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Theory · Everything Else

Chenghua Liu, Minbo Gao, Zhengfeng Ji, Ying

Graph sparsification serves as a foundation for many algorithms, such as approximation algorithms for graph cuts and Laplacian system solvers. As its natural generalization, hypergraph sparsification has recently gained increasing attention, with broad applications in graph machine learning and other areas. In this work, we propose the first quantum algorithm for hypergraph sparsification, addressing an open problem proposed by Apers and de Wolf (FOCS'20). For a weighted hypergraph with $n$ vertices, $m$ hyperedges, and rank $r$, our algorithm outputs a near-linear size $\varepsilon$-spectral sparsifier in time $\widetilde O(r\sqrt{mn}/\varepsilon)$. This algorithm matches the quantum lower bound for constant $r$ and demonstrates quantum speedup when compared with the state-of-the-art $\widetilde O(mr)$-time classical algorithm. As applications, our algorithm implies quantum speedups for computing hypergraph cut sparsifiers, approximating hypergraph mincuts and hypergraph $s$-$t$ mincuts.

Reinforcement Learning

Qingyuan Wu, Yuhui Wang, Simon Zhan, Yixuan Wang, Chung-Wei Lin, Chen Lv, Qi Zhu, Jürgen Schmidhuber, Chao Huang

Reinforcement learning (RL) with delays is challenging as sensory perceptions lag behind the actual events: the RL agent needs to estimate the real state of its environment based on past observations. State-of-the-art (SOTA) methods typically employ recursive, step-by-step forecasting of states. This can cause the accumulation of compounding errors. To tackle this problem, our novel belief estimation method, named Directly Forecasting Belief Transformer (DFBT), directly forecasts states from observations without incrementally estimating intermediate states step-by-step. We theoretically demonstrate that DFBT greatly reduces compounding errors of existing recursively forecasting methods, yielding stronger performance guarantees. In experiments with D4RL offline datasets, DFBT reduces compounding errors with remarkable prediction accuracy. DFBT's capability to forecast state sequences also facilitates multi-step bootstrapping, thus greatly improving learning efficiency. On the MuJoCo benchmark, our DFBT-based method substantially outperforms SOTA baselines. Code is available at \href{https://github.com/QingyuanWuNothing/DFBT}{https://github.com/QingyuanWuNothing/DFBT}.

Theory · Learning Theory

Gen Li, Yuchen Jiao

Diffusion models have emerged as a powerful framework for generative modeling, with guidance techniques playing a crucial role in enhancing sample quality. Despite their empirical success, a comprehensive theoretical understanding of the guidance effect remains limited. Existing studies only focus on case studies, where the distribution conditioned on each class is either isotropic Gaussian or supported on a one-dimensional interval with some extra conditions. How to analyze the guidance effect beyond these case studies remains an open question. Towards closing this gap, we make an attempt to analyze diffusion guidance under general data distributions. Rather than demonstrating uniform sample quality improvement, which does not hold in some distributions, we prove that guidance can improve the whole sample quality, in the sense that the ratio of bad samples (measured by the classifier probability) decreases in the presence of guidance. This aligns with the motivation of introducing guidance.

Deep Learning · Large Language Models

Dachuan Shi, Yonggan Fu, Xiangchi Yuan, Zhongzhi Yu, Haoran You, Sixu Li, Xin Dong, Jan Kautz, Pavlo Molchanov, Yingyan (Celine) Lin

Recent advancements in Large Language Models (LLMs) have spurred interest in numerous applications requiring robust long-range capabilities, essential for processing extensive input contexts and continuously generating extended outputs. As sequence lengths increase, the number of Key-Value (KV) pairs in LLMs escalates, creating a significant efficiency bottleneck.In this paper, we propose a new KV cache optimization paradigm called LaCache, a training-free method for efficient and accurate generative inference of LLMs. LaCache enables LLMs to simultaneously address both of the critical challenges in long-range modeling: robust long-range capabilities and continuous generation without running out-of-memory (OOM). Specifically, LaCache integrates two key innovations: (1) a ladder-shaped KV cache pattern that stores KV pairs not only sequentially (left-to-right within each layer) but also across layers (from shallow to deep), providing an extended span for capturing long-range dependencies under a fixed storage budget, thereby boosting long-range capabilities; and (2) an iterative compaction mechanism that progressively compresses older caches, freeing up space for new tokens within a fixed cache size. This token distance-based dynamic compression enables more effective continuous generation under constrained cache budgets.Experiments across various tasks, benchmarks, and LLM models consistently validate LaCache's effectiveness in enhancing LLMs' long-range capabilities. Our code is available at https://github.com/GATECH-EIC/LaCache.

