The study of machine learning-based logical query-answering enables reasoning with large-scale and incomplete knowledge graphs. This paper further advances this line of research by considering the uncertainty in the knowledge. The uncertain nature of knowledge is widely observed in the real world, but does not align seamlessly with the first-order logic underpinning existing studies. To bridge this gap, we study the setting of soft queries on uncertain knowledge, which is motivated by the establishment of soft constraint programming. We further propose an ML-based approach with both forward inference and backward calibration to answer soft queries on large-scale, incomplete, and uncertain knowledge graphs. Theoretical discussions reveal that our method ensures there are no catastrophic cascading errors in our forward inference algorithm while maintaining the same complexity as state-of-the-art inference algorithms for first-order queries. Empirical results justify the superior performance of our approach against previous ML-based methods with number embedding extensions.
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First-order logic (FOL) is often used to represent logical entailment, but determining natural language (NL) entailment using FOL remains a challenge. To address this, we propose the Entailment-Preserving FOL representations (EPF) task and introduce reference-free evaluation metrics for EPF (Entailment-Preserving Rate (EPR) family). In EPF, one should generate FOL representations from multi-premise NL entailment data (e.g., EntailmentBank) so that the automatic prover’s result preserves the entailment labels. Furthermore, we propose a training method specialized for the task, iterative learning-to-rank, which trains an NL-to-FOL translator by using the natural language entailment labels as verifiable rewards. Our method achieves a 1.8–2.7% improvement in EPR and a 17.4–20.6% increase in EPR@16 compared to diverse baselines in three datasets. Further analyses reveal that iterative learning-to-rank effectively suppresses the arbitrariness of FOL representation by reducing the diversity of predicate signatures, and maintains strong performance across diverse inference types and out-of-domain data.
Transformers, as the fundamental deep learning architecture, have demonstrated great capability in reasoning. This paper studies the generalizable first-order logical reasoning ability of transformers with their *parameterized* knowledge and how to improve it. Transformers’ capability of first-order reasoning is further captured by whether they can conduct first-order logical entailment, which is quantitatively measured by their performance in answering knowledge graph queries. We establish the connections between (1) two types of distribution shifts studied in out-of-distribution generalization and (2) unseen knowledge and query settings discussed in the task of knowledge graph query answering, which makes it possible to characterize the fine-grained generalizability. Results on our comprehensive dataset showed that transformers **outperform** previous methods designed particularly for this task and provided detailed empirical evidence about the impact of the input query syntax, token embedding, and transformer architectures on the reasoning capability of transformers. Interestingly, our results revealed the mismatch of positional encoding and other design choices of transformer architectures in previous practices. Motivated by this, we propose **TEGA**, a logic-aware architecture that significantly improves the performance in generalizable first-order logical entailment.
Given the high computational cost of preference alignment training of large language models (LLMs), exploring efficient methods to reduce the training overhead remains an important and compelling research problem. Motivated by the observation that alignment training typically involves only small parameter changes without injecting new knowledge into models, we propose a straightforward method called ExPO (model extrapolation) to expedite LLMs’ alignment with human preferences. Given a partially-trained model and its initial SFT checkpoint, ExPO improves the implicit optimization objective of alignment training by simply amplifying the parameter change based on a first-order approximation, without any additional training overhead. Through controlled experiments, we demonstrate that ExPO boosts a DPO model trained with only 20% steps to outperform the fully-trained one. Moreover, we show that ExPO notably improves existing open-source LLMs (ranging from 1.8B to 70B parameters) on the leading AlpacaEval 2.0 and MT-Bench benchmarks, which highlights ExPO’s broader utility in efficiently enhancing LLM alignment.
