通用机器学习 · supervised learning

This paper introduces a novel framework for survival analysis by reinterpreting it as a form of density estimation. Our algorithm post-processes density estimation outputs to derive survival functions, enabling the application of any density estimation model to effectively estimate survival functions. This approach broadens the toolkit for survival analysis and enhances the flexibility and applicability of existing techniques. Our framework is versatile enough to handle various survival analysis scenarios, including competing risk models for multiple event types. It can also address dependent censoring when prior knowledge of the dependency between event time and censoring time is available in the form of a copula. In the absence of such information, our framework can estimate the upper and lower bounds of survival functions, accounting for the associated uncertainty.

Model ensemble adversarial attack has become a powerful method for generating transferable adversarial examples that can target even unknown models, but its theoretical foundation remains underexplored. To address this gap, we provide early theoretical insights that serve as a roadmap for advancing model ensemble adversarial attack. We first define transferability error to measure the error in adversarial transferability, alongside concepts of diversity and empirical model ensemble Rademacher complexity. We then decompose the transferability error into vulnerability, diversity, and a constant, which rigidly explains the origin of transferability error in model ensemble attack: the vulnerability of an adversarial example to ensemble components, and the diversity of ensemble components. Furthermore, we apply the latest mathematical tools in information theory to bound the transferability error using complexity and generalization terms, validating three practical guidelines for reducing transferability error: (1) incorporating more surrogate models, (2) increasing their diversity, and (3) reducing their complexity in cases of overfitting. Finally, extensive experiments with 54 models validate our theoretical framework, representing a significant step forward in understanding transferable model ensemble adversarial attacks.

Empirical risk minimization (ERM) with a computationally feasible surrogate loss is a widely accepted approach for classification. Notably, the convexity and calibration (CC) properties of a loss function ensure consistency of ERM in maximizing accuracy, thereby offering a wide range of options for surrogate losses. In this article, we propose a novel ensemble method, namely *EnsLoss*, which extends the ensemble learning concept to combine loss functions within the ERM framework. A key feature of our method is the consideration on preserving the "legitimacy" of the combined losses, i.e., ensuring the CC properties. Specifically, we first transform the CC conditions of losses into loss-derivatives, thereby bypassing the need for explicit loss functions and directly generating calibrated loss-derivatives. Therefore, inspired by Dropout, *EnsLoss* enables loss ensembles through one training process with doubly stochastic gradient descent (i.e., random batch samples and random calibrated loss-derivatives). We theoretically establish the statistical consistency of our approach and provide insights into its benefits. The numerical effectiveness of *EnsLoss* compared to fixed loss methods is demonstrated through experiments on a broad range of 45 pairs of CIFAR10 datasets, the PCam image dataset, and 14 OpenML tabular datasets and with various deep learning architectures. Python repository and source code are available on our Github (https://github.com/statmlben/ensLoss).

We present a principled and simplified design of the projector and loss function for non-contrastive self-supervised learning based on hyperdimensional computing. We theoretically demonstrate that this design introduces an inductive bias that encourages representations to be simultaneously decorrelated and clustered, without explicitly enforcing these properties. This bias provably enhances generalization and suffices to avoid known training failure modes, such as representation, dimensional, cluster, and intracluster collapses. We validate our theoretical findings on image datasets, including SVHN, CIFAR-10, CIFAR-100, and ImageNet-100. Our approach effectively combines the strengths of feature decorrelation and cluster-based self-supervised learning methods, overcoming training failure modes while achieving strong generalization in clustering and linear classification tasks.

