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Theory

Ahmad Beirami, Alekh Agarwal, Jonathan Berant, Alexander D'Amour, Jacob Eisenstein, Chirag Nagpal, Ananda Suresh

A simple and effective method for the inference-time alignment of generative models is the best-of-$n$ policy, where $n$ samples are drawn from a reference policy, ranked based on a reward function, and the highest ranking one is selected. A commonly used analytical expression in the literature claims that the KL divergence between the best-of-$n$ policy and the reference policy is equal to $\log (n) - (n-1)/n.$ We disprove the validity of this claim, and show that it is an upper bound on the actual KL divergence. We also explore the tightness of this upper bound in different regimes, and propose a new estimator for the KL divergence and empirically show that it provides a tight approximation. We also show that the win rate of the best-of-$n$ policy against the reference policy is upper bounded by $n/(n+1)$ and derive bounds on the tightness of this characterization. We conclude with analyzing the tradeoffs between win rate and KL divergence of the best-of-$n$ alignment policy, which demonstrate that very good tradeoffs are achievable with $n < 1000$.

Deep Learning · Algorithms

Connor Schenck, Isaac Reid, Mithun Jacob, Alex Bewley, Joshua Ainslie, David Rendleman, Deepali Jain, Mohit Sharma, Kumar Avinava Dubey, Ayzaan Wahid 等

We introduce $\textbf{STRING}$: Separable Translationally Invariant Position Encodings. STRING extends Rotary Position Encodings, a recently proposed and widely used algorithm in large language models, via a unifying theoretical framework. Importantly, STRING still provides $\textbf{exact}$ translation invariance, including token coordinates of arbitrary dimensionality, whilst maintaining a low computational footprint. These properties are especially important in robotics, where efficient 3D token representation is key. We integrate STRING into Vision Transformers with RGB(-D) inputs (color plus optional depth), showing substantial gains, e.g. in open-vocabulary object detection and for robotics controllers.We complement our experiments with a rigorous mathematical analysis, proving the universality of our methods. Videos of STRING-based robotics controllers can be found here: https://sites.google.com/view/string-robotics.

Theory · Everything Else

Arya Mazumdar, Neha Sangwan

We consider the problem of *exact* recovery of a $k$-sparse binary vector from generalized linear measurements (such as *logistic regression*). We analyze the *linear estimation* algorithm (Plan, Vershynin, Yudovina, 2017), and also show information theoretic lower bounds on the number of required measurements. As a consequence of our results, for noisy one bit quantized linear measurements ($\mathsf{1bCS}$), we obtain a sample complexity of $O((k+\sigma^2)\log{n})$, where $\sigma^2$ is the noise variance. This is shown to be optimal due to the information theoretic lower bound. We also obtain tight sample complexity characterization for logistic regression.Since $\mathsf{1bCS}$ is a strictly harder problem than noisy linear measurements ($\mathsf{SparseLinearReg}$) because of added quantization, the same sample complexity is achievable for $\mathsf{SparseLinearReg}$. While this sample complexity can be obtained via the popular lasso algorithm, linear estimation is computationally more efficient. Our lower bound holds for any set of measurements for $\mathsf{SparseLinearReg}$ (similar bound was known for Gaussian measurement matrices) and is closely matched by the maximum-likelihood upper bound. For $\mathsf{SparseLinearReg}$, it was conjectured in Gamarnik and Zadik, 2017 that there is a statistical-computational gap and the number of measurements should be at least $(2k+\sigma^2)\log{n}$ for efficient algorithms to exist. It is worth noting that our results imply that there is no such statistical-computational gap for $\mathsf{1bCS}$ and logistic regression.

Optimization · Discrete and Combinatorial Optimization

Thore Gerlach, Loong Kuan Lee, Frederic BARBARESCO, Nico Piatkowski

Multi-Agent Path Finding (MAPF) focuses on determining conflict-free paths for multiple agents navigating through a shared space to reach specified goal locations. This problem becomes computationally challenging, particularly when handling large numbers of agents, as frequently encountered in practical applications like coordinating autonomous vehicles. Quantum Computing (QC) is a promising candidate in overcoming such limits. However, current quantum hardware is still in its infancy and thus limited in terms of computing power and error robustness. In this work, we present the first optimal hybrid quantum-classical MAPF algorithms which are based on branch-and-cut-and-prize. QC is integrated by iteratively solving QUBO problems, based on conflict graphs. Experiments on actual quantum hardware and results on benchmark data suggest that our approach dominates previous QUBO formulations and state-of-the-art MAPF solvers.