This paper introduces RuleArena, a novel and challenging benchmark designed to evaluate the ability of large language models (LLMs) to follow complex, real-world rules in reasoning. Covering three practical domains – airline baggage fees, NBA transactions, and tax regulations – RuleArena assesses LLMs’ proficiency in handling intricate natural language instructions that demand long-context understanding, logical reasoning, and accurate mathematical computation. Two key attributes distinguish RuleArena from traditional rule-based reasoning benchmarks: (1) it extends beyond standard first-order logic representations, and (2) it is grounded in authentic, practical scenarios, providing insights into the suitability and reliability of LLMs for real-world applications. Our findings reveal several notable limitations in LLMs: (1) they struggle to identify and apply the appropriate rules, frequently becoming confused by similar but distinct regulations, (2) they cannot consistently perform accurate mathematical computations, even when they correctly identify the relevant rules, and (3) in general, they perform poorly in the benchmark. We also observe a significant performance boost when LLMs are provided with external tools for oracle math and logic operations. These results highlight significant challenges and promising research directions in advancing LLMs’ rule-guided reasoning capabilities in real-life applications. Our codes and data are publicly available on https://github.com/skyriver-2000/rulearena.
Applications · Language, Speech and Dialog
Traditional video-to-audio generation techniques primarily focus on perspective video and non-spatial audio, often missing the spatial cues necessary for accurately representing sound sources in 3D environments. To address this limitation, we introduce a novel task, \textbf{360V2SA}, to generate spatial audio from 360-degree videos, specifically producing First-order Ambisonics (FOA) audio - a standard format for representing 3D spatial audio that captures sound directionality and enables realistic 3D audio reproduction. We first create \textbf{Sphere360}, a novel dataset tailored for this task that is curated from real-world data. We also design an efficient semi-automated pipeline for collecting and cleaning paired video-audio data. To generate spatial audio from 360-degree video, we propose a novel framework \textbf{OmniAudio}, which leverages self-supervised pre-training using both spatial audio data (in FOA format) and large-scale non-spatial data. Furthermore, OmniAudio features a dual-branch framework that utilizes both panoramic and perspective video inputs to capture comprehensive local and global information from 360-degree videos. Experimental results demonstrate that OmniAudio achieves state-of-the-art performance across both objective and subjective metrics on Sphere360. Code and datasets are available at~\href{https://github.com/liuhuadai/OmniAudio}{\texttt{github.com/liuhuadai/OmniAudio}}. The project website is available at \href{https://OmniAudio-360V2SA.github.io}{\texttt{OmniAudio-360V2SA.github.io}}.
Deep Learning · Everything Else
Deep learning models with a large number of parameters, often referred to as over-parameterized models, have achieved exceptional performance across various tasks. Despite concerns about overfitting, these models frequently generalize well to unseen data, thanks to effective regularization techniques, with data augmentation being among the most widely used. While data augmentation has shown great success in classification tasks using label-preserving transformations, its application in regression problems has received less attention. Recently, a novel manifold learning approach for generating synthetic data was proposed, utilizing a first-order approximation of the data manifold. Building on this foundation, we present a theoretical framework and practical tools for approximating and sampling general data manifolds. Furthermore, we introduce the Curvature-Enhanced Manifold Sampling (CEMS) method for regression tasks. CEMS leverages a second-order representation of the data manifold to enable efficient sampling and reconstruction of new data points. Extensive evaluations across multiple datasets and comparisons with state-of-the-art methods demonstrate that CEMS delivers superior performance in both in-distribution and out-of-distribution scenarios, while introducing only minimal computational overhead. Code is available at https://github.com/azencot-group/CEMS.
General Machine Learning · Representation Learning
Neural Architecture Search (NAS) has recently outperformed hand-designed networks in various artificial intelligence areas. However, previous works only target a pre-defined task. For a new task in few-shot learning (FSL) scenarios, the architecture is either searched from scratch, which is neither efficient nor flexible, or borrowed architecture from the ones obtained on other tasks, which may lead to sub-optimal. Can we select the best neural architectures without involving any training and eliminate a significant portion of the search cost for new tasks in FSL? In this work, we provide an affirmative answer by proposing a novel information bottleneck (IB) theory driven \textit{Few-shot Neural Architecture Search} (dubbed, IBFS) framework to address this issue. We first derive that the global convergence of Model-agnostic meta-learning (MAML) can be guaranteed by only considering the first-order loss landscape. Moreover, motivated by the observation that IB provides a unified view toward understanding machine learning models, we propose a novel Zero-Cost method tailored for FSL to rank and select architectures based on their \textit{expressivity} obtained by IB mechanisms. Extensive experiments show that IBFS achieves state-of-the-art performance in FSL without training, which demonstrates the effectiveness of our IBFS.