Modern semi-supervised learning (SSL) methods rely on pseudolabeling and consistency regularization. Pseudolabeling is typically performed by comparing the model's confidence scores and a predefined threshold. While several heuristics have been proposed to improve threshold selection, the underlying issues of overconfidence and miscalibration in confidence scores remain largely unaddressed, leading to inaccurate pseudolabels, degraded test accuracy, and prolonged training. We take a first-principles approach to learn confidence scores and thresholds with an explicit knob for error. This flexible framework addresses the fundamental question of optimal scores and threshold selection in pseudolabeling. Moreover, it gives practitioners a principled way to control the quality and quantity of pseudolabels. Such control is vital in SSL, where balancing pseudolabel quality and quantity directly affects model performance and training efficiency. Our experiments show that, by integrating this framework with modern SSL methods, we achieve significant improvements in accuracy and training efficiency. In addition, we provide novel insights on the trade-offs between the choices of the error parameter and the end model's performance.

Network quantization, one of the most widely studied model compression methods, effectively quantizes a floating-point model to obtain a fixed-point one with negligible accuracy loss. Although great success was achieved in reducing the model size, it may exacerbate the unfairness in model accuracy across different groups of datasets. This paper considers two widely used algorithms: Post-Training Quantization (PTQ) and Quantization-Aware Training (QAT), with an attempt to understand how they cause this critical issue. Theoretical analysis with empirical verifications reveals two responsible factors, as well as how they influence a metric of fairness in depth. A comparison between PTQ and QAT is then made, explaining an observation that QAT behaves even worse than PTQ in fairness, although it often preserves a higher accuracy at lower bit-widths in quantization. Finally, the paper finds out that several simple data augmentation methods can be adopted to alleviate the disparate impacts of quantization, based on a further observation that class imbalance produces distinct values of the aforementioned factors among different attribute classes. We experiment on either imbalanced (UTK-Face and FER2013) or balanced (CIFAR-10 and MNIST) datasets using ResNet and VGG models for empirical evaluation.

The K-means algorithm is one of the most widely studied clustering algorithms in machine learning. While extensive research has focused on its ability to achieve a globally optimal solution, there still lacks a rigorous analysis of its local optimality guarantees. In this paper, we first present conditions under which the K-means algorithm converges to a locally optimal solution. Based on this, we propose simple modifications to the K-means algorithm which ensure local optimality in both the continuous and discrete sense, with the same computational complexity as the original K-means algorithm. As the dissimilarity measure, we consider a general Bregman divergence, which is an extension of the squared Euclidean distance often used in the K-means algorithm. Numerical experiments confirm that the K-means algorithm does not always find a locally optimal solution in practice, while our proposed methods provide improved locally optimal solutions with reduced clustering loss. Our code is available at https://github.com/lmingyi/LO-K-means.

With rapid advancements in machine learning, first-order algorithms have emerged as the backbone of modern optimization techniques, owing to their computational efficiency and low memory requirements. Recently, the connection between accelerated gradient methods and damped heavy-ball motion, particularly within the framework of Hamiltonian dynamics, has inspired the development of innovative quantum algorithms for continuous optimization. One such algorithm, Quantum Hamiltonian Descent (QHD), leverages quantum tunneling to escape saddle points and local minima, facilitating the discovery of global solutions in complex optimization landscapes. However, QHD faces several challenges, including slower convergence rates compared to classical gradient methods and limited robustness in highly non-convex problems due to the non-local nature of quantum states. Furthermore, the original QHD formulation primarily relies on function value information, which limits its effectiveness. Inspired by insights from high-resolution differential equations that have elucidated the acceleration mechanisms in classical methods, we propose an enhancement to QHD by incorporating gradient information, leading to what we call gradient-based QHD. This gradient-based QHD achieves faster convergence and significantly increases the likelihood of identifying global solutions. Numerical simulations on challenging problem instances demonstrate that this gradient-based QHD outperforms existing quantum and classical methods by at least an order of magnitude.

