arXiv subjects

Shiva Prasad Kasiviswanathan

Publications and source records attributed to Shiva Prasad Kasiviswanathan.

At least 19 recordsLinked to original sources

arXiv2026

Optimal Transportation and Alignment Between Gaussian Measures

Optimal transport (OT) and Gromov-Wasserstein (GW) alignment provide interpretable geometric frameworks for comparing, transforming, and aggregating heterogeneous datasets---tasks ubiquitous in data science and machine learning. Because these frameworks are computationally expensive, large-scale applications often rely on closed-form solutions for Gaussian distributions under quadratic cost. This work provides a comprehensive treatment of Gaussian, quadratic cost OT and inner product GW (IGW) alignment, closing several gaps in the literature to broaden applicability. First, we treat the open problem of IGW alignment between uncentered Gaussians on separable Hilbert spaces by giving an exact variational characterization through a quadratic optimization over isometries and co-isometries (orthogonal matrices in finite dimensions), for which we derive tight analytic upper and lower bounds. If at least one Gaussian measure is centered, the solution reduces to a fully closed-form expression, which we further extend to an analytic solution for the IGW barycenter between centered Gaussians. We also present a reduction of Gaussian multimarginal OT with pairwise quadratic costs to a tractable optimization problem and prove that every second-order stationary point of this problem is globally optimal. To demonstrate utility, we compare embedding distributions of already-trained language-model distillations and cluster synthetic users using covariance spectra of their text embeddings.

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arXiv2026

Counterfactual Generation via Flow Matching: Coupling-Sensitive End-to-End Rates

Counterfactual generation seeks to sample outcomes under a hypothetical intervention or decision using observational data collected under the factual assignment mechanism. We develop a flow-matching approach that combines a sample-split, doubly robust training objective with a learned coupling between observed source outcomes and target outcomes drawn from a fitted conditional outcome model. To enable finite-step generation, we leverage a score-corrected stochastic sampler based on a Gaussian-smoothed interpolation. Our main theoretical contribution is a coupling-sensitive KL bound for constant-step Euler discretization: the error is controlled by moments of the source--target displacement under the chosen coupling, rather than by global uniform regularity of the velocity field, and has near-linear dependence on the ambient dimension. We also establish finite-sample non-parametric guarantees for the learned velocity and score fields when both the conditional outcome model and the source-target coupling are estimated from data. These bounds separate approximation, coupling-replacement, nuisance-estimation, generalization, and Monte Carlo errors and, combined with the sampler analysis, yield an end-to-end guarantee for counterfactual generation. Experiments on synthetic and semi-synthetic image benchmarks support the coupling-dependent theory and show that, at finite discretization budgets, the stochastic sampler can outperform the corresponding deterministic ODE sampler.

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arXiv2026

Group Adaptive Clipping Policy Optimization

Group relative policy optimization for reinforcement learning with verifiable rewards (RLVR) typically uses a fixed importance-sampling (IS) ratio clipping boundary across all rollouts. We identify a key limitation: rare correct rollouts on harder problems and abundant correct rollouts on easier problems are clipped at comparable rates, despite contributing very different learning signals. Rollouts with low group success exhibit larger IS ratios and carry stronger gradient signal for exploration and solving new problems, yet are disproportionately suppressed by fixed clipping. To address this, we propose Group Adaptive Clipping Policy Optimization (GAPO), a plug-in modification to GRPO methods that adapts the clipping boundary to the rollout advantage. GAPO is motivated by a reverse-KL trust-region perspective, which suggests that rollouts with larger learning signal should receive proportionally greater update headroom. GAPO requires no reward shaping and preserves the standard PPO/GSPO surrogate while adapting only the clipping threshold. Across Qwen and Llama models, GAPO consistently improves both Pass@1 and Pass@k over fixed clipping and advantage-shaping baselines on math reasoning and coding benchmarks where the pass rates by the base model are relatively low.