General Machine Learning · Sequential, Network, and Time Series Modeling

Yu-Yang Qian, Yuan-Ze Xu, Zhen-Yu Zhang, Peng Zhao, Zhi-Hua Zhou

Many real-world applications collect data in a streaming environment, where learning tasks are encountered sequentially. This necessitates *continual learning* (CL) to update models online, enabling adaptation to new tasks while preserving past knowledge to prevent catastrophic forgetting. Nowadays, with the flourish of *large pre-trained models* (LPMs), *efficiency* has become increasingly critical for CL, due to their substantial computational demands and growing parameter sizes. In this paper, we introduce TreeLoRA (K-D Tree of Low-Rank Adapters), a novel approach that constructs *layer-wise* adapters by leveraging hierarchical gradient similarity to enable efficient CL, particularly for LPMs. To reduce the computational burden of task similarity estimation, we employ *bandit* techniques to develop an algorithm based on lower confidence bounds to efficiently explore the task structure. Furthermore, we use sparse gradient updates to facilitate parameter optimization, making the approach better suited for LPMs. Theoretical analysis is provided to justify the rationale behind our approach, and experiments on both *vision transformers* (ViTs) and *large language models* (LLMs) demonstrate the effectiveness and efficiency of our approach across various domains, including vision and natural language processing tasks.

General Machine Learning · Clustering

Yazhou Ren, Junlong Ke, Zichen Wen, Tianyi Wu, Yang Yang, Xiaorong Pu, Lifang He

Multi-view clustering has gained significant attention for integrating multi-view information in multimedia applications. With the growing complexity of graph data, multi-view graph clustering (MVGC) has become increasingly important. Existing methods primarily use Graph Neural Networks (GNNs) to encode structural and feature information, but applying GNNs within contrastive learning poses specific challenges, such as integrating graph data with node features and handling both homophilic and heterophilic graphs. To address these challenges, this paper introduces Node-Guided Contrastive Encoding (NGCE), a novel MVGC approach that leverages node features to guide embedding generation. NGCE enhances compatibility with GNN filtering, effectively integrates homophilic and heterophilic information, and strengthens contrastive learning across views. Extensive experiments demonstrate its robust performance on six homophilic and heterophilic multi-view benchmark datasets.

Deep Learning · Graph Neural Networks

Gleb Rodionov, Liudmila Prokhorenkova

Neural algorithmic reasoning aims to capture computations with neural networks by training models to imitate the execution of classic algorithms. While common architectures are expressive enough to contain the correct model in the weights space, current neural reasoners struggle to generalize well on out-of-distribution data. On the other hand, classic computations are not affected by distributional shifts as they can be described as transitions between discrete computational states. In this work, we propose to force neural reasoners to maintain the execution trajectory as a combination of finite predefined states. To achieve this, we separate discrete and continuous data flows and describe the interaction between them. Trained with supervision on the algorithm's state transitions, such models are able to perfectly align with the original algorithm. To show this, we evaluate our approach on multiple algorithmic problems and achieve perfect test scores both in single-task and multitask setups. Moreover, the proposed architectural choice allows us to prove the correctness of the learned algorithms for any test data.

Theory

Mikhail Mironov, Liudmila Prokhorenkova

This paper addresses the problem of quantifying diversity for a set of objects. First, we conduct a systematic review of existing diversity measures and explore their undesirable behavior in certain cases. Based on this review, we formulate three desirable properties (axioms) of a reliable diversity measure: monotonicity, uniqueness, and continuity. We show that none of the existing measures has all three properties and thus these measures are not suitable for quantifying diversity. Then, we construct two examples of measures that have all the desirable properties, thus proving that the list of axioms is not self-contradictory. Unfortunately, the constructed examples are too computationally expensive (NP-hard) for practical use. Thus, we pose an open problem of constructing a diversity measure that has all the listed properties and can be computed in practice or proving that all such measures are NP-hard to compute.