Retrieval-augmented classification and generation models benefit from *early-stage fusion* of high-quality text-based metadata, often called memory, but face high latency and noise sensitivity. In extreme classification (XC), where low latency is crucial, existing methods use *late-stage fusion* for efficiency and robustness. To enhance accuracy while maintaining low latency, we propose MOGIC, a novel approach to metadata-infused oracle guidance for XC. We train an early-fusion oracle classifier with access to both query-side and label-side ground-truth metadata in textual form and subsequently use it to guide existing memory-based XC disciple models via regularization. The MOGIC algorithm improves precision@1 and propensity-scored precision@1 of XC disciple models by 1-2% on six standard datasets, at no additional inference-time cost. We show that MOGIC can be used in a plug-and-play manner to enhance memory-free XC models such as NGAME or DEXA. Lastly, we demonstrate the robustness of the MOGIC algorithm to missing and noisy metadata. The code is publicly available at [https://github.com/suchith720/mogic](https://github.com/suchith720/mogic).

Continual learning with vision-language models like CLIP offers a pathway toward scalable machine learning systems by leveraging its transferable representations. Existing CLIP-based methods adapt the pre-trained image encoder by adding multiple sets of learnable parameters, with each task using a partial set of parameters. This requires selecting the expected parameters for input images during inference, which is prone to error that degrades performance. To address this problem, we introduce LADA (**L**abel-specific **ADA**pter). Instead of partitioning parameters across tasks, LADA appends lightweight, label-specific memory units to the frozen CLIP image encoder, enabling discriminative feature generation by aggregating task-agnostic knowledge. To prevent catastrophic forgetting, LADA employs feature distillation for seen classes, preventing their features from being interfered with by new classes. Positioned after the image encoder, LADA prevents gradient flow to the frozen CLIP parameters, ensuring efficient training. Extensive results show that LADA achieves state-of-the-art performance in continual learning settings. The implementation code is available at [https://github.com/MaolinLuo/LADA](https://github.com/MaolinLuo/LADA).

The hierarchical structure inherent in many real-world datasets makes the modeling of such hierarchies a crucial objective in both unsupervised and supervised machine learning. While recent advancements have introduced deep architectures specifically designed for hierarchical clustering, we adopt a critical perspective on this line of research. Our findings reveal that these methods face significant limitations in scalability and performance when applied to realistic datasets.~Given these findings, we present an alternative approach and introduce a lightweight method that builds on pre-trained non-hierarchical clustering models. Remarkably, our approach outperforms specialized deep models for hierarchical clustering, and it is broadly applicable to any pre-trained clustering model that outputs logits, without requiring any fine-tuning. To highlight the generality of our approach, we extend its application to a supervised setting, demonstrating its ability to recover meaningful hierarchies from a pre-trained ImageNet classifier. Our results establish a practical and effective alternative to existing deep hierarchical clustering methods, with significant advantages in efficiency, scalability and performance.

DINO and DINOv2 are two model families being widely used to learn representations from unlabeled imagery data at large scales. Their learned representations often enable state-of-the-art performance for downstream tasks, such as image classification and segmentation. However, they employ many empirically motivated design choices and their training pipelines are highly complex and unstable --- many hyperparameters need to be carefully tuned to ensure that the representations do not collapse --- which poses considerable difficulty to improving them or adapting them to new domains. In this work, we posit that we can remove most such-motivated idiosyncrasies in the pre-training pipelines, and only need to add an explicit coding rate term in the loss function to avoid collapse of the representations. As a result, we obtain highly simplified variants of the DINO and DINOv2 which we call SimDINO and SimDINOv2, respectively. Remarkably, these simplified models are more robust to different design choices, such as network architecture and hyperparameters, and they learn even higher-quality representations, measured by performance on downstream tasks, offering a Pareto improvement over the corresponding DINO and DINOv2 models. This work highlights the potential of using simplifying design principles to improve the empirical practice of deep learning. Code and model checkpoints are available at https://github.com/RobinWu218/SimDINO.