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arXiv2026

Sample Complexity of Multicalibration for Multilevel Properties

Calibration requires a predictor to be unbiased after conditioning on its own predictions. Multicalibration asks for this guarantee simultaneously across a collection of groups. Many prediction tasks ask for several related features of the same conditional outcome distribution: variance is defined relative to the mean, skewness relative to both mean and variance, and conditional value at risk relative to a quantile. We study multicalibration for a sequence of $k$ properties in which each property is identifiable once the preceding properties are fixed. This framework includes Bayes pairs but does not require the properties to arise from a single loss. For every fixed $k\ge2$, we establish matching upper and lower sample-complexity bounds up to logarithmic factors under regularity conditions. Even with only polylogarithmically many binary groups, achieving multicalibration error $\varepsilon$ requires $\widetildeΩ(\varepsilon^{-(k+2)})$ samples. Conversely, for any finite group family $\mathcal G$, we give a randomized learner using $O(\varepsilon^{-(k+2)}+\varepsilon^{-2}\log|\mathcal G|)$ samples. Thus the sample complexity is $\widetildeΘ(\varepsilon^{-(k+2)})$ for polynomial-size group families. We instantiate the theory for three canonical examples.

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arXiv2026

FoundCause: Causal Discovery with Latent Confounders from Observational Data

Causal discovery from observational data remains challenging due to the need to recover directed structure and latent confounding without interventions. We propose FoundCause, an amortized causal discovery model trained entirely on synthetic data that maps datasets directly to causal graphs in a single forward pass. By learning from large collections of simulated structural causal models, FoundCause captures transferable statistical patterns that generalize beyond individual datasets. The architecture incorporates several key inductive biases for causal discovery. It uses a permutation-invariant transformer encoder with alternating attention over samples and variables to jointly model cross-variable dependence and per-variable distributions. Pairwise statistical features derived from classical asymmetry measures are injected through statistics-conditioned attention, guiding the model toward known causal signals. A factorized decoder separates edge existence from direction, while a triangular refinement module enables reasoning over higher-order causal motifs such as chains and colliders. In addition, a dedicated confounder module based on learnable latent tokens explicitly models hidden common causes, and the model explicitly handles missing data via its masked input representation. To our knowledge, FoundCause is the first amortized causal discovery approach to explicitly model latent confounding. FoundCause outperforms 11 classical non-amortized methods (e.g., PC, GES, NOTEARS-style optimization) and 4 amortized causal discovery methods on 15 real-world datasets, achieving +9.6% improvement in $F_1$, +1.2% in AUROC, and an 18.9% reduction in structural Hamming distance relative to the strongest non-amortized methods, while performing inference in a single forward pass.

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arXiv2026

A Quantitative Characterization of Forgetting in Post-Training

Continual post-training of generative models is widely used, yet a principled understanding of when and why forgetting occurs remains limited. We develop theoretical results under a two-mode mixture abstraction (representing old and new tasks), proposed by Chen et al. (2025) (arXiv:2510.18874), and formalize forgetting in two forms: (i) mass forgetting, where the old mixture weight collapses to zero, and (ii) old-component drift, where an already-correct old component shifts during training. For equal-covariance Gaussian modes, we prove that forward-KL objectives trained on data from the new distribution drive the old weight to zero, while reverse-KL objectives converge to the true target (thereby avoiding mass forgetting) and perturb the old mean only through overlap-gated misassignment probabilities controlled by the Bhattacharyya coefficient, yielding drift that decays exponentially with mode separation and a locally well-conditioned geometry with exponential convergence. We further quantify how replay interacts with these objectives. For forward-KL, replay must modify the training distribution to change the population optimum; for reverse-KL, replay leaves the population objective unchanged but prevents finite-batch old-mode starvation through bounded importance weighting. Finally, we analyze three recently proposed near-on-policy post-training methods, SDFT (arxiv:2601.19897), TTT-Discover (arxiv:2601.16175), and OAPL (arxiv:2602.19362), via the same lens and derive explicit conditions under which each retains old mass and exhibits overlap-controlled drift. Overall, our results show that forgetting can by precisely quantified based on the interaction between divergence direction, geometric behavioral overlap, sampling regime, and the visibility of past behavior during training.

