Large language models (LLMs) have achieved remarkable performance but face critical challenges: hallucinations and high inference costs. Leveraging multiple experts offers a solution: deferring uncertain inputs to more capable experts improves reliability, while routing simpler queries to smaller, distilled models enhances efficiency. This motivates the problem of learning with multiple-expert deferral. This thesis presents a comprehensive study of this problem and the related problem of learning with abstention, supported by strong consistency guarantees. First, for learning with abstention (a special case of deferral), we analyze score-based and predictor-rejector formulations in multi-class classification. We introduce new families of surrogate losses and prove strong non-asymptotic, hypothesis set-specific consistency guarantees, resolving two existing open questions. We analyze both single-stage and practical two-stage settings, with experiments on CIFAR-10, CIFAR-100, and SVHN demonstrating the superior performance of our algorithms. Second, we address general multi-expert deferral in classification. We design new surrogate losses for both single-stage and two-stage scenarios and prove they benefit from strong $H$-consistency bounds. For the two-stage scenario, we show that our surrogate losses are realizable $H$-consistent for constant cost functions, leading to effective new algorithms. Finally, we introduce a novel framework for regression with deferral to address continuous label spaces. Our versatile framework accommodates multiple experts and various cost structures, supporting both single-stage and two-stage methods. It subsumes recent work on regression with abstention. We propose new surrogate losses with proven $H$-consistency and demonstrate the empirical effectiveness of the resulting algorithms.

Part qualification is crucial in additive manufacturing (AM) because it ensures that additively manufactured parts can be consistently produced and reliably used in critical applications. Part qualification aims at verifying that an additively manufactured part meets performance requirements; therefore, predicting the complex stress-strain behaviors of additively manufactured parts is critical. We develop a dynamic time warping (DTW)-transfer learning (TL) framework for additive manufacturing part qualification by transferring knowledge of the stress-strain behaviors of additively manufactured low-cost polymers to metals. Specifically, the framework employs DTW to select a polymer dataset as the source domain that is the most relevant to the target metal dataset. Using a long short-term memory (LSTM) model, four source polymers (i.e., Nylon, PLA, CF-ABS, and Resin) and three target metals (i.e., AlSi10Mg, Ti6Al4V, and carbon steel) that are fabricated by different AM techniques are utilized to demonstrate the effectiveness of the DTW-TL framework. Experimental results show that the DTW-TL framework identifies the closest match between polymers and metals to select one single polymer dataset as the source domain. The DTW-TL model achieves the lowest mean absolute percentage error of 12.41% and highest coefficient of determination of 0.96 when three metals are used as the target domain, respectively, outperforming the vanilla LSTM model without TL as well as the TL model pre-trained on four polymer datasets as the source domain.

Reasoning reinforcement learning (RL) has recently revealed a new scaling effect: test-time scaling. Thinking models such as R1 and o1 improve their reasoning accuracy at test time as the length of the reasoning context increases. However, compared with training-time scaling, test-time scaling is fundamentally limited by the limited context length of base models, which remains orders of magnitude smaller than the amount of tokens consumed during training. We revisit test-time enhancement techniques through the lens of scaling effect and introduce a unified framework of multi-dimensional test-time scaling to extend the capacity of test-time reasoning. Beyond conventional context-length scaling, we consider two additional dimensions: batch scaling, where accuracy improves with parallel sampling, and turn scaling, where iterative self-refinement enhances reasoning quality. Building on this perspective, we propose 3D test-time scaling, which integrates context, batch, and turn scaling. We show that: (1) each dimension demonstrates a test-time scaling effect, but with a bounded capacity; (2) combining all three dimensions substantially improves the reasoning performance of challenging testbeds, including IOI, IMO, and CPHO, and further benefits from human preference feedback; and (3) the human-in-the-loop framework naturally extends to a more open-ended domain, i.e., embodied learning, which enables the design of humanoid control behaviors.

As such, we prevent policies from merely exploiting heuristic rewards without improving the task reward.

Attribution maps are one of the most established tools to explain the functioning of computer vision models. They assign importance scores to input features, indicating how relevant each feature is for the prediction of a deep neural network.