Theory · Learning Theory

Udaya Ghai, Karan Singh

Boosting provides a practical and provably effective framework for constructing accurate learning algorithms from inaccurate rules of thumb. It extends the promise of sample-efficient learning to settings where direct Empirical Risk Minimization (ERM) may not be implementable efficiently. In the realizable setting, boosting is known to offer this computational reprieve without compromising on sample efficiency. However, in the agnostic case, existing boosting algorithms fall short of achieving the optimal sample complexity. We highlight a previously unexplored avenue of improvement: unlabeled samples. We design a computationally efficient agnostic boosting algorithm that matches the sample complexity of ERM, given polynomially many additional unlabeled samples. In fact, we show that the total number of samples needed, unlabeled and labeled inclusive, is never more than that for the best known agnostic boosting algorithm -- so this result is never worse -- while only a vanishing fraction of these need to be labeled for the algorithm to succeed. This is particularly fortuitous for learning-theoretic applications of agnostic boosting, which often take place in the distribution-specific setting, where unlabeled samples can be availed for free. We also prove that the resultant guarantee is resilient against mismatch between the distributions governing the labeled and unlabeled samples. Finally, we detail an application of this result in reinforcement learning.

Applications

Anna Thomas, Adam Yee, Andrew Mayne, Maya Mathur, Dan Jurafsky, Kristina Gligoric

Food systems are responsible for a third of human-caused greenhouse gas emissions. We investigate what Large Language Models (LLMs) can contribute to reducing the environmental impacts of food production. We define a typology of design and prediction tasks based on the sustainable food literature and collaboration with domain experts, and evaluate six LLMs on four tasks in our typology. For example, for a sustainable protein design task, food science experts estimated that collaboration with an LLM can reduce time spent by 45% on average, compared to 22% for collaboration with another expert human food scientist. However, for a sustainable menu design task, LLMs produce suboptimal solutions when instructed to consider both human satisfaction and climate impacts. We propose a general framework for integrating LLMs with combinatorial optimization to improve reasoning capabilities. Our approach decreases emissions of food choices by 79% in a hypothetical restaurant while maintaining participants' satisfaction with their set of choices. Our results demonstrate LLMs' potential, supported by optimization techniques, to accelerate sustainable food development and adoption.

Deep Learning

Thanh Tran, Viet Hoang Tran, Thanh Chu, Trang Pham, Laurent Ghaoui, Tam Le, Tan Nguyen

Tree-Sliced methods have recently emerged as an alternative to the traditional Sliced Wasserstein (SW) distance, replacing one-dimensional lines with tree-based metric spaces and incorporating a splitting mechanism for projecting measures. This approach enhances the ability to capture the topological structures of integration domains in Sliced Optimal Transport while maintaining low computational costs. Building on this foundation, we propose a novel nonlinear projectional framework for the Tree-Sliced Wasserstein (TSW) distance, substituting the linear projections in earlier versions with general projections, while ensuring the injectivity of the associated Radon Transform and preserving the well-definedness of the resulting metric. By designing appropriate projections, we construct efficient metrics for measures on both Euclidean spaces and spheres. Finally, we validate our proposed metric through extensive numerical experiments for Euclidean and spherical datasets. Applications include gradient flows, self-supervised learning, and generative models, where our methods demonstrate significant improvements over recent SW and TSW variants.

Reinforcement Learning

Tyler Kastner, Mark Rowland, Yunhao Tang, Murat Erdogdu, Amir-massoud Farahmand

We study the problem of distributional reinforcement learning using categorical parametrisations and a KL divergence loss. Previous work analyzing categorical distributional RL has done so using a Cramér distance-based loss, simplifying the analysis but creating a theory-practice gap. We introduce a preconditioned version of the algorithm, and prove that it is guaranteed to converge. We further derive the asymptotic variance of the categorical estimates under different learning rate regimes, and compare to that of classical reinforcement learning. We finally empirically validate our theoretical results and perform an empirical investigation into the relative strengths of using KL losses, and derive a number of actionable insights for practitioners.

General Machine Learning · Everything Else

Tam Le, Truyen Nguyen, Hideitsu Hino, Kenji Fukumizu

We investigate the Sobolev IPM problem for probability measures supported on a graph metric space. Sobolev IPM is an important instance of integral probability metrics (IPM), and is obtained by constraining a critic function within a unit ball defined by the Sobolev norm. In particular, it has been used to compare probability measures and is crucial for several theoretical works in machine learning. However, to our knowledge, there are no efficient algorithmic approaches to compute Sobolev IPM effectively, which hinders its practical applications. In this work, we establish a relation between Sobolev norm and weighted $L^p$-norm, and leverage it to propose a *novel regularization* for Sobolev IPM. By exploiting the graph structure, we demonstrate that the regularized Sobolev IPM provides a *closed-form* expression for fast computation. This advancement addresses long-standing computational challenges, and paves the way to apply Sobolev IPM for practical applications, even in large-scale settings. Additionally, the regularized Sobolev IPM is negative definite. Utilizing this property, we design positive-definite kernels upon the regularized Sobolev IPM, and provide preliminary evidences of their advantages for comparing probability measures on a given graph for document classification and topological data analysis.