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arXiv2026

Training Large Language Models To Reason In Parallel With Global Forking Tokens

Although LLMs have demonstrated improved performance by scaling parallel test-time compute, doing so relies on generating reasoning paths that are both diverse and accurate. For challenging problems, the forking tokens that trigger diverse yet correct reasoning modes are typically deep in the sampling tree. Consequently, common strategies to encourage diversity, such as temperature scaling, encounter a worsened trade-off between diversity and accuracy. Motivated by this challenge, we treat parallel reasoning as a set-of-next-token-prediction problem and incorporate a set-based global loss into Supervised Fine-Tuning (SFT) using bipartite matching between global forking tokens and unique reasoning traces. We observe that whereas naive fine-tuning with multiple reasoning traces collapses these unique reasoning modes, our proposed method, Set Supervised Fine-Tuning (SSFT), preserves these modes and produces emergent global forking tokens. Global Forking Policy Optimization (GFPO) leverages these maximally steerable tokens to incentivize complex reasoning, and the resulting models consistently outperform their SFT counterparts with GRPO on both math reasoning and execution-based code generation benchmarks.

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arXiv2026

Learning to Answer from Correct Demonstrations

We study the problem of learning to generate an answer (or completion) to a question (or prompt), where there could be multiple correct answers, any one of which is acceptable at test time. Learning is based on demonstrations of some correct answer to each training question, as in Supervised Fine Tuning (SFT). We formalize the problem as imitation learning (i.e., apprenticeship learning) in contextual bandits, with offline demonstrations from some expert (optimal, or very good) policy, without explicitly observed rewards. In contrast to prior work, which assumes the demonstrator belongs to a bounded-complexity policy class, we propose relying only on the underlying reward model (i.e., specifying which answers are correct) being in a bounded-complexity class, which we argue is a strictly weaker assumption. We show that likelihood-maximization methods can fail in this setting, and instead present an approach that learns to answer nearly as well as the demonstrator, with sample complexity logarithmic in the cardinality of the reward class. Our method is similar to Syed and Schapire 2007, when adapted to a contextual bandit (i.e., single step) setup, but is a simple one-pass online approach that enjoys an "optimistic rate" (i.e., $1/\varepsilon$ when the demonstrator is optimal, versus $1/\varepsilon^2$ in Syed and Schapire), and works even with arbitrarily adaptive demonstrations.

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arXiv2026

Dependence-Aware Label Aggregation for LLM-as-a-Judge via Ising Models

Large-scale AI evaluation increasingly relies on aggregating binary judgments from $K$ annotators, including LLMs used as judges. Most classical methods, e.g., Dawid-Skene or (weighted) majority voting, assume annotators are conditionally independent given the true label $Y\in\{0,1\}$, an assumption often violated by LLM judges due to shared data, architectures, prompts, and failure modes. Ignoring such dependencies can yield miscalibrated posteriors and even confidently incorrect predictions. We study label aggregation through a hierarchy of dependence-aware models based on Ising graphical models and latent factors. For class-dependent Ising models, the Bayes log-odds is generally quadratic in votes; for class-independent couplings, it reduces to a linear weighted vote with correlation-adjusted parameters. We present finite-$K$ examples showing that methods based on conditional independence can flip the Bayes label despite matching per-annotator marginals. We prove separation results demonstrating that these methods remain strictly suboptimal as the number of judges grows, incurring nonvanishing excess risk under latent factors. Finally, we evaluate the proposed method on three real-world datasets, demonstrating improved performance over the classical baselines.

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arXiv2025

What Causes Postoperative Aspiration?