In the area of explainable artificial intelligence, Symbolic Regression (SR) has emerged as a promising approach by discovering interpretable mathematical expressions that fit data. However, SR faces two main challenges: most methods are evaluated on scientific datasets with well-understood relationships, limiting generalization, and SR primarily targets single-output regression, whereas many real-world problems involve multi-target outputs with interdependent variables. To address these issues, we propose multi-task regression GINN-LP (MTRGINN-LP), an interpretable neural network for multi-target symbolic regression. By integrating GINN-LP with a multi-task deep learning, the model combines a shared backbone including multiple power-term approximator blocks with task-specific output layers, capturing inter-target dependencies while preserving interpretability. We validate multi-task GINN-LP on practical multi-target applications, including energy efficiency prediction and sustainable agriculture. Experimental results demonstrate competitive predictive performance alongside high interpretability, effectively extending symbolic regression to broader real-world multi-output tasks.

In this paper, we consider the problem of differentially private (DP) algorithms for isotonic regression. For the most general problem of isotonic regression over a partially ordered set (poset) X and for any Lipschitz loss function, we obtain a pure-DP algorithm that, given n input points, has an expected excess empirical risk of roughly width(X) log |X| /n, where width(X) is the width of the poset. In contrast, we also obtain a near-matching lower bound of roughly (width(X) + log |X|) /n, that holds even for approximate-DP algorithms. Moreover, we show that the above bounds are essentially the best that can be obtained without utilizing any further structure of the poset.

In Appendix A we introduce some basic definitions that are needed for our theoretical results. In Appendix C and Appendix D we prove the error bounds for PPI and PQI. All the other dynamics are preserved. Rewards are 0 for the absorbing action and unchanged elsewhere. Algorithm 1 and 2. As some of the notations is actually a function of the MDP, we clarify the usage Recall the definition of semi-norm of any function of state-action pairs.

Sequence generation and prediction form a cornerstone of modern machine learning, with applications spanning natural language processing, program synthesis, and time-series forecasting. These tasks are typically modeled in an autoregressive fashion, where each token is generated conditional on the preceding ones, and beam search is commonly used to balance exploration and fluency during decoding. While deep learning models and Large Language Models (LLMs) excel at capturing statistical patterns in this setting, they remain ill-equipped to guarantee compliance with formal constraints. In this paper, we introduce ABS: a general and model-agnostic inference-time algorithm that guarantees compliance with any constraint that can be compiled into a Deterministic Finite Automaton (DFA), without requiring retraining. ABS leverages the DFA to guide a constrained variant of beam search: at each decoding step, transitions leading to violations are masked, while remaining paths are dynamically re-ranked according to both the model's probabilities and the automaton's acceptance structure. We formally prove that the resulting sequences are guaranteed to satisfy the given constraints, and we empirically demonstrate that ABS also improves output quality. We validate our approach on three distinct tasks: constrained image-stream classification, controlled text generation, and text infilling. In all settings, ABS achieves perfect constraint satisfaction, while outperforming or matching state-of-the-art baselines on standard quality metrics and efficiency.

Language models (LMs) are increasingly being deployed to perform autonomous data analyses. However, their data awareness -- the ability to recognize, reason over, and appropriately handle data artifacts such as missing values, outliers, and logical inconsistencies -- remains underexplored. These artifacts are especially common in real-world tabular data and, if mishandled, can significantly compromise the validity of analytical conclusions. To address this gap, we present RADAR, a benchmark for systematically evaluating data-aware reasoning on tabular data. We develop a framework to simulate data artifacts via programmatic perturbations to enable targeted evaluation of model behavior. RADAR comprises 2980 table query pairs, grounded in real-world data spanning 9 domains and 5 data artifact types. In addition to evaluating artifact handling, RADAR systematically varies table size to study how reasoning performance holds when increasing table size. Our evaluation reveals that, despite decent performance on tables without data artifacts, frontier models degrade significantly when data artifacts are introduced, exposing critical gaps in their capacity for robust, data-aware analysis. Designed to be flexible and extensible, RADAR supports diverse perturbation types and controllable table sizes, offering a valuable resource for advancing tabular reasoning.