In Reinforcement Learning (RL), tasks with instantaneous hard constraints present significant challenges, particularly when the decision space is non-convex or non-star-convex. This issue is especially relevant in domains like autonomous vehicles and robotics, where constraints such as collision avoidance often take a non-convex form. In this paper, we establish a regret bound of $\tilde{\mathcal{O}}((1 + \tfrac{1}{\tau}) \sqrt{\log(\frac{1}{\tau}) d^3 H^4 K})$, applicable to both star-convex and non-star-convex cases, where $d$ is the feature dimension, $H$ the episode length, $K$ the number of episodes, and $\tau$ the safety threshold. Moreover, the violation of safety constraints is zero with high probability throughout the learning process. A key technical challenge in these settings is bounding the covering number of the value-function class, which is essential for achieving value-aware uniform concentration in model-free function approximation. For the star-convex setting, we develop a novel technique called *Objective–Constraint Decomposition* (OCD) to properly bound the covering number. This result also resolves an error in a previous work on constrained RL. In non-star-convex scenarios, where the covering number can become infinitely large, we propose a two-phase algorithm, Non-Convex Safe Least Squares Value Iteration (NCS-LSVI), which first reduces uncertainty about the safe set by playing a known safe policy. After that, it carefully balances exploration and exploitation to achieve the regret bound. Finally, numerical simulations on an autonomous driving scenario demonstrate the effectiveness of NCS-LSVI.

Collecting gold-standard phenotype data via manual extraction is typically labor-intensive and slow, whereas automated computational phenotypes (ACPs) offer a systematic and much faster alternative. However, simply replacing the gold-standard with ACPs, without acknowledging their differences, could lead to biased results and misleading conclusions. Motivated by the complexity of incorporating ACPs while maintaining the validity of downstream analyses, in this paper, we consider a semi-supervised learning setting that consists of both labeled data (with gold-standard) and unlabeled data (without gold-standard), under the covariate shift framework. We develop doubly robust and semiparametrically efficient estimators that leverage ACPs for general target parameters in the unlabeled and combined populations. In addition, we carefully analyze the efficiency gains achieved by incorporating ACPs, comparing scenarios with and without their inclusion. Notably, we identify that ACPs for the unlabeled data, instead of for the labeled data, drive the enhanced efficiency gains. To validate our theoretical findings, we conduct comprehensive synthetic experiments and apply our method to multiple real-world datasets, confirming the practical advantages of our approach.

Applications such as engineering design often require us to optimize a black-box function, i.e., a system whose inner processing is not analytically known and whose gradients are not available. Practitioners often have a fixed budget for the number of function evaluations and the performance of an optimization algorithm is measured by its simple regret. In this paper, we study the class of ``Optimistic Optimization'' algorithms for black-box optimization that use a partitioning scheme for the domain. We develop algorithms that learn a good partitioning scheme and use flexible surrogate models such as neural networks in the optimization procedure. For multi-index functions on an $m$-dimensional subspace within $d$ dimensions, our algorithm attains $\tilde{O}(n^{-\beta / d})$ regret, where $\beta = 1 + \frac{d-m}{2m-1}$, as opposed to $\tilde{O}(n^{-1/d})$ for SequOOL, a state-of-the-art optimistic optimization algorithm. Our approach is competitive across a wide range of numerical benchmarks. Additionally, we introduce weight quantization in a large language model as a novel task for black-box optimization. Our approach improves the quality of Activation-aware Weight Quantization (AWQ) of the OPT-1.3B model, achieving an approximate 10\% improvement in performance relative to the best possible unquantized model.

Deep models have recently emerged as promising tools to solve partial differential equations (PDEs), known as neural PDE solvers. While neural solvers trained from either simulation data or physics-informed loss can solve PDEs reasonably well, they are mainly restricted to a few instances of PDEs, e.g. a certain equation with a limited set of coefficients. This limits their generalization to diverse PDEs, preventing them from being practical surrogate models of numerical solvers. In this paper, we present Unisolver, a novel Transformer model trained on diverse data and conditioned on diverse PDEs, aiming towards a universal neural PDE solver capable of solving a wide scope of PDEs. Instead of purely scaling up data and parameters, Unisolver stems from the theoretical analysis of the PDE-solving process. Inspired by the mathematical structure of PDEs that a PDE solution is fundamentally governed by a series of PDE components such as equation symbols and boundary conditions, we define a complete set of PDE components and flexibly embed them as domain-wise and point-wise deep conditions for Transformer PDE solvers. Integrating physical insights with recent Transformer advances, Unisolver achieves consistent state-of-the-art on three challenging large-scale benchmarks, showing impressive performance and generalizability. Code is available at [https://github.com/thuml/Unisolver](https://github.com/thuml/Unisolver).

