arXiv subjects

Ambuj Tewari

Publications and source records attributed to Ambuj Tewari.

At least 19 recordsLinked to original sources

arXiv2026

A Unified Framework for Probability Estimation of Data-Dependent Events

We study the general problem of estimating $D(\dde(S))$, the probability that an unknown distribution $D$ assigns to an event determined by a sample $S$ of $n$ i.i.d.\ draws from $D$ through a known mapping $\dde$. The estimation algorithm knows $\dde$ and $S$ but does not have access to any additional samples from $D$. This formulation captures classical missing mass, the data-dependent targets of adaptive data analysis and post-selection inference, and the test error of a data-trained predictor, whose estimation was recently studied by \new{Gastpar et al.\ (2024a,b)}. Within this framework we examine the two classical approaches to estimation. The error of the empirical plug-in estimator is exactly a generalization gap, so generalization bounds transfer to it directly. The leave-one-out estimator, which recovers the Good--Turing estimator, is accurate for every mapping that is stable under the deletion of one sample point, including new structured examples such as neighborhoods of the sample and pierced sets. The main application of our framework is to error estimation for a predictor that combines a base classifier with memorized exceptions, a structure common in theory and in practice. For it, the test error is exactly the missing mass restricted to the error region of the base classifier, a region selected by the same sample. We formulate the general problem of \emph{adaptive missing mass estimation} to address such dependence and propose a natural hybrid estimator, the Good--Turing estimator restricted to the selected region. We show that the generalization of the base classifier alone does not guarantee the accuracy of this estimator, and derive two bounds on its error: the first one based on the VC dimension of possible error regions and another based on the mutual information of the selected region with the sample.

cs.LG↗

arXiv2026

On Generation in Metric Spaces

We study generation in separable metric instance spaces. We extend the language generation framework from Kleinberg and Mullainathan [2024] beyond countable domains by defining novelty through metric separation and allowing asymmetric novelty parameters for the adversary and the generator. We introduce the $(\varepsilon,\varepsilon')$-closure dimension, a scale-sensitive analogue of closure dimension, which yields characterizations of uniform and non-uniform generatability and a sufficient condition for generation in the limit. Along the way, we identify a sharp geometric contrast. Namely, in doubling spaces, including all finite-dimensional normed spaces, generatability is stable across novelty scales and invariant under equivalent metrics. In general metric spaces, however, generatability can be highly scale-sensitive and metric-dependent; even in the natural infinite-dimensional Hilbert space $\ell^2$, all notions of generation may fail abruptly as the novelty parameters vary.

stat.ML↗

arXiv2026

Combinatorial Characterizations of the Learnability of Conditional Distributions

We study the PAC-learnability of function classes that map inputs to probability distributions over a finite space. The learner observes i.i.d. input-label pairs, with each label sampled from the conditional distribution of an unknown target hypothesis in the class. We measure learning through excess risk under a bounded proper loss that satisfies two mild assumptions. We introduce the \textbf{fat$_γ$Natarajan dimension}, which generalizes both fat$_γ$ and Natarajan dimension, and prove that its finiteness at every positive scale is necessary and sufficient for learnability. We also introduce a \textbf{fat$_γ$Graph} dimension extending the classical \gra dimension and establish inequalities comparing the two dimensions at different scales, leading to an equivalent characterization of learnability. Finally, we show that a distribution-valued function class is learnable if and only if each of its coordinate classes is learnable in the probabilistic concept model.

stat.ML↗

arXiv2026

No-Regret Language Generation

We introduce no-regret generation, which requires a generator to make a sublinear number of mistakes uniformly over all demonstration sequences and compatible target languages. We also formulate an agnostic variant that allows arbitrary demonstrations that may not be compatible with any languages. For both settings, we introduce tree-based mistake-forcing dimensions that exactly characterize finite-horizon minimax complexity and establish necessary and sufficient conditions for no-regret generation. Our characterizations reveal a rich spectrum of generation rates: up to constant rescaling, every admissible nondecreasing profile is attainable in both the realizable and agnostic settings. Finally, we connect generation complexity to online prediction: for language classes of finite Littlestone dimension $d$, we obtain realizable mistake bounds of $O(d\log(1+T/d))$ and agnostic regret bounds of $O(\sqrt{dT\log(1+T/d)})$. The realizable bound is optimal up to universal constants.

