (ICL), where they can adapt to new tasks based on contextual examples, without parameter updates. In a specific form of ICL, which we refer to as \textit{contextual recall}, models pretrained on open-ended text leverage pairwise examples to recall specific facts in novel prompt formats. We investigate whether contextual recall emerges from pretraining alone, what finetuning is required, and what mechanisms drive the necessary representations. For this, we introduce a controlled synthetic framework where pretraining sequences consist of subject-grammar-attribute tuples, with attribute types tied to grammar statistics. We demonstrate that while such pretraining successfully yields factual knowledge, it is insufficient for contextual recall: models fail to implicitly infer attribute types when the grammar statistics are removed in ICL prompts. However, we show that finetuning on tasks requiring implicit inference, distinct from the ICL evaluation, using a subset of subjects, triggers the emergence of contextual recall across all subjects. This transition is accompanied by the formation of low-dimensional latent encodings of the shared attribute type. For mechanistic insight, we derive a construction for an attention-only transformer that replicates the transition from factual to contextual recall, corroborated by empirical validation.

cs.LG↗

arXiv2026

A Unified Approach to Memory-Sample Tradeoffs for Detecting Planted Structures

We present a unified framework for proving memory lower bounds for multi-pass streaming algorithms that detect planted structures. Planted structures -- such as cliques or bicliques in graphs, and sparse signals in high-dimensional data -- arise in numerous applications, and our framework yields multi-pass memory lower bounds for many such fundamental settings. We show memory lower bounds for the planted $k$-biclique detection problem in random bipartite graphs and for detecting sparse Gaussian means. We also show the first memory-sample tradeoffs for the sparse principal component analysis (PCA) problem in the spiked covariance model. For all these problems to which we apply our unified framework, we obtain bounds which are nearly tight in the low, $O(\log n)$ memory regime. We also leverage our bounds to establish new multi-pass streaming lower bounds, in the vertex arrival model, for two well-studied graph streaming problems: approximating the size of the largest biclique and approximating the maximum density of bounded-size subgraphs. To show these bounds, we study a general distinguishing problem over matrices, where the goal is to distinguish a null distribution from one that plants an outlier distribution over a random submatrix. Our analysis builds on a new distributed data processing inequality that provides sufficient conditions for memory hardness in terms of the likelihood ratio between the averaged planted and null distributions. This result generalizes the inequality of [Braverman et al., STOC 2016] and may be of independent interest. The inequality enables us to measure information cost under the null distribution -- a key step for applying subsequent direct-sum-type arguments and incorporating the multi-pass information cost framework of [Braverman et al., STOC 2024].

cs.CC↗

arXiv2025

Simultaneous Swap Regret Minimization via KL-Calibration

Calibration is a fundamental concept that aims at ensuring the reliability of probabilistic predictions by aligning them with real-world outcomes. There is a surge of studies on new calibration measures that are easier to optimize compared to the classical $\ell_1$-Calibration while still having strong implications for downstream applications. One recent such example is the work by Fishelson et al. (2025) who show that it is possible to achieve $O(T^{1/3})$ pseudo $\ell_2$-Calibration error via minimizing pseudo swap regret of the squared loss, which in fact implies the same bound for all bounded proper losses with a smooth univariate form. In this work, we significantly generalize their result in the following ways: (a) in addition to smooth univariate forms, our algorithm also simultaneously achieves $O(T^{1/3})$ swap regret for any proper loss with a twice continuously differentiable univariate form (such as Tsallis entropy); (b) our bounds hold not only for pseudo swap regret that measures losses using the forecaster's distributions on predictions, but also hold for the actual swap regret that measures losses using the forecaster's actual realized predictions. We achieve so by introducing a new stronger notion of calibration called (pseudo) KL-Calibration, which we show is equivalent to the (pseudo) swap regret for log loss. We prove that there exists an algorithm that achieves $O(T^{1/3})$ KL-Calibration error and provide an explicit algorithm that achieves $O(T^{1/3})$ pseudo KL-Calibration error. Moreover, we show that the same algorithm achieves $O(T^{1/3}(\log T)^{-1/3}\log(T/δ))$ swap regret w.p. $\ge 1-δ$ for any proper loss with a smooth univariate form, which implies $O(T^{1/3})$ $\ell_2$-Calibration error. A technical contribution of our work is a new randomized rounding procedure and a non-uniform discretization scheme to minimize the swap regret for log loss.