Background: Aspiration, the inhalation of foreign material into the lungs, significantly impacts surgical patient morbidity and mortality. This study develops a machine learning (ML) model to predict postoperative aspiration, enabling timely preventative interventions. Methods: From the MIMIC-IV database of over 400,000 hospital admissions, we identified 826 surgical patients (mean age: 62, 55.7\% male) who experienced aspiration within seven days post-surgery, along with a matched non-aspiration cohort. Three ML models: XGBoost, Multilayer Perceptron, and Random Forest were trained using pre-surgical hospitalization data to predict postoperative aspiration. To investigate causation, we estimated Average Treatment Effects (ATE) using Augmented Inverse Probability Weighting. Results: Our ML model achieved an AUROC of 0.86 and 77.3\% sensitivity on a held-out test set. Maximum daily opioid dose, length of stay, and patient age emerged as the most important predictors. ATE analysis identified significant causative factors: opioids (0.25 +/- 0.06) and operative site (neck: 0.20 +/- 0.13, head: 0.19 +/- 0.13). Despite equal surgery rates across genders, men were 1.5 times more likely to aspirate and received 27\% higher maximum daily opioid dosages compared to women. Conclusion: ML models can effectively predict postoperative aspiration risk, enabling targeted preventative measures. Maximum daily opioid dosage and operative site significantly influence aspiration risk. The gender disparity in both opioid administration and aspiration rates warrants further investigation. These findings have important implications for improving postoperative care protocols and aspiration prevention strategies.

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arXiv2025

From Guess2Graph: When and How Can Unreliable Experts Safely Boost Causal Discovery in Finite Samples?

Causal discovery algorithms often perform poorly with limited samples. While integrating expert knowledge (including from LLMs) as constraints promises to improve performance, guarantees for existing methods require perfect predictions or uncertainty estimates, making them unreliable for practical use. We propose the Guess2Graph (G2G) framework, which uses expert guesses to guide the sequence of statistical tests rather than replacing them. This maintains statistical consistency while enabling performance improvements. We develop two instantiations of G2G: PC-Guess, which augments the PC algorithm, and gPC-Guess, a learning-augmented variant designed to better leverage high-quality expert input. Theoretically, both preserve correctness regardless of expert error, with gPC-Guess provably outperforming its non-augmented counterpart in finite samples when experts are "better than random." Empirically, both show monotonic improvement with expert accuracy, with gPC-Guess achieving significantly stronger gains.

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arXiv2025

Sequential Kernelized Independence Testing

Independence testing is a classical statistical problem that has been extensively studied in the batch setting when one fixes the sample size before collecting data. However, practitioners often prefer procedures that adapt to the complexity of a problem at hand instead of setting sample size in advance. Ideally, such procedures should (a) stop earlier on easy tasks (and later on harder tasks), hence making better use of available resources, and (b) continuously monitor the data and efficiently incorporate statistical evidence after collecting new data, while controlling the false alarm rate. Classical batch tests are not tailored for streaming data: valid inference after data peeking requires correcting for multiple testing which results in low power. Following the principle of testing by betting, we design sequential kernelized independence tests that overcome such shortcomings. We exemplify our broad framework using bets inspired by kernelized dependence measures, e.g., the Hilbert-Schmidt independence criterion. Our test is also valid under non-i.i.d., time-varying settings. We demonstrate the power of our approaches on both simulated and real data.

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arXiv2025

A Classical View on Benign Overfitting: The Role of Sample Size

Benign overfitting is a phenomenon in machine learning where a model perfectly fits (interpolates) the training data, including noisy examples, yet still generalizes well to unseen data. Understanding this phenomenon has attracted considerable attention in recent years. In this work, we introduce a conceptual shift, by focusing on almost benign overfitting, where models simultaneously achieve both arbitrarily small training and test errors. This behavior is characteristic of neural networks, which often achieve low (but non-zero) training error while still generalizing well. We hypothesize that this almost benign overfitting can emerge even in classical regimes, by analyzing how the interaction between sample size and model complexity enables larger models to achieve both good training fit but still approach Bayes-optimal generalization. We substantiate this hypothesis with theoretical evidence from two case studies: (i) kernel ridge regression, and (ii) least-squares regression using a two-layer fully connected ReLU neural network trained via gradient flow. In both cases, we overcome the strong assumptions often required in prior work on benign overfitting. Our results on neural networks also provide the first generalization result in this setting that does not rely on any assumptions about the underlying regression function or noise, beyond boundedness. Our analysis introduces a novel proof technique based on decomposing the excess risk into estimation and approximation errors, interpreting gradient flow as an implicit regularizer, that helps avoid uniform convergence traps. This analysis idea could be of independent interest.