cs.LG↗

arXiv2026

A Greedy PDE Router for Blending Neural Operators and Classical Methods

When solving PDEs, classical numerical solvers are often computationally expensive, while machine learning methods can suffer from spectral bias, failing to capture high-frequency components. Designing an optimal hybrid iterative solver--where, at each iteration, a solver is selected from an ensemble of solvers to leverage their complementary strengths--poses a challenging combinatorial problem. While greedy selection is desirable for its constant-factor approximation guarantee to the optimal solution under Lipschitz assumptions, it requires knowledge of the true error at each step, which is unavailable in practice. We address this by proposing an approximate greedy router that efficiently mimics a greedy approach to solver selection. Empirical results on the Poisson, convection-diffusion, and anisotropic diffusion equations show that our method consistently reduces time-to-solution relative to single-solver baselines and existing hybrid approaches such as HINTS.

stat.ME↗

arXiv2026

Compute Aligned Training: Optimizing for Test Time Inference

Scaling test-time compute has emerged as a powerful mechanism for enhancing Large Language Model (LLM) performance. However, standard post-training paradigms, Supervised Fine-Tuning (SFT) and Reinforcement Learning (RL), optimize the likelihood of individual samples under a base policy, creating a misalignment with test time procedures that rely on aggregated or filtered outputs. In this work, we propose Compute Aligned Training, which aligns training objectives with test-time strategies. By conceptualizing inference strategies as operators on the base policy, we derive new loss functions that maximize performance when said strategies are applied. We instantiate such loss functions for SFT and RL across common test time strategies. Finally, we provide empirical evidence that this training method substantially improves test time scaling over standard training.

cs.LG↗

arXiv2026

Robust Detection of LLM-Generated Text under Contamination

We study the detection of LLM-generated text under editing and contamination. Modeling human and machine text as finite-order Markov processes with Huber contamination, we characterize an exact boundary for reliable detection under our assumptions. Detection is impossible when contamination is sufficiently large relative to clean-source separation. Below this boundary, a collection of clipped likelihood-ratio tests achieves vanishing worst-case errors. This construction motivates clipping as a simple modification of existing statistical detectors. For a broad class of additive scores, we identify conditions under which the clipped test is consistent while the raw test's worst-case power tends to zero. We evaluate seven detectors across three datasets and three generation models, and on the RAID benchmark. Clipping improves robustness in both studies, with gains varying across detectors and contamination settings. For example, at a target false-positive rate of 5\%, clipping improves the log-likelihood--log-rank ratio (LRR) detector's true-positive rate by a median of 8.3 percentage points in the controlled study and 2.1 and 4.3 points in rate- and attack-specific RAID evaluations, respectively.

stat.ML↗

arXiv2026

Entropy Regularization: A Free Correction to Cross-Entropy for Verified Demonstrations

Large language models are often post-trained on expert demonstrations using cross-entropy (CE), even when the downstream objective is not to imitate the demonstrated solution but to produce any output accepted by a verifier. This mismatch is seen in verifiable domains with multiple correct solutions, such as mathematical reasoning and code generation, where training data may contain only one expert solution per problem. We show that minimizing cross-entropy can be misaligned with minimizing verifier risk; two policies can assign identical likelihood to the observed demonstrations while placing different probability mass on incorrect outputs. This is formalized through a learning-theoretic counterexample in which CE minimization selects a suboptimal policy. We identify that controlling the support of the learned policy can solve this problem by preventing probability mass from spreading to unsupported outputs. Since support size is non-differentiable and computationally intractable, we propose entropy-regularized cross-entropy (ER-CE), using token-level Shannon entropy as a tractable proxy. Finally, across mathematical reasoning and code-generation benchmarks, we find that entropy-regularized training consistently improves verifier accuracy over standard cross-entropy. Our results identify a simple failure mode of imitation-based post-training in verifiable tasks and provide a practical objective that is better aligned with producing correct outputs.