cs.LG↗

arXiv2025

An External Fairness Evaluation of LinkedIn Talent Search

We conduct an independent, third-party audit for bias of LinkedIn's Talent Search ranking system, focusing on potential ranking bias across two attributes: gender and race. To do so, we first construct a dataset of rankings produced by the system, collecting extensive Talent Search results across a diverse set of occupational queries. We then develop a robust labeling pipeline that infers the two demographic attributes of interest for the returned users. To evaluate potential biases in the collected dataset of real-world rankings, we utilize two exposure disparity metrics: deviation from group proportions and MinSkew. Our analysis reveals an under-representation of minority groups in early ranks across many queries. We further examine potential causes of this disparity, and discuss why they may be difficult or, in some cases, impossible to fully eliminate among the early ranks of queries. Beyond static metrics, we also investigate the concept of subgroup fairness over time, highlighting temporal disparities in exposure and retention, which are often more difficult to audit for in practice. In employer recruiting platforms such as LinkedIn Talent Search, the persistence of a particular candidate over multiple days in the ranking can directly impact the probability that the given candidate is selected for opportunities. Our analysis reveals demographic disparities in this temporal stability, with some groups experiencing greater volatility in their ranked positions than others. We contextualize all our findings alongside LinkedIn's published self-audits of its Talent Search system and reflect on the methodological constraints of a black-box external evaluation, including limited observability and noisy demographic inference.

cs.CY↗

arXiv2025

Efficient Swap Multicalibration of Elicitable Properties

Multicalibration [HJKRR18] is an algorithmic fairness perspective that demands that the predictions of a predictor are correct conditional on themselves and membership in a collection of potentially overlapping subgroups of a population. The work of [NR23] established a surprising connection between multicalibration for an arbitrary property $Γ$ (e.g., mean or median) and property elicitation: a property $Γ$ can be multicalibrated if and only if it is elicitable, where elicitability is the notion that the true property value of a distribution can be obtained by solving a regression problem over the distribution. In the online setting, [NR23] proposed an inefficient algorithm that achieves $\sqrt T$ $\ell_2$-multicalibration error for a hypothesis class of group membership functions and an elicitable property $Γ$, after $T$ rounds of interaction between a forecaster and adversary. In this paper, we generalize multicalibration for an elicitable property $Γ$ from group membership functions to arbitrary bounded hypothesis classes and introduce a stronger notion -- swap multicalibration, following [GKR23]. Subsequently, we propose an oracle-efficient algorithm which, when given access to an online agnostic learner, achieves $T^{1/(r+1)}$ $\ell_r$-swap multicalibration error with high probability (for $r\ge2$) for a hypothesis class with bounded sequential Rademacher complexity and an elicitable property $Γ$. For the special case of $r=2$, this implies an oracle-efficient algorithm that achieves $T^{1/3}$ $\ell_2$-swap multicalibration error, which significantly improves on the previously established bounds for the problem [NR23, GMS25, LSS25a], and completely resolves an open question raised in [GJRR24] on the possibility of an oracle-efficient algorithm that achieves $\sqrt{T}$ $\ell_2$-mean multicalibration error by answering it in a strongly affirmative sense.

