arXiv subjects

Yutao Zhong

Publications and source records attributed to Yutao Zhong.

At least 19 recordsLinked to original sources

arXiv2026

A Theoretical Framework for Modular Learning of Robust Generative Models

Training large-scale generative models is resource-intensive and relies heavily on heuristic dataset weighting. We address two fundamental questions: Can we train Large Language Models (LLMs) modularly, combining small, domain-specific experts to match monolithic performance, and can we do so robustly for any data mixture, eliminating heuristic tuning? We present a theoretical framework for modular generative modeling where a set of pre-trained experts are combined via a gating mechanism. We define the space of normalized gating functions $\mathcal{G}_{1}$ and formulate the problem as a minimax game to find a single robust gate that minimizes divergence to the worst-case data mixture. We prove the existence of such a robust gate using Kakutani's fixed-point theorem and show that modularity acts as a strong regularizer, with generalization bounds scaling with the lightweight gate's complexity. Furthermore, we prove that this modular approach can theoretically outperform models retrained on aggregate data, with the gap characterized by the Jensen-Shannon Divergence. Finally, we introduce a scalable Stochastic Primal-Dual algorithm and a Structural Distillation method for efficient inference. Empirical results on synthetic and real-world datasets confirm that our modular architecture effectively mitigates gradient conflict and can robustly outperform monolithic baselines.

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arXiv2026

Optimized Deferral for Imbalanced Settings

Learning algorithms can be significantly improved by routing complex or uncertain inputs to specialized experts, balancing accuracy with computational cost. This approach, known as learning to defer, is essential in domains like natural language generation, medical diagnosis, and computer vision, where an effective deferral can reduce errors at low extra resource consumption. However, the two-stage learning to defer setting, which leverages existing predictors such as a collection of LLMs or other classifiers, often faces challenges due to an expert imbalance problem. This imbalance can lead to suboptimal performance, with deferral algorithms favoring the majority expert. We present a comprehensive study of two-stage learning to defer in expert imbalance settings. We cast the deferral loss optimization as a novel cost-sensitive learning problem over the input-expert domain. We derive new margin-based loss functions and guarantees tailored to this setting, and develop novel algorithms for cost-sensitive learning. Leveraging these results, we design principled deferral algorithms, MILD (Margin-based Imbalanced Learning to Defer), specifically suited for expert imbalance settings. Extensive experiments demonstrate the effectiveness of our approach, showing clear improvements over existing baselines on both image classification and real-world Large Language Model (LLM) routing tasks.

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arXiv2026

Mind the Gap: Structure-Aware Consistency in Preference Learning

Aligning Large Language Models (LLMs) with human intent, whether through explicit reward modeling or direct methods such as DPO, fundamentally relies on minimizing a surrogate loss as a proxy for the true pairwise ranking objective. We prove that this reliance is flawed for the standard surrogate losses used: for the equicontinuous hypothesis sets characteristic of neural networks, no standard surrogate provides a meaningful consistency guarantee. Minimizing the surrogate loss to zero can leave the true ranking error arbitrarily high. To resolve this, we formulate LLM alignment within a margin-shifted ranking framework and derive $H$-consistency bounds showing that enforcing a confidence margin $γ$ is not merely beneficial but necessary for consistency. We further introduce Structure-Aware $H$-consistency and a corresponding objective (SA-DPO) that adapts the margin to the semantic distance between responses, preventing instability on near-synonymous pairs. Finally, we analyze the trade-off between the margin required for consistency and the model's finite capacity to satisfy it, revealing a strict hierarchy of surrogate losses: heavy-tailed surrogates (e.g., the Polynomial Hinge family) offer strictly superior consistency guarantees for capacity-bounded models compared to the logistic loss used in DPO. Experiments on UltraFeedback and Argilla DPO-Mix-7k confirm that SA-DPO consistently outperforms DPO and SimPO, with a 58.5% head-to-head win-rate in downstream generation quality.