cs.LG↗

arXiv2026

Direct Optimization of Generators for Search in Automated Theorem Proving

Fine-tuned Large Language Models (LLMs) significantly advance Automated Theorem Proving (ATP), but are often deployed as guiding policies within tree search rather than for single-attempt generation. Recent work shows cross entropy is suboptimal for an LLM used in flat search strategies such as aggregation or filtering and that work has developed new loss functions to correct this misalignment. Extending this alignment to tree search is more challenging: proof discovery depends on exploration and recovery through off-trace states that supervised demonstrations do not reveal. We extend Compute-Aligned Training (CAT) to this setting through an abstraction of policy-guided search, deriving tractable, trace-supported losses. Alongside these search-aware losses, we introduce a search-agnostic uniform-allocation (UA) loss that accounts for the budget without specifying the specific search. Both induce scalar weights on per-tactic cross-entropy gradients. We characterize how off-trace behavior affects the search-aware weights, including conditions for vanishing approximation error at large budgets. On a Lean benchmark, both approaches achieve higher observed proof-success rates than cross-entropy across six search strategies, with strong results from a single shared UA adapter. Budget sweeps show larger gains over cross-entropy at 16 than at 256 expansions, implying CAT scales with test time compute.

cs.AI↗

arXiv2026

A Training-free Method for LLM Text Attribution

Verifying the provenance of text is increasingly important for firms, educational institutions, and online platforms as Large Language Models (LLMs) produce output that is nearly indistinguishable from human-generated content. We study the problem of determining whether a given text was generated by a particular LLM while controlling the false positive rate. We model LLM-generated text as a sequential stochastic process and develop training-free statistical tests to (i) distinguish between text produced by two known sets of LLMs and (ii) determine whether text was generated by a known LLM or by a distinguishable unknown source, such as a human or another model. We prove that both Type I and Type II errors decay exponentially with text length, establish analogous guarantees for black-box access via sampling, and provide an information-theoretic lower bound showing that there exist model pairs for which no statistical test can make both errors decay faster than exponentially with text length. Numerical experiments empirically evaluate the tests in practical settings and demonstrate strong overall performance, including under many adversarial edits. Our framework provides rigorous guarantees for LLM provenance detection, with applications to content verification, institutional compliance, and misinformation mitigation.

stat.ML↗

arXiv2026

A General-Purpose Molecular Foundation Model Transfers Across Diverse Olfactory Tasks

Foundation models have transformed molecular property prediction, yet it remains unclear whether a molecular foundation model, fine-tuned on a single canonical olfactory prediction task, can learn representations that transfer across diverse machine olfaction problems. We investigate this question by fine-tuning Uni-Mol2 on the GS-LF benchmark for multi-label odor descriptor prediction and evaluating the resulting model, without additional deep-learning training, on four complementary downstream settings: cross-dataset odor descriptor prediction, odorous-versus-odorless classification, enantiomer evaluation, and odor mixture discriminability. The fine-tuned model matches or exceeds the performance of the state-of-the-art olfaction-specific baseline on the primary GS-LF benchmark and consistently transfers across these downstream evaluations. The enantiomer analysis further shows that three-dimensional molecular representations distinguish mirror-image molecules in a way that two-dimensional graph models fundamentally cannot, although accurately predicting the perceptual consequences of stereochemistry remains an open challenge. Together, these results support a train-once, transfer-across-tasks paradigm for machine olfaction and suggest that chemically pretrained molecular representations provide a strong foundation for transferable olfactory prediction.