cs.LG↗

arXiv2025

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

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 simplifying abstractions as follows: First, we use imbalanced data as a testbed. Second, we study the canonical form of such optimizers, which is Spectral Gradient Descent (SpecGD) -- each update step is $UV^T$ where $U\Sigma V^T$ is the truncated SVD of the gradient. Third, within this framework we identify a canonical setting for which we precisely quantify when SpecGD outperforms vanilla Euclidean GD. For a Gaussian mixture data model and both linear and bilinear models, we show that unlike GD, which prioritizes learning dominant principal components of the data first, SpecGD learns all principal components of the data at equal rates. We demonstrate how this translates to a growing gap in class balanced loss favoring SpecGD early in training and further show that the gap remains consistent even when the GD counterpart uses adaptive step-sizes via normalization. By extending the analysis to deep linear models, we show that depth amplifies these effects. We empirically verify our theoretical findings on a variety of imbalanced datasets. Our experiments compare practical variants of spectral methods, like Muon and Shampoo, against their Euclidean counterparts and Adam. The results validate our findings that these spectral optimizers achieve superior generalization by promoting a more balanced learning of the data's underlying components.

cs.LG↗

arXiv2025

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

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 (NNs) trained with SGD are known to exhibit simplicity bias -- a tendency to find simple solutions. In contrast, we show that Adam is more resistant to such simplicity bias. First, we investigate the differences in the implicit biases of Adam and GD when training two-layer ReLU NNs on a binary classification task with Gaussian data. We find that GD exhibits a simplicity bias, resulting in a linear decision boundary with a suboptimal margin, whereas Adam leads to much richer and more diverse features, producing a nonlinear boundary that is closer to the Bayes' optimal predictor. This richer decision boundary also allows Adam to achieve higher test accuracy both in-distribution and under certain distribution shifts. We theoretically prove these results by analyzing the population gradients. Next, to corroborate our theoretical findings, we present extensive empirical results showing that this property of Adam leads to superior generalization across various datasets with spurious correlations where NNs trained with SGD are known to show simplicity bias and do not generalize well under certain distributional shifts.

cs.LG↗

arXiv2025

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

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 $L$-layer model can compute connectivity in graphs with diameters up to $3^L$, implementing an algorithm equivalent to computing powers of the adjacency matrix. By analyzing training dynamics, we prove that whether the model learns this strategy hinges on whether most training instances are within this model capacity. Within-capacity graphs (diameter $\leq 3^L$) drive the learning of the algorithmic solution while beyond-capacity graphs drive the learning of a simple heuristic based on node degrees. Finally, we empirically show that restricting training data to stay within a model's capacity makes both standard and Disentangled Transformers learn the exact algorithm.

cs.LG↗

arXiv2025

Latent Concept Disentanglement in Transformer-based Language Models

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 controlled tasks, studying this question using mechanistic interpretability. First, we show that in transitive reasoning tasks with a latent, discrete concept, the model successfully identifies the latent concept and does step-by-step concept composition. This builds upon prior work that analyzes single-step reasoning. Then, we consider tasks parameterized by a latent numerical concept. We discover low-dimensional subspaces in the model's representation space, where the geometry cleanly reflects the underlying parameterization. Overall, we show that small and large models can indeed disentangle and utilize latent concepts that they learn in-context from a handful of abbreviated demonstrations.

cs.LG↗

arXiv2025

Limitations on Accurate, Trusted, Human-level Reasoning

We identify a fundamental incompatibility between the goals of accuracy, trust, and human-level reasoning in artificial intelligence (AI) systems, for strict mathematical definitions of these notions. We define accuracy of a system as the property that it never makes any false claims when it has the ability to abstain from making a prediction on any input, and trust as the assumption that the system is accurate. We define human-level reasoning as the property of an AI system always matching or exceeding human capability. Our core finding is that -- for our formal definitions of these notions -- an accurate and trusted AI system cannot be a human-level reasoning system: for such an accurate, trusted system there are task instances which are easily and provably solvable by a human but not by the system. Our proofs draw parallels to G\"odel's incompleteness theorems and Turing's proof of the undecidability of the halting problem, and can be regarded as interpretations of G\"odel's and Turing's results. Key to our proof is the formalization of the notion of trust, which allows us to separate the intrinsic property of a system (being accurate) from its epistemic status (being trusted).