Optimization · Stochastic
This paper considers a canonical problem in kernel regression: how good are the model performances when it is trained by the popular online first-order algorithms, compared to the offline ones, such as ridge and ridgeless regression? In this paper, we analyze the foundational single-pass Stochastic Gradient Descent (SGD) in kernel regression under source condition where the optimal predictor can even not belong to the RKHS, i.e. the model is misspecified. Specifically, we focus on the inner product kernel over the sphere and characterize the exact orders of the excess risk curves under different scales of sample sizes $n$ concerning the input dimension $d$. Surprisingly, we show that SGD achieves min-max optimal rates up to constants among all the scales, $without$ suffering the saturation, a prevalent phenomenon observed in (ridge) regression, except when the model is highly misspecified and the learning is in a final stage where $n\gg d^\gamma$ with any constant $\gamma >0$. The main reason for SGD to overcome the curse of saturation is the exponentially decaying step size schedule, a common practice in deep neural network training. As a byproduct, we provide the $first$ provable advantage of the scheme over the iterative averaging method in the common setting.
General Machine Learning · Everything Else
Diversity has been one of the most crucial factors on the design of adversarial ensemble methods. This work focuses on the fundamental problems: How to define the diversity for the adversarial ensemble, and how to correlate with algorithmic performance. We first show that it is an NP-Hard problem to precisely calculate the diversity of two networks in adversarial ensemble learning, which makes it different from prior diversity analysis. We present the first diversity decomposition under the first-order approximation for the adversarial ensemble learning. Specifically, the adversarial ensemble loss can be decomposed into average of individual adversarial losses, gradient diversity, prediction diversity and cross diversity. Hence, it is not sufficient to merely consider the gradient diversity on the characterization of diversity as in previous adversarial ensemble methods. We present diversity decomposition for classification with cross-entropy loss similarly. Based on the theoretical analysis, we develop new ensemble method via orthogonal adversarial predictions to simultaneously improve gradient diversity and cross diversity. We finally conduct experiments to validate the effectiveness of our method.
General Machine Learning · Supervised Learning
Multi-view classification (MVC) based on the Dempster-Shafer theory has gained significant recognition for its reliability in safety-critical applications. However, existing methods predominantly focus on providing confidence levels for decision outcomes without explaining the reasoning behind these decisions. Moreover, the reliance on first-order statistical magnitudes of belief masses often inadequately capture the intrinsic uncertainty within the evidence. To address these limitations, we propose a novel framework termed Trusted Multi-view Classification Constrained with Expert Knowledge (TMCEK). TMCEK integrates expert knowledge to enhance feature-level interpretability and introduces a distribution-aware subjective opinion mechanism to derive more reliable and realistic confidence estimates. The theoretical superiority of the proposed uncertainty measure over conventional approaches is rigorously established. Extensive experiments conducted on three multi-view datasets for sleep stage classification demonstrate that TMCEK achieves state-of-the-art performance while offering interpretability at both the feature and decision levels. These results position TMCEK as a robust and interpretable solution for MVC in safety-critical domains. The code is available at https://github.com/jie019/TMCEK_ICML2025.