Reinforcement Learning · Planning

Qiuhao Wang, Yuqi Zha, Chin Pang Ho, Marek Petrik

Robust Markov Decision Processes (MDPs) offer a promising framework for computing reliable policies under model uncertainty. While policy gradient methods have gained increasing popularity in robust discounted MDPs, their application to the average-reward criterion remains largely unexplored. This paper proposes a Robust Projected Policy Gradient (RP2G), the first generic policy gradient method for robust average-reward MDPs (RAMDPs) that is applicable beyond the typical rectangularity assumption on transition ambiguity. In contrast to existing robust policy gradient algorithms, RP2G incorporates an adaptive decreasing tolerance mechanism for efficient policy updates at each iteration. We also present a comprehensive convergence analysis of RP2G for solving ergodic tabular RAMDPs. Furthermore, we establish the first study of the inner worst-case transition evaluation problem in RAMDPs, proposing two gradient-based algorithms tailored for rectangular and general ambiguity sets, each with provable convergence guarantees. Numerical experiments confirm the global convergence of our new algorithm and demonstrate its superior performance.

Deep Learning · Generative Models and Autoencoders

Zhicheng Zhang, Wuyou Xia, Chenxi Zhao, Zhou Yan, Xiaoqiang Liu, Yongjie Zhu, Wenyu Qin, Pengfei Wan, Di ZHANG, Jufeng Yang

Multimodal large language models (MLLMs) recently showed strong capacity in integrating data among multiple modalities, empowered by generalizable attention architecture. Advanced methods predominantly focus on language-centric tuning while less exploring multimodal tokens mixed through attention, posing challenges in high-level tasks that require fine-grained cognition and emotion understanding. In this work, we identify the attention deficit disorder problem in multimodal learning, caused by inconsistent cross-modal attention and layer-by-layer decayed attention activation. To address this, we propose a novel attention mechanism, termed MOdular Duplex Attention (MODA), simultaneously conducting the inner-modal refinement and inter-modal interaction. MODA employs a correct-after-align strategy to effectively decouple modality alignment from cross-layer token mixing. In the alignment phase, tokens are mapped to duplex modality spaces based on the basis vectors, enabling the interaction between visual and language modality. Further, the correctness of attention scores is ensured through adaptive masked attention, which enhances the model's flexibility by allowing customizable masking patterns for different modalities. Extensive experiments on 21 benchmark datasets verify the effectiveness of MODA in perception, cognition, and emotion tasks.

Deep Learning · Large Language Models

Yongchao Chen, Yilun Hao, Yueying Liu, Yang Zhang, Chuchu Fan

Existing methods fail to effectively steer Large Language Models (LLMs) between textual reasoning and code generation, leaving symbolic computing capabilities underutilized. We introduce CodeSteer, an effective method for guiding LLM code/text generation. We construct a comprehensive benchmark SymBench comprising 37 symbolic tasks with adjustable complexity and also synthesize datasets of 12k multi-turn guidance/generation trajectories and 5.5k guidance comparison pairs. We fine-tune the Llama-3-8B model with a newly designed multi-turn supervised fine-tuning (SFT) and direct preference optimization (DPO). The resulting model, CodeSteerLLM, augmented with the proposed symbolic and self-answer checkers, effectively guides the code/text generation of larger models. Augmenting GPT-4o with CodeSteer raises its average performance score from 53.3 to 86.4, even outperforming the existing best LLM OpenAI o1 (82.7), o1-preview (74.8), and DeepSeek R1 (76.8) across all 37 tasks (28 seen, 9 unseen). Trained for GPT-4o, CodeSteer demonstrates superior generalizability, providing an average 41.8 performance boost on Claude, Mistral, and GPT-3.5. CodeSteer-guided LLMs fully harness symbolic computing to maintain strong performance on highly complex tasks. Models, Datasets, and Codes are available at https://github.com/yongchao98/CodeSteer-v1.0 and https://huggingface.co/yongchao98.