cs.LG↗

arXiv2025

Auditability and the Landscape of Distance to Multicalibration

Calibration is a critical property for establishing the trustworthiness of predictors that provide uncertainty estimates. Multicalibration is a strengthening of calibration which requires that predictors be calibrated on a potentially overlapping collection of subsets of the domain. As multicalibration grows in popularity with practitioners, an essential question is: how do we measure how multicalibrated a predictor is? Błasiok et al. (2023) considered this question for standard calibration by introducing the distance to calibration framework (dCE) to understand how calibration metrics relate to each other and the ground truth. Building on the dCE framework, we consider the auditability of the distance to multicalibration of a predictor $f$. We begin by considering two natural generalizations of dCE to multiple subgroups: worst group dCE (wdMC), and distance to multicalibration (dMC). We argue that there are two essential properties of any multicalibration error metric: 1) the metric should capture how much $f$ would need to be modified in order to be perfectly multicalibrated; and 2) the metric should be auditable in an information theoretic sense. We show that wdMC and dMC each fail to satisfy one of these two properties, and that similar barriers arise when considering the auditability of general distance to multigroup fairness notions. We then propose two (equivalent) multicalibration metrics which do satisfy these requirements: 1) a continuized variant of dMC; and 2) a distance to intersection multicalibration, which leans on intersectional fairness desiderata. Along the way, we shed light on the loss-landscape of distance to multicalibration and the geometry of the set of perfectly multicalibrated predictors. Our findings may have implications for the development of stronger multicalibration algorithms as well as multigroup auditing more generally.

cs.LG↗

arXiv2025

On the Inherent Privacy of Zeroth Order Projected Gradient Descent

Differentially private zeroth-order optimization methods have recently gained popularity in private fine tuning of machine learning models due to their reduced memory requirements. Current approaches for privatizing zeroth-order methods rely on adding Gaussian noise to the estimated zeroth-order gradients. However, since the search direction in the zeroth-order methods is inherently random, researchers including Tang et al. (2024) and Zhang et al. (2024a) have raised an important question: is the inherent noise in zeroth-order estimators sufficient to ensure the overall differential privacy of the algorithm? This work settles this question for a class of oracle-based optimization algorithms where the oracle returns zeroth-order gradient estimates. In particular, we show that for a fixed initialization, there exist strongly convex objective functions such that running (Projected) Zeroth-Order Gradient Descent (ZO-GD) is not differentially private. Furthermore, we show that even with random initialization and without revealing (initial and) intermediate iterates, the privacy loss in ZO-GD can grow superlinearly with the number of iterations when minimizing convex objective functions.

math.OC↗

arXiv2025

From Calibration to Collaboration: LLM Uncertainty Quantification Should Be More Human-Centered

Large Language Models (LLMs) are increasingly assisting users in the real world, yet their reliability remains a concern. Uncertainty quantification (UQ) has been heralded as a tool to enhance human-LLM collaboration by enabling users to know when to trust LLM predictions. We argue that current practices for uncertainty quantification in LLMs are not optimal for developing useful UQ for human users making decisions in real-world tasks. Through an analysis of 40 LLM UQ methods, we identify three prevalent practices hindering the community's progress toward its goal of benefiting downstream users: 1) evaluating on benchmarks with low ecological validity; 2) considering only epistemic uncertainty; and 3) optimizing metrics that are not necessarily indicative of downstream utility. For each issue, we propose concrete user-centric practices and research directions that LLM UQ researchers should consider. Instead of hill-climbing on unrepresentative tasks using imperfect metrics, we argue that the community should adopt a more human-centered approach to LLM uncertainty quantification.