Optimization · Convex
This paper investigates the convergence properties of the hypergradient descent method ($\texttt{HDM}$), a 25-year-old heuristic originally proposed for adaptive stepsize selection in stochastic first-order methods. We provide the first rigorous convergence analysis of $\texttt{HDM}$ using the online learning framework and apply this analysis to develop a new state-of-the-art adaptive gradient methods with empirical and theoretical support. Notably, $\texttt{HDM}$ automatically identifies the optimal stepsize for the local optimization landscape and achieves local superlinear convergence. Our analysis explains the instability of $\texttt{HDM}$ reported in the literature and proposes efficient strategies to address it. We also develop two $\texttt{HDM}$ variants with heavy-ball and Nesterov momentum. Experiments on deterministic convex problems show $\texttt{HDM}$ with heavy-ball momentum ($\texttt{HDM-HB}$) exhibits robust performance and significantly outperforms other adaptive first-order methods. Moreover, $\texttt{HDM-HB}$ often matches the performance of $\texttt{L-BFGS}$, an efficient and practical quasi-Newton method, using less memory and cheaper iterations.
Deep Learning · Generative Models and Autoencoders
Score-based generative models are essential in various machine learning applications, with strong capabilities in generation quality. In particular, high-order derivatives (scores) of data density offer deep insights into data distributions, building on the proven effectiveness of first-order scores for modeling and generating synthetic data, unlocking new possibilities for applications. However, learning them typically requires complete data, which is often unavailable in domains such as healthcare and finance due to data corruption, acquisition constraints, or incomplete records. To tackle this challenge, we introduce MissScore, a novel framework for estimating high-order scores in the presence of missing data. We derive objective functions for estimating high-order scores under different missing data mechanisms and propose a new algorithm specifically designed to handle missing data effectively. Our empirical results demonstrate that MissScore accurately and efficiently learns the high-order scores from incomplete data and generates high-quality samples, resulting in strong performance across a range of downstream tasks.
Deep Learning · Generative Models and Autoencoders
Though Rectified Flows (ReFlows) with distillation offer a promising way for fast sampling, its fast inversion transforms images back to structured noise for recovery and following editing remains unsolved. This paper introduces FireFlow, an embarrassingly simple yet effective zero-shot approach that inherits the startling capacity of ReFlow-based models (such as FLUX) in generation while extending its capabilities to accurate inversion and editing in **8** steps. We first demonstrate that a carefully designed numerical solver is pivotal for ReFlow inversion, enabling accurate inversion and reconstruction with the precision of a second-order solver while maintaining the practical efficiency of a first-order Euler method. This solver achieves a $3\times$ runtime speedup compared to state-of-the-art ReFlow inversion and editing techniques while delivering smaller reconstruction errors and superior editing results in a training-free mode. The code is available at [this-URL](https://github.com/HolmesShuan/FireFlow-Fast-Inversion-of-Rectified-Flow-for-Image-Semantic-Editing).
General Machine Learning · Online Learning, Active Learning and Bandits
Online linear programming (OLP) has found broad applications in revenue management and resource allocation. State-of-the-art OLP algorithms achieve low regret by repeatedly solving linear programming (LP) subproblems that incorporate updated resource information. However, LP-based methods are computationally expensive and often inefficient for large-scale applications. By contrast, recent first-order OLP algorithms are more computationally efficient but typically suffer from weaker regret guarantees. To address these shortcomings, we propose a new algorithm that combines the strengths of LP-based and first-order OLP algorithms. Our algorithm re-solves the LP subproblems periodically at a predefined frequency $f$ and uses the latest dual prices to guide online decision-making. In parallel, a first-order method runs during each interval between LP re-solves and smooths resource consumption. Our algorithm achieves $\mathcal{O}(\log (T/f) + \sqrt{f})$ regret and delivers a "wait-less" online decision-making process that balances computational efficiency and regret guarantees. Extensive experiments demonstrate at least $10$-fold improvements in regret over first-order methods and $100$-fold improvements in runtime over LP-based methods.