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arXiv2026

Linear-Core Surrogates: Smooth Loss Functions with Linear Rates for Classification and Structured Prediction

A fundamental dichotomy in the theory of classification sets smoothness against statistical efficiency: smooth surrogate losses such as the logistic loss enable fast $O(1/T)$ optimization but yield slow square-root $H$-consistency bounds, while piecewise-linear losses like the Hinge loss achieve optimal linear $H$-consistency rates but are non-differentiable. We introduce Linear-Core (LC) Surrogates, the first family of explicit convex loss functions that provably resolve this tension. By stitching a linear core to a smooth tail, we construct surrogates that are differentiable everywhere ($C^1$, and even $C^2$ under mild conditions) while retaining strict linear $H$-consistency bounds, the strongest known form of consistency guarantee. We establish these linear bounds across three increasingly complex settings: binary classification, multi-class classification, and structured prediction. To our knowledge, this is the first explicit construction to simultaneously achieve smoothness and linear $H$-consistency in any of these settings. Beyond their theoretical appeal, Linear-Core Surrogates offer practical advantages. In multi-class classification, their constant gradient profile near the decision boundary provides natural robustness to instance-dependent label noise, outperforming Cross-Entropy by 2.6% on corrupted CIFAR-10. In structured prediction, their smoothness enables an unbiased stochastic gradient estimator that bypasses the $O(|Y|^2)$ per-step complexity of exact inference, yielding a 23$\times$ speedup over Structured SVMs on large-vocabulary sequence tagging tasks.

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arXiv2026

Principled Algorithms for Optimizing Generalized Metrics in Multi-Label Learning

Many real-world classification tasks require predicting multiple labels per instance, necessitating the optimization of complex evaluation metrics such as the $F$-measure and Jaccard index. While the Empirical Utility Maximization (EUM) framework is natural for these population-level metrics, existing theoretical results are largely limited to asymptotic Bayes-consistency. In this paper, we develop principled learning algorithms for optimizing a broad class of generalized metrics within the EUM framework, grounded in the stronger notion of $H$-consistency. Our key contribution is the design of novel surrogate loss functions for multi-label learning that admit provable $H$-consistency bounds, enabling optimization with non-asymptotic guarantees tailored to the hypothesis class and finite samples. Crucially, we prove these combinatorially formulated surrogates decompose exactly, operating in strictly $O(l)$ time without approximations. Building on this foundation, we introduce MMO (Multi-Label Metric Optimization), a new family of algorithms for optimizing generalized linear-fractional metrics. We validate our approach through extensive experiments, demonstrating robust scalability and superior performance over state-of-the-art continuous baselines on large-scale datasets (MS-COCO, Reuters-21578) in high-sparsity, deep learning regimes. Our results offer both theoretical rigor and practical effectiveness for general multi-label metric optimization.

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arXiv2026

Generalized Distributional Alignment Games for Unbiased Answer-Level Fine-Tuning

The Distributional Alignment Game framework provides a powerful variational perspective on Answer-Level Fine-Tuning (ALFT). However, standard algorithms for these games rely on estimating logarithmic rewards from small batches, introducing a systematic bias due to Jensen's inequality that can destabilize training. In this paper, we systematically resolve this structural estimation bias. First, we generalize the alignment game to arbitrary Bregman divergences, showing that for a family of geometries inducing polynomial rewards, we can construct provably exact and unbiased estimators using U-statistics. Second, for the canonical KL divergence game where an exact solution is impossible, we derive a globally robust minimax polynomial estimator that is provably optimal, achieving the fundamental statistical error limit of $Θ(1/K^2)$, which we establish via the Ditzian-Totik theorem. Finally, we synthesize these two approaches to propose a novel Variance-Optimal Augmented Polynomial Optimization Program (AQP) Estimator, proving that by systematically reducing variance, our method achieves not only optimal bias but also provably accelerated game convergence, leading to more efficient and stable training with zero online computational overhead.

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arXiv2025

Improved Balanced Classification with Theoretically Grounded Loss Functions

The balanced loss is a widely adopted objective for multi-class classification under class imbalance. By assigning equal importance to all classes, regardless of their frequency, it promotes fairness and ensures that minority classes are not overlooked. However, directly minimizing the balanced classification loss is typically intractable, which makes the design of effective surrogate losses a central question. This paper introduces and studies two advanced surrogate loss families: Generalized Logit-Adjusted (GLA) loss functions and Generalized Class-Aware weighted (GCA) losses. GLA losses generalize Logit-Adjusted losses, which shift logits based on class priors, to the broader general cross-entropy loss family. GCA loss functions extend the standard class-weighted losses, which scale losses inversely by class frequency, by incorporating class-dependent confidence margins and extending them to the general cross-entropy family. We present a comprehensive theoretical analysis of consistency for both loss families. We show that GLA losses are Bayes-consistent, but only $H$-consistent for complete (i.e., unbounded) hypothesis sets. Moreover, their $H$-consistency bounds depend inversely on the minimum class probability, scaling at least as $1/\mathsf p_{\min}$. In contrast, GCA losses are $H$-consistent for any hypothesis set that is bounded or complete, with $H$-consistency bounds that scale more favorably as $1/\sqrt{\mathsf p_{\min}}$, offering significantly stronger theoretical guarantees in imbalanced settings. We report the results of experiments demonstrating that, empirically, both the GCA losses with calibrated class-dependent confidence margins and GLA losses can greatly outperform straightforward class-weighted losses as well as the LA losses. GLA generally performs slightly better in common benchmarks, whereas GCA exhibits a slight edge in highly imbalanced settings.