cs.CL↗

arXiv2025

Improved Bounds for Swap Multicalibration and Swap Omniprediction

In this paper, we consider the related problems of multicalibration -- a multigroup fairness notion and omniprediction -- a simultaneous loss minimization paradigm, both in the distributional and online settings. The recent work of Garg et al. (2024) raised the open problem of whether it is possible to efficiently achieve $O(\sqrt{T})$ $\ell_{2}$-multicalibration error against bounded linear functions. In this paper, we answer this question in a strongly affirmative sense. We propose an efficient algorithm that achieves $O(T^{\frac{1}{3}})$ $\ell_{2}$-swap multicalibration error (both in high probability and expectation). On propagating this bound onward, we obtain significantly improved rates for $\ell_{1}$-swap multicalibration and swap omniprediction for a loss class of convex Lipschitz functions. In particular, we show that our algorithm achieves $O(T^{\frac{2}{3}})$ $\ell_{1}$-swap multicalibration and swap omniprediction errors, thereby improving upon the previous best-known bound of $O(T^{\frac{7}{8}})$. As a consequence of our improved online results, we further obtain several improved sample complexity rates in the distributional setting. In particular, we establish a $O(\varepsilon ^ {-3})$ sample complexity of efficiently learning an $\varepsilon$-swap omnipredictor for the class of convex and Lipschitz functions, $O(\varepsilon ^{-2.5})$ sample complexity of efficiently learning an $\varepsilon$-swap agnostic learner for the squared loss, and $O(\varepsilon ^ {-5}), O(\varepsilon ^ {-2.5})$ sample complexities of learning $\ell_{1}, \ell_{2}$-swap multicalibrated predictors against linear functions, all of which significantly improve on the previous best-known bounds.

cs.LG↗

arXiv2025

Textual Steering Vectors Can Improve Visual Understanding in Multimodal Large Language Models

Steering methods have emerged as effective and targeted tools for guiding large language models' (LLMs) behavior without modifying their parameters. Multimodal large language models (MLLMs), however, do not currently enjoy the same suite of techniques, due in part to their recency and architectural diversity. Inspired by this gap, we investigate whether MLLMs can be steered using vectors derived from their text-only LLM backbone, via sparse autoencoders (SAEs), mean shift, and linear probing. We find that text-derived steering consistently enhances multimodal accuracy across diverse MLLM architectures and visual tasks. In particular, mean shift boosts spatial relationship accuracy on CV-Bench by up to +7.3% and counting accuracy by up to +3.3%, outperforming prompting and exhibiting strong generalization to out-of-distribution datasets. These results highlight textual steering vectors as a powerful, efficient mechanism for enhancing grounding in MLLMs with minimal additional data collection and computational overhead.

cs.LG↗

arXiv2025

Proper Learnability and the Role of Unlabeled Data

Proper learning refers to the setting in which learners must emit predictors in the underlying hypothesis class $H$, and often leads to learners with simple algorithmic forms (e.g. empirical risk minimization (ERM), structural risk minimization (SRM)). The limitation of proper learning, however, is that there exist problems which can only be learned improperly, e.g. in multiclass classification. Thus, we ask: Under what assumptions on the hypothesis class or the information provided to the learner is a problem properly learnable? We first demonstrate that when the unlabeled data distribution is given, there always exists an optimal proper learner governed by distributional regularization, a randomized generalization of regularization. We refer to this setting as the distribution-fixed PAC model, and continue to evaluate the learner on its worst-case performance over all distributions. Our result holds for all metric loss functions and any finite learning problem (with no dependence on its size). Further, we demonstrate that sample complexities in the distribution-fixed PAC model can shrink by only a logarithmic factor from the classic PAC model, strongly refuting the role of unlabeled data in PAC learning (from a worst-case perspective). We complement this with impossibility results which obstruct any characterization of proper learnability in the realizable PAC model. First, we observe that there are problems whose proper learnability is logically undecidable, i.e., independent of the ZFC axioms. We then show that proper learnability is not a monotone property of the underlying hypothesis class, and that it is not a local property (in a precise sense). Our impossibility results all hold even for the fundamental setting of multiclass classification, and go through a reduction of EMX learning (Ben-David et al., 2019) to proper classification which may be of independent interest.

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