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arXiv2025

QA-Calibration of Language Model Confidence Scores

To use generative question-and-answering (QA) systems for decision-making and in any critical application, these systems need to provide well-calibrated confidence scores that reflect the correctness of their answers. Existing calibration methods aim to ensure that the confidence score is, *on average*, indicative of the likelihood that the answer is correct. We argue, however, that this standard (average-case) notion of calibration is difficult to interpret for decision-making in generative QA. To address this, we generalize the standard notion of average calibration and introduce QA-calibration, which ensures calibration holds across different question-and-answer groups. We then propose discretized posthoc calibration schemes for achieving QA-calibration. We establish distribution-free guarantees on the performance of this method and validate our method on confidence scores returned by elicitation prompts across multiple QA benchmarks and large language models (LLMs).

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arXiv2024

Modeling Causal Mechanisms with Diffusion Models for Interventional and Counterfactual Queries

We consider the problem of answering observational, interventional, and counterfactual queries in a causally sufficient setting where only observational data and the causal graph are available. Utilizing the recent developments in diffusion models, we introduce diffusion-based causal models (DCM) to learn causal mechanisms, that generate unique latent encodings. These encodings enable us to directly sample under interventions and perform abduction for counterfactuals. Diffusion models are a natural fit here, since they can encode each node to a latent representation that acts as a proxy for exogenous noise. Our empirical evaluations demonstrate significant improvements over existing state-of-the-art methods for answering causal queries. Furthermore, we provide theoretical results that offer a methodology for analyzing counterfactual estimation in general encoder-decoder models, which could be useful in settings beyond our proposed approach.

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arXiv2024

Benign Overfitting for Regression with Trained Two-Layer ReLU Networks

We study the least-square regression problem with a two-layer fully-connected neural network, with ReLU activation function, trained by gradient flow. Our first result is a generalization result, that requires no assumptions on the underlying regression function or the noise other than that they are bounded. We operate in the neural tangent kernel regime, and our generalization result is developed via a decomposition of the excess risk into estimation and approximation errors, viewing gradient flow as an implicit regularizer. This decomposition in the context of neural networks is a novel perspective of gradient descent, and helps us avoid uniform convergence traps. In this work, we also establish that under the same setting, the trained network overfits to the data. Together, these results, establishes the first result on benign overfitting for finite-width ReLU networks for arbitrary regression functions.

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arXiv2024

Differentially Private Conditional Independence Testing

Conditional independence (CI) tests are widely used in statistical data analysis, e.g., they are the building block of many algorithms for causal graph discovery. The goal of a CI test is to accept or reject the null hypothesis that $X \perp \!\!\! \perp Y \mid Z$, where $X \in \mathbb{R}, Y \in \mathbb{R}, Z \in \mathbb{R}^d$. In this work, we investigate conditional independence testing under the constraint of differential privacy. We design two private CI testing procedures: one based on the generalized covariance measure of Shah and Peters (2020) and another based on the conditional randomization test of Candès et al. (2016) (under the model-X assumption). We provide theoretical guarantees on the performance of our tests and validate them empirically. These are the first private CI tests with rigorous theoretical guarantees that work for the general case when $Z$ is continuous.

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arXiv2023

Debiasing Conditional Stochastic Optimization

In this paper, we study the conditional stochastic optimization (CSO) problem which covers a variety of applications including portfolio selection, reinforcement learning, robust learning, causal inference, etc. The sample-averaged gradient of the CSO objective is biased due to its nested structure, and therefore requires a high sample complexity for convergence. We introduce a general stochastic extrapolation technique that effectively reduces the bias. We show that for nonconvex smooth objectives, combining this extrapolation with variance reduction techniques can achieve a significantly better sample complexity than the existing bounds. Additionally, we develop new algorithms for the finite-sum variant of the CSO problem that also significantly improve upon existing results. Finally, we believe that our debiasing technique has the potential to be a useful tool for addressing similar challenges in other stochastic optimization problems.

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