Handling missing values at test time is challenging for machine learning models, especially when aiming for both high accuracy and interpretability. Established approaches often add bias through imputation or excessive model complexity via missingness indicators. Moreover, either method can obscure interpretability, making it harder to understand how the model utilizes the observed variables in predictions. We propose *missingness-avoiding* (MA) machine learning, a general framework for training models to rarely require the values of missing (or imputed) features at test time. We create tailored MA learning algorithms for decision trees, tree ensembles, and sparse linear models by incorporating classifier-specific regularization terms in their learning objectives. The tree-based models leverage contextual missingness by reducing reliance on missing values based on the observed context. Experiments on real-world datasets demonstrate that **MA-DT, MA-LASSO, MA-RF**, and **MA-GBT** effectively reduce the reliance on features with missing values while maintaining predictive performance competitive with their unregularized counterparts. This shows that our framework gives practitioners a powerful tool to maintain interpretability in predictions with test-time missing values.

Label distribution learning (LDL) is an effective method to predict the relative label description degree (a.k.a. label distribution) of a sample. However, the label distribution is not a complete representation of an instance because it overlooks the absolute intensity of each label. Specifically, it's impossible to obtain the total description degree of hidden labels that not in the label space, which leads to the loss of information and confusion in instances. To solve the above problem, we come up with a new concept named background concentration to serve as the absolute description degree term of the label distribution and introduce it into the LDL process, forming the improved paradigm of concentration distribution learning. Moreover, we propose a novel model by probabilistic methods and neural networks to learn label distributions and background concentrations from existing LDL datasets. Extensive experiments prove that the proposed approach is able to extract background concentrations from label distributions while producing more accurate prediction results than the state-of-the-art LDL methods. The code is available in https://github.com/seutjw/CDL-LD.

Recent advances in operator learning have produced two distinct approaches for solving partial differential equations (PDEs): attention-based methods offering point-level adaptability but lacking spectral constraints, and spectral-based methods providing domain-level continuity priors but limited in local flexibility. This dichotomy has hindered the development of PDE solvers with both strong flexibility and generalization capability. This work introduces Holistic Physics Mixer (HPM), a novel framework that bridges this gap by integrating spectral and physical information in a unified space. HPM unifies both approaches as special cases while enabling more powerful spectral-physical interactions beyond either method alone. This enables HPM to inherit both the strong generalization of spectral methods and the flexibility of attention mechanisms while avoiding their respective limitations. Through extensive experiments across diverse PDE problems, we demonstrate that HPM consistently outperforms state-of-the-art methods in both accuracy and computational efficiency, while maintaining strong generalization capabilities with limited training data and excellent zero-shot performance on unseen resolutions.

Symbolic Regression (SR) algorithms select expressions based on prediction performance while also keeping the expression lengths short to produce explainable white box models. In this context, SR algorithms can be evaluated by measuring the extent to which the expressions discovered are Pareto-optimal, in the sense of having the best R-squared score for a given expression length. This evaluation is most commonly done based on relative performance, in the sense that an SR algorithm is judged on whether it Pareto-dominates other SR algorithms selected in the analysis, without any indication on efficiency or attainable limits. In this paper, we explore absolute Pareto-optimal (APO) solutions instead, which have the optimal tradeoff between the multiple SR objectives, for 34 datasets in the widely-used SR benchmark, SRBench, by performing exhaustive search. Additionally, we include comparisons between eight numerical optimization methods. We extract, for every dataset, an APO front of expressions that can serve as a universal baseline for SR algorithms that informs researchers of the best attainable performance for selected sizes. The APO fronts provided serves as an important benchmark and performance limit for SR algorithms and is made publicly available at: https://github.com/kentridgeai/SRParetoFronts