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arXiv2025

Balancing the Scales: A Theoretical and Algorithmic Framework for Learning from Imbalanced Data

Class imbalance remains a major challenge in machine learning, especially in multi-class problems with long-tailed distributions. Existing methods, such as data resampling, cost-sensitive techniques, and logistic loss modifications, though popular and often effective, lack solid theoretical foundations. As an example, we demonstrate that cost-sensitive methods are not Bayes-consistent. This paper introduces a novel theoretical framework for analyzing generalization in imbalanced classification. We propose a new class-imbalanced margin loss function for both binary and multi-class settings, prove its strong $H$-consistency, and derive corresponding learning guarantees based on empirical loss and a new notion of class-sensitive Rademacher complexity. Leveraging these theoretical results, we devise novel and general learning algorithms, IMMAX (Imbalanced Margin Maximization), which incorporate confidence margins and are applicable to various hypothesis sets. While our focus is theoretical, we also present extensive empirical results demonstrating the effectiveness of our algorithms compared to existing baselines.

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arXiv2025

Mastering Multiple-Expert Routing: Realizable $H$-Consistency and Strong Guarantees for Learning to Defer

The problem of learning to defer with multiple experts consists of optimally assigning input instances to experts, balancing the trade-off between their accuracy and computational cost. This is a critical challenge in natural language generation, but also in other fields such as image processing, and medical diagnostics. Recent studies have proposed surrogate loss functions to optimize deferral, but challenges remain in ensuring their consistency properties. This paper introduces novel surrogate loss functions and efficient algorithms with strong theoretical learning guarantees. We address open questions regarding realizable $H$-consistency, $H$-consistency bounds, and Bayes-consistency for both single-stage (jointly learning predictor and deferral function) and two-stage (learning only the deferral function with a fixed expert) learning scenarios. For single-stage deferral, we introduce a family of new realizable $H$-consistent surrogate losses and further prove $H$-consistency for a selected member. For two-stage deferral, we derive new surrogate losses that achieve realizable $H$-consistency, $H$-consistency bounds, and Bayes-consistency for the two-expert scenario and, under natural assumptions, multiple-expert scenario. Additionally, we provide enhanced theoretical guarantees under low-noise assumptions for both scenarios. Finally, we report the results of experiments using our proposed surrogate losses, comparing their performance against existing baselines.

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arXiv2025

Principled Algorithms for Optimizing Generalized Metrics in Binary Classification

In applications with significant class imbalance or asymmetric costs, metrics such as the $F_β$-measure, AM measure, Jaccard similarity coefficient, and weighted accuracy offer more suitable evaluation criteria than standard binary classification loss. However, optimizing these metrics present significant computational and statistical challenges. Existing approaches often rely on the characterization of the Bayes-optimal classifier, and use threshold-based methods that first estimate class probabilities and then seek an optimal threshold. This leads to algorithms that are not tailored to restricted hypothesis sets and lack finite-sample performance guarantees. In this work, we introduce principled algorithms for optimizing generalized metrics, supported by $H$-consistency and finite-sample generalization bounds. Our approach reformulates metric optimization as a generalized cost-sensitive learning problem, enabling the design of novel surrogate loss functions with provable $H$-consistency guarantees. Leveraging this framework, we develop new algorithms, METRO (Metric Optimization), with strong theoretical performance guarantees. We report the results of experiments demonstrating the effectiveness of our methods compared to prior baselines.