cs.LG↗

arXiv2026

From Non-Convex to Strongly Convex: Curvature-Adaptive FTPL for Online Optimization

Curvature adaptivity is a classical theme in online optimization: for convex Lipschitz losses, adaptive methods interpolate between the optimal $O(\sqrt{T})$ regret for general convex losses and $O(\log T)$ regret under strong convexity. Recent work has shown that Follow-the-Perturbed-Leader (FTPL) achieves optimal $O(\sqrt{T})$ regret even for online non-convex Lipschitz losses, assuming access to an approximate offline-optimization oracle, but these guarantees do not exploit curvature. We show that FTPL can be made curvature-adaptive in the non-convex setting, without knowing in advance how curvature will accumulate over time. Our algorithm replaces the fixed perturbation scale of standard FTPL with a time-varying scale chosen using only past information. We give a simple follow-the-leader tuning rule for this scale and show that it competes, up to constants, with the best choice in hindsight. The resulting method achieves $O(\sqrt{T})$ regret for arbitrary non-convex Lipschitz losses and improves as cumulative curvature grows; with sufficiently accurate oracle calls, it achieves $O(\log T)$ regret when cumulative curvature grows linearly, which includes the classical strongly convex regime. We complement these upper bounds with matching lower bounds for prescribed cumulative-curvature sequences, already for one-dimensional convex losses, showing that the tradeoff between worst-case non-convex regret and curvature-driven fast rates is intrinsic.

cs.LG↗

arXiv2026

Is Zero-Shot Super-Resolution Possible in Operator Learning?

Neural operators are often reported to exhibit zero-shot super-resolution, a phenomenon in which a model trained on coarse grids produces accurate predictions on finer testing grids without additional retraining. Despite strong empirical evidence, the theoretical foundations of this phenomenon remain unclear. In this work, we provide a systematic theoretical study of zero-shot super-resolution in operator learning. We first show that zero-shot super-resolution can be information-theoretically impossible even in benign settings such as when the input functions are available over the entire continuum and the ground truth is a simple rank-one linear operator. We then identify H{\" o}lder smoothness of the output functions as a sufficient condition for zero-shot super-resolution and derive corresponding generalization bounds. Finally, we also validate the identified failure modes through experimental results.

stat.ML↗

arXiv2026

Offline Constrained Reinforcement Learning under Partial Data Coverage

We study offline constrained reinforcement learning with general function approximation in discounted constrained Markov decision processes. Prior methods either require full data coverage for evaluating intermediate policies, lack oracle efficiency, or requires the knowledge of data-generating distribution for policy extraction. We propose PDOCRL, an oracle-efficient primal-dual algorithm based on a decomposed linear-programming formulation that makes the policy an explicit optimization variable. This avoids policy extraction that requires the knowledge of data-generating distribution, and only uses standard policy-optimization, online linear-optimization, and linear-minimization oracles. We show that saddle-point formulations using general function approximation can have spurious saddle points even when an optimal solution is realizable, and identify a stronger realizability condition under which every restricted saddle point is optimal. Under this condition and partial coverage of an optimal policy, PDOCRL returns a near-optimal, near-feasible policy with a $\widetilde{\mathcal O}(ε^{-2})$ sample guarantee, without access to the data-generating distribution. Empirically, PDOCRL is competitive with strong baselines on standard offline constrained RL benchmarks.