Deep Learning · Theory

Blake Bordelon, Cengiz Pehlevan

We theoretically characterize gradient descent dynamics in deep linear networks trained at large width from random initialization and on large quantities of random data. Our theory captures the ``wider is better" effect of mean-field/maximum-update parameterized networks as well as hyperparameter transfer effects, which can be contrasted with the neural-tangent parameterization where optimal learning rates shift with model width. We provide asymptotic descriptions of both non-residual and residual neural networks, the latter of which enables an infinite depth limit when branches are scaled as $1/\sqrt{\text{depth}}$. We also compare training with one-pass stochastic gradient descent to the dynamics when training data are repeated at each iteration. Lastly, we show that this model recovers the accelerated power law training dynamics for power law structured data in the rich regime observed in recent works.

Reinforcement Learning · Online

Zhengpeng Xie, Qiang Zhang, Fan Yang, Marco Hutter, Renjing Xu

Model-free reinforcement learning algorithms have seen remarkable progress, but key challenges remain. Trust Region Policy Optimization (TRPO) is known for ensuring monotonic policy improvement through conservative updates within a trust region, backed by strong theoretical guarantees. However, its reliance on complex second-order optimization limits its practical efficiency. Proximal Policy Optimization (PPO) addresses this by simplifying TRPO's approach using ratio clipping, improving efficiency but sacrificing some theoretical robustness. This raises a natural question: Can we combine the strengths of both methods? In this paper, we introduce Simple Policy Optimization (SPO), a novel unconstrained first-order algorithm. By slightly modifying the policy loss used in PPO, SPO can achieve the best of both worlds. Our new objective improves upon ratio clipping, offering stronger theoretical properties and better constraining the probability ratio within the trust region. Empirical results demonstrate that SPO outperforms PPO with a simple implementation, particularly for training large, complex network architectures end-to-end.

Social Aspects · Safety

Hengrui Lou, Zunlei Feng, Jinsong Geng, Erteng Liu, Jie Lei, Lechao Cheng, Jie Song, Mingli Song, Yijun Bei

With the rise of AIGC technologies, particularly diffusion models, highly realistic fake images that can deceive human visual perception has become feasible. Consequently, various forgery detection methods have emerged. However, existing methods treat the generation process of fake images as either a black-box or an auxiliary tool, offering limited insights into its underlying mechanisms. In this paper, we propose Spatio-Temporal Distribution Fitting Deviation (STD-FD) for AIGC forgery detection, which explores the generative process in detail. By decomposing and reconstructing data within generative diffusion models, initial experiments reveal temporal distribution fitting deviations during the image reconstruction process. These deviations are captured through reconstruction noise maps for each spatial semantic unit, derived via a super-resolution algorithm. Critical discriminative patterns, termed DFactors, are identified through statistical modeling of these deviations. Extensive experiments show that STD-FD effectively captures distribution patterns in AIGC-generated data, demonstrating strong robustness and generalizability while outperforming state-of-the-art (SOTA) methods on major datasets. The source code is available at [this link](https://github.com/HengruiLou/STDFD).

Deep Learning · Large Language Models

Jiale Fu, Yuchu Jiang, Junkai Chen, Jiaming Fan, Xin Geng, Xu Yang

Large Language Model (LLM) collaborative decoding techniques improve output quality by combining the outputs of multiple models at each generation step, but they incur high computational costs. In this paper, we introduce **Collaborative decoding via Speculation (CoS)**, a novel framework that accelerates collaborative decoding without compromising performance. Inspired by Speculative Decoding—where a small proposal model generates tokens sequentially, and a larger target model verifies them in parallel, our approach builds on two key insights: (1) the verification distribution can be the combined distribution of both the proposal and target models, and (2) alternating each model as the proposer and verifier can further enhance efficiency. We generalize this method to collaboration among *n* models and theoretically prove that CoS is never slower than standard collaborative decoding, typically achieving faster speed. Extensive experiments demonstrate CoS is **1.11x–2.23x** faster than standard collaborative decoding without compromising generation quality. Our code is available at https://github.com/Kamichanw/CoS/.