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arXiv2025

Enhanced $H$-Consistency Bounds

Recent research has introduced a key notion of $H$-consistency bounds for surrogate losses. These bounds offer finite-sample guarantees, quantifying the relationship between the zero-one estimation error (or other target loss) and the surrogate loss estimation error for a specific hypothesis set. However, previous bounds were derived under the condition that a lower bound of the surrogate loss conditional regret is given as a convex function of the target conditional regret, without non-constant factors depending on the predictor or input instance. Can we derive finer and more favorable $H$-consistency bounds? In this work, we relax this condition and present a general framework for establishing enhanced $H$-consistency bounds based on more general inequalities relating conditional regrets. Our theorems not only subsume existing results as special cases but also enable the derivation of more favorable bounds in various scenarios. These include standard multi-class classification, binary and multi-class classification under Tsybakov noise conditions, and bipartite ranking.

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arXiv2025

Fundamental Novel Consistency Theory: $H$-Consistency Bounds

In machine learning, the loss functions optimized during training often differ from the target loss that defines task performance due to computational intractability or lack of differentiability. We present an in-depth study of the target loss estimation error relative to the surrogate loss estimation error. Our analysis leads to $H$-consistency bounds, which are guarantees accounting for the hypothesis set $H$. These bounds offer stronger guarantees than Bayes-consistency or $H$-calibration and are more informative than excess error bounds. We begin with binary classification, establishing tight distribution-dependent and -independent bounds. We provide explicit bounds for convex surrogates (including linear models and neural networks) and analyze the adversarial setting for surrogates like $ρ$-margin and sigmoid loss. Extending to multi-class classification, we present the first $H$-consistency bounds for max, sum, and constrained losses, covering both non-adversarial and adversarial scenarios. We demonstrate that in some cases, non-trivial $H$-consistency bounds are unattainable. We also investigate comp-sum losses (e.g., cross-entropy, MAE), deriving their first $H$-consistency bounds and introducing smooth adversarial variants that yield robust learning algorithms. We develop a comprehensive framework for deriving these bounds across various surrogates, introducing new characterizations for constrained and comp-sum losses. Finally, we examine the growth rates of $H$-consistency bounds, establishing a universal square-root growth rate for smooth surrogates in binary and multi-class tasks, and analyze minimizability gaps to guide surrogate selection.

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arXiv2025

Beyond Tsybakov: Model Margin Noise and $\mathcal{H}$-Consistency Bounds

We introduce a new low-noise condition for classification, the Model Margin Noise (MM noise) assumption, and derive enhanced $\mathcal{H}$-consistency bounds under this condition. MM noise is weaker than Tsybakov noise condition: it is implied by Tsybakov noise condition but can hold even when Tsybakov fails, because it depends on the discrepancy between a given hypothesis and the Bayes-classifier rather than on the intrinsic distributional minimal margin (see Figure 1 for an illustration of an explicit example). This hypothesis-dependent assumption yields enhanced $\mathcal{H}$-consistency bounds for both binary and multi-class classification. Our results extend the enhanced $\mathcal{H}$-consistency bounds of Mao, Mohri, and Zhong (2025a) with the same favorable exponents but under a weaker assumption than the Tsybakov noise condition; they interpolate smoothly between linear and square-root regimes for intermediate noise levels. We also instantiate these bounds for common surrogate loss families and provide illustrative tables.

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arXiv2025

Budgeted Multiple-Expert Deferral

Learning to defer uncertain predictions to costly experts offers a powerful strategy for improving the accuracy and efficiency of machine learning systems. However, standard training procedures for deferral algorithms typically require querying all experts for every training instance, an approach that becomes prohibitively expensive when expert queries incur significant computational or resource costs. This undermines the core goal of deferral: to limit unnecessary expert usage. To overcome this challenge, we introduce the budgeted deferral framework, which aims to train effective deferral algorithms while minimizing expert query costs during training. We propose new algorithms for both two-stage and single-stage multiple-expert deferral settings that selectively query only a subset of experts per training example. While inspired by active learning, our setting is fundamentally different: labels are already known, and the core challenge is to decide which experts to query in order to balance cost and predictive performance. We establish theoretical guarantees for both of our algorithms, including generalization bounds and label complexity analyses. Empirical results across several domains show that our algorithms substantially reduce training costs without sacrificing prediction accuracy, demonstrating the practical value of our budget-aware deferral algorithms.