Social Aspects · Safety
Out-of-distribution (OOD) detection is essential for ensuring the reliability of deep learning models operating in open-world scenarios. Current OOD detectors mainly rely on statistical models to identify unusual patterns in the latent representations of a deep neural network. This work proposes to augment existing OOD detectors with probabilistic reasoning, utilizing Markov logic networks (MLNs). MLNs connect first-order logic with probabilistic reasoning to assign probabilities to inputs based on weighted logical constraints defined over human-understandable concepts, which offers improved explainability. Through extensive experiments on multiple datasets, we demonstrate that MLNs can significantly enhance the performance of a wide range of existing OOD detectors while maintaining computational efficiency. Furthermore, we introduce a simple algorithm for learning logical constraints for OOD detection from a dataset and showcase its effectiveness.
Deep Learning · Algorithms
Diffusion models, which iteratively denoise data samples to synthesize high-quality outputs, have achieved empirical success across domains. However, optimizing these models for downstream tasks often involves nested bilevel structures, such as tuning hyperparameters for fine-tuning tasks or noise schedules in training dynamics, where traditional bilevel methods fail due to the infinite-dimensional probability space and prohibitive sampling costs. We formalize this challenge as a generative bilevel optimization problem and address two key scenarios: (1) fine-tuning pre-trained models via an inference-only lower-level solver paired with a sample-efficient gradient estimator for the upper level, and (2) training diffusion model from scratch with noise schedule optimization by reparameterizing the lower-level problem and designing a computationally tractable gradient estimator. Our first-order bilevel framework overcomes the incompatibility of conventional bilevel methods with diffusion processes, offering theoretical grounding and computational practicality. Experiments demonstrate that our method outperforms existing fine-tuning and hyperparameter search baselines.
Optimization · Large Scale, Parallel and Distributed
This paper investigates the problem of certifying optimality for sparse generalized linear models (GLMs), where sparsity is enforced through an $\ell_0$ cardinality constraint. While branch-and-bound (BnB) frameworks can certify optimality by pruning nodes using dual bounds, existing methods for computing these bounds are either computationally intensive or exhibit slow convergence, limiting their scalability to large-scale problems. To address this challenge, we propose a first-order proximal gradient algorithm designed to solve the perspective relaxation of the problem within a BnB framework. Specifically, we formulate the relaxed problem as a composite optimization problem and demonstrate that the proximal operator of the non-smooth component can be computed exactly in log-linear time complexity, eliminating the need to solve a computationally expensive second-order cone program. Furthermore, we introduce a simple restart strategy that enhances convergence speed while maintaining low per-iteration complexity. Extensive experiments on synthetic and real-world datasets show that our approach significantly accelerates dual bound computations and is highly effective in providing optimality certificates for large-scale problems.
Optimization · Non-Convex
We address the challenge of optimizing meta-parameters (hyperparameters) in machine learning, a key factor for efficient training and high model performance. Rather than relying on expensive meta-parameter search methods, we introduce MetaOptimize: a dynamic approach that adjusts meta-parameters, particularly step sizes (also known as learning rates), during training. More specifically, MetaOptimize can wrap around any first-order optimization algorithm, tuning step sizes on the fly to minimize a specific form of regret that considers the long-term impact of step sizes on training, through a discounted sum of future losses. We also introduce lower-complexity variants of MetaOptimize that, in conjunction with its adaptability to various optimization algorithms, achieve performance comparable to those of the best hand-crafted learning rate schedules across diverse machine learning tasks.
Deep Learning · Algorithms
Approximate second-order optimization methods often exhibit poorer generalization compared to first-order approaches. In this work, we look into this issue through the lens of the loss landscape and find that existing second-order methods tend to converge to sharper minima compared to SGD.In response, we propose Sassha, a novel second-order method designed to enhance generalization by explicitly reducing sharpness of the solution, while stabilizing the computation of approximate Hessians along the optimization trajectory.In fact, this sharpness minimization scheme is crafted also to accommodate lazy Hessian updates, so as to secure efficiency besides flatness.To validate its effectiveness, we conduct a wide range of standard deep learning experiments where Sassha demonstrates its outstanding generalization performance that is comparable to, and mostly better than, other methods.We provide a comprehensive set of analyses including convergence, robustness, stability, efficiency, and cost.