stat.ML↗

arXiv2026

Online Conformal Prediction: Enforcing monotonicity via Online Optimization

Conformal prediction provides a principled framework for uncertainty quantification with finite-sample coverage guarantees. While recent work has extended conformal prediction to online and sequential settings, existing methods typically focus on a single coverage level and do not ensure consistency across multiple confidence levels. In many real-world applications, such as weather forecasting, macroeconomic prediction, and risk management, different users operate under heterogeneous risk tolerances and require calibrated uncertainty estimates across a range of coverage levels. In such settings, it is desirable to produce prediction sets corresponding to different coverage levels that are nested and valid simultaneously. In this paper, we propose two novel online conformal prediction methods that output \emph{nested prediction sets} across a range of coverage levels, enabling simultaneous uncertainty quantification across the entire risk spectrum. Beyond interpretability, jointly estimating multiple coverage levels is known to improve statistical efficiency in classical quantile regression by enforcing non-crossing constraints and sharing information across quantiles. Our approaches leverage an online optimization perspective with small regret that translates to quantile estimation error control while enforcing nestedness of prediction sets. Empirical results on synthetic and real-world datasets, including applications in forecasting tasks with heterogeneous risk requirements, demonstrate that our method achieves stable coverage across all levels, strictly nested prediction sets, and improved efficiency compared to existing online conformal baselines.

stat.ML↗

arXiv2026

Operator Learning for Schrödinger Equation: Unitarity, Error Bounds, and Time Generalization

We consider the problem of learning the evolution operator for the time-dependent Schrödinger equation, where the Hamiltonian may vary with time. Existing neural network-based surrogates often ignore fundamental properties of the Schrödinger equation, such as linearity and unitarity, and lack theoretical guarantees on prediction error or time generalization. To address this, we introduce a linear estimator for the evolution operator that preserves a weak form of unitarity. We establish both upper bounds and lower bounds on the prediction error of the proposed estimator that hold uniformly over classes of sufficiently smooth initial wave functions. Additionally, we derive time generalization bounds that quantify how the estimator extrapolates beyond the time points seen during training. Experiments across real-world Hamiltonians -- including hydrogen atoms, ion traps for qubit design, and optical lattices -- show that our estimator achieves relative errors up to two orders of magnitude smaller than state-of-the-art methods such as the Fourier Neural Operator and DeepONet.

stat.ML↗

arXiv2026

Characterizing the Multiclass Learnability of Forgiving 0-1 Loss Functions

In this paper we will give a characterization of the learnability of forgiving 0-1 loss functions in the multiclass setting with effectively finite cardinality of the output and label space. To do this, we create a new combinatorial dimension that is based off of the Natarajan Dimension and we show that a hypothesis class is learnable in our setting if and only if this Generalized Natarajan Dimension is finite. We also show how this dimension characterizes other known learning settings such as a vast amount of instantiations of learning with set-valued feedback and a modified version of list learning.

cs.LG↗

arXiv2026

Distribution-Free Robust Predict-Then-Optimize in Function Spaces

The need to rapidly solve PDEs in engineering design workflows has spurred the rise of neural surrogate models. In particular, neural operator models provide a discretization-invariant surrogate by retaining the infinite-dimensional, functional form of their arguments. Despite improved throughput, such methods lack guarantees on accuracy, unlike classical numerical PDE solvers. Optimizing engineering designs under these potentially miscalibrated surrogates thus runs the risk of producing designs that perform poorly upon deployment. In a similar vein, there is growing interest in automated decision-making under black-box predictors in the finite-dimensional setting, where a similar risk of suboptimality exists under poorly calibrated models. For this reason, methods have emerged that produce adversarially robust decisions under uncertainty estimates of the upstream model. One such framework leverages conformal prediction, a distribution-free post-hoc uncertainty quantification method, to provide these estimates due to its natural pairing with black-box predictors. We herein extend this line of conformally robust decision-making to infinite-dimensional function spaces. We first extend the typical conformal prediction guarantees over finite-dimensional spaces to infinite-dimensional Sobolev spaces. We then demonstrate how such uncertainty can be leveraged to robustly formulate engineering design tasks and characterize the suboptimality of the resulting robust optimal designs. We then empirically demonstrate the generality of our functional conformal coverage method across a diverse collection of PDEs, including the Poisson and heat equations, and showcase the significant improvement of such robust design in a quantum state discrimination task.

cs.LG↗