Deep Learning

Florian Peter Busch, Roshni Ramanna Kamath, Rupert Mitchell, Wolfgang Stammer, Kristian Kersting, Martin Mundt

A dataset is confounded if it is most easily solved via a spurious correlation which fails to generalize to new data. In this work, we show that, in a continual learning setting where confounders may vary in time across tasks, the challenge of mitigating the effect of confounders far exceeds the standard forgetting problem normally considered. In particular, we provide a formal description of such continual confounders and identify that, in general, spurious correlations are easily ignored when training for all tasks jointly, but it is harder to avoid confounding when they are considered sequentially. These descriptions serve as a basis for constructing a novel CLEVR-based continually confounded dataset, which we term the ConCon dataset. Our evaluations demonstrate that standard continual learning methods fail to ignore the dataset's confounders. Overall, our work highlights the challenges of confounding factors, particularly in continual learning settings, and demonstrates the need for developing continual learning methods to robustly tackle these.

Deep Learning · Large Language Models

Seongho Son, William Bankes, Sayak Ray Chowdhury, Brooks Paige, Ilija Bogunovic

Current Large Language Model (LLM) preference optimization algorithms do not account for temporal preference drift, which can lead to severe misalignment. To address this limitation, we propose **Non-Stationary Direct Preference Optimisation (NS-DPO)** that models time-dependent reward functions with a Dynamic Bradley-Terry model. NS-DPO proposes a computationally efficient solution by introducing only a single discount parameter in the loss function, which is used for exponential weighting that proportionally focuses learning on more time-relevant datapoints. We theoretically analyze the convergence of NS-DPO in a general setting where the exact nature of the preference drift is not known, providing upper bounds on the estimation error and regret caused by non-stationary preferences. Finally, we demonstrate the effectiveness of NS-DPO for fine-tuning LLMs under drifting preferences. Using scenarios where various levels of preference drift is introduced, with popular LLM reward models and datasets, we show that NS-DPO fine-tuned LLMs remain robust under non-stationarity, significantly outperforming baseline algorithms that ignore temporal preference changes, without sacrificing performance in stationary cases.

Deep Learning · Algorithms

Kaixuan Zhang, HuWang, Minxian Li, Mingwu Ren, Mao Ye, Xiatian Zhu

High Dynamic Range Novel View Synthesis (HDR-NVS) aims to establish a 3D scene HDR model from Low Dynamic Range (LDR) imagery. Typically, multiple-exposure LDR images are employed to capture a wider range of brightness levels in a scene, as a single LDR image cannot represent both the brightest and darkest regions simultaneously. While effective, this multiple-exposure HDR-NVS approach has significant limitations, including susceptibility to motion artifacts (e.g., ghosting and blurring), high capture and storage costs.To overcome these challenges, we introduce, for the first time, the single-exposure HDR-NVS problem, where only single exposure LDR images are available during training. We further introduce a novel approach, Mono-HDR-3D, featuring two dedicated modules formulated by the LDR image formation principles, one for converting LDR colors to HDR counterparts, and the other for transforming HDR images to LDR format so that unsupervised learning is enabled in a closed loop. Designed as a meta-algorithm, our approach can be seamlessly integrated with existing NVS models. Extensive experiments show that Mono-HDR-3D significantly outperforms previous methods.Source code is released at https://github.com/prinasi/Mono-HDR-3D.

Deep Learning · Robustness

Zhiyao Ren, Siyuan Liang, Aishan Liu, Dacheng Tao

In-context learning (ICL) has demonstrated remarkable success in large language models (LLMs) due to its adaptability and parameter-free nature. However, it also introduces a critical vulnerability to backdoor attacks, where adversaries can manipulate LLM behaviors by simply poisoning a few ICL demonstrations. In this paper, we propose, for the first time, the dual-learning hypothesis, which posits that LLMs simultaneously learn both the task-relevant latent concepts and backdoor latent concepts within poisoned demonstrations, jointly influencing the probability of model outputs. Through theoretical analysis, we derive an upper bound for ICL backdoor effects, revealing that the vulnerability is dominated by the concept preference ratio between the task and the backdoor. Motivated by these findings, we propose ICLShield, a defense mechanism that dynamically adjusts the concept preference ratio. Our method encourages LLMs to select clean demonstrations during the ICL phase by leveraging confidence and similarity scores, effectively mitigating susceptibility to backdoor attacks. Extensive experiments across multiple LLMs and tasks demonstrate that our method achieves state-of-the-art defense effectiveness, significantly outperforming existing approaches (+26.02\% on average). Furthermore, our method exhibits exceptional adaptability and defensive performance even for closed-source models (*e.g.*, GPT-4).