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arXiv2024

Realizable $H$-Consistent and Bayes-Consistent Loss Functions for Learning to Defer

We present a comprehensive study of surrogate loss functions for learning to defer. We introduce a broad family of surrogate losses, parameterized by a non-increasing function $Ψ$, and establish their realizable $H$-consistency under mild conditions. For cost functions based on classification error, we further show that these losses admit $H$-consistency bounds when the hypothesis set is symmetric and complete, a property satisfied by common neural network and linear function hypothesis sets. Our results also resolve an open question raised in previous work (Mozannar et al., 2023) by proving the realizable $H$-consistency and Bayes-consistency of a specific surrogate loss. Furthermore, we identify choices of $Ψ$ that lead to $H$-consistent surrogate losses for any general cost function, thus achieving Bayes-consistency, realizable $H$-consistency, and $H$-consistency bounds simultaneously. We also investigate the relationship between $H$-consistency bounds and realizable $H$-consistency in learning to defer, highlighting key differences from standard classification. Finally, we empirically evaluate our proposed surrogate losses and compare them with existing baselines.

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arXiv2024

Multi-Label Learning with Stronger Consistency Guarantees

We present a detailed study of surrogate losses and algorithms for multi-label learning, supported by $H$-consistency bounds. We first show that, for the simplest form of multi-label loss (the popular Hamming loss), the well-known consistent binary relevance surrogate suffers from a sub-optimal dependency on the number of labels in terms of $H$-consistency bounds, when using smooth losses such as logistic losses. Furthermore, this loss function fails to account for label correlations. To address these drawbacks, we introduce a novel surrogate loss, multi-label logistic loss, that accounts for label correlations and benefits from label-independent $H$-consistency bounds. We then broaden our analysis to cover a more extensive family of multi-label losses, including all common ones and a new extension defined based on linear-fractional functions with respect to the confusion matrix. We also extend our multi-label logistic losses to more comprehensive multi-label comp-sum losses, adapting comp-sum losses from standard classification to the multi-label learning. We prove that this family of surrogate losses benefits from $H$-consistency bounds, and thus Bayes-consistency, across any general multi-label loss. Our work thus proposes a unified surrogate loss framework benefiting from strong consistency guarantees for any multi-label loss, significantly expanding upon previous work which only established Bayes-consistency and for specific loss functions. Additionally, we adapt constrained losses from standard classification to multi-label constrained losses in a similar way, which also benefit from $H$-consistency bounds and thus Bayes-consistency for any multi-label loss. We further describe efficient gradient computation algorithms for minimizing the multi-label logistic loss.

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arXiv2024

Cardinality-Aware Set Prediction and Top-$k$ Classification

We present a detailed study of cardinality-aware top-$k$ classification, a novel approach that aims to learn an accurate top-$k$ set predictor while maintaining a low cardinality. We introduce a new target loss function tailored to this setting that accounts for both the classification error and the cardinality of the set predicted. To optimize this loss function, we propose two families of surrogate losses: cost-sensitive comp-sum losses and cost-sensitive constrained losses. Minimizing these loss functions leads to new cardinality-aware algorithms that we describe in detail in the case of both top-$k$ and threshold-based classifiers. We establish $H$-consistency bounds for our cardinality-aware surrogate loss functions, thereby providing a strong theoretical foundation for our algorithms. We report the results of extensive experiments on CIFAR-10, CIFAR-100, ImageNet, and SVHN datasets demonstrating the effectiveness and benefits of our cardinality-aware algorithms.

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arXiv2024

A Universal Growth Rate for Learning with Smooth Surrogate Losses

This paper presents a comprehensive analysis of the growth rate of $H$-consistency bounds (and excess error bounds) for various surrogate losses used in classification. We prove a square-root growth rate near zero for smooth margin-based surrogate losses in binary classification, providing both upper and lower bounds under mild assumptions. This result also translates to excess error bounds. Our lower bound requires weaker conditions than those in previous work for excess error bounds, and our upper bound is entirely novel. Moreover, we extend this analysis to multi-class classification with a series of novel results, demonstrating a universal square-root growth rate for smooth comp-sum and constrained losses, covering common choices for training neural networks in multi-class classification. Given this universal rate, we turn to the question of choosing among different surrogate losses. We first examine how $H$-consistency bounds vary across surrogates based on the number of classes. Next, ignoring constants and focusing on behavior near zero, we identify minimizability gaps as the key differentiating factor in these bounds. Thus, we thoroughly analyze these gaps, to guide surrogate loss selection, covering: comparisons across different comp-sum losses, conditions where gaps become zero, and general conditions leading to small gaps. Additionally, we demonstrate the key role of minimizability gaps in comparing excess error bounds and $H$-consistency bounds.

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