Deep Learning · Algorithms

Yucheng Xie, Fu Feng, Ruixiao Shi, Jing Wang, Yong Rui, Xin Geng

Pre-trained models have become the preferred backbone due to the increasing complexity of model parameters. However, traditional pre-trained models often face deployment challenges due to their fixed sizes, and are prone to negative transfer when discrepancies arise between training tasks and target tasks.To address this, we propose **KIND**, a novel pre-training method designed to construct decomposable models.KIND integrates knowledge by incorporating Singular Value Decomposition (SVD) as a structural constraint, with each basic component represented as a combination of a column vector, singular value, and row vector from $U$, $\Sigma$, and $V^\top$ matrices.These components are categorized into **learngenes** for encapsulating class-agnostic knowledge and \textbf{tailors} for capturing class-specific knowledge, with knowledge diversion facilitated by a class gate mechanism during training.Extensive experiments demonstrate that models pre-trained with KIND can be decomposed into learngenes and tailors, which can be adaptively recombined for diverse resource-constrained deployments. Moreover, for tasks with large domain shifts, transferring only learngenes with task-agnostic knowledge, when combined with randomly initialized tailors, effectively mitigates domain shifts.Code will be made available at https://github.com/Te4P0t/KIND.

General Machine Learning · Representation Learning

Peter Sorrenson, Daniel Behrend-Uriarte, Christoph Schnörr, Ullrich Koethe

Density-based distances (DBDs) provide a principled approach to metric learning by defining distances in terms of the underlying data distribution. By employing a Riemannian metric that increases in regions of low probability density, shortest paths naturally follow the data manifold. Fermat distances, a specific type of DBD, have attractive properties, but existing estimators based on nearest neighbor graphs suffer from poor convergence due to inaccurate density estimates. Moreover, graph-based methods scale poorly to high dimensions, as the proposed geodesics are often insufficiently smooth. We address these challenges in two key ways. First, we learn densities using normalizing flows. Second, we refine geodesics through relaxation, guided by a learned score model. Additionally, we introduce a dimension-adapted Fermat distance that scales intuitively to high dimensions and improves numerical stability. Our work paves the way for the practical use of density-based distances, especially in high-dimensional spaces.

Probabilistic Methods · Gaussian Processes

Sidhanth Holalkere, David S Bindel, Silvia Sellán, Alexander Terenin

Poisson Surface Reconstruction is a widely-used algorithm for reconstructing a surface from an oriented point cloud. To facilitate applications where only partial surface information is available, or scanning is performed sequentially, a recent line of work proposes to incorporate uncertainty into the reconstructed surface via Gaussian process models. The resulting algorithms first perform Gaussian process interpolation, then solve a set of volumetric partial differential equations globally in space, resulting in a computationally expensive two-stage procedure. In this work, we apply recently-developed techniques from geometric Gaussian processes to combine interpolation and surface reconstruction into a single stage, requiring only one linear solve per sample. The resulting reconstructed surface samples can be queried locally in space, without the use of problem-dependent volumetric meshes or grids. These capabilities enable one to (a) perform probabilistic collision detection locally around the region of interest, (b) perform ray casting without evaluating points not on the ray's trajectory, and (c) perform next-view planning on a per-ray basis. They also do not requiring one to approximate kernel matrix inverses with diagonal matrices as part of intermediate computations, unlike prior methods. Results show that our approach provides a cleaner, more-principled, and more-flexible stochastic surface reconstruction pipeline.

Applications · Everything Else

Yao Zhu, Zhenyuan LI, yangyang wei, Shouling Ji

Provenance graphs describe data flows and causal dependencies of host activities, enabling to track the data propagation and manipulation throughout the systems, which provide a foundation for intrusion detection. However, these Provenance-based Intrusion Detection Systems (PIDSes) face significant challenges in storage, representation, and analysis, which impede the efficacy of machine learning models such as Graph Neural Networks (GNNs) in processing and learning from these graphs. This paper presents a novel learning-based anomaly detection method designed to efficiently embed and analyze large-scale provenance graphs. Our approach integrates dynamic graph processing with adaptive encoding, facilitating compact embeddings that effectively address out-of-vocabulary (OOV) elements and adapt to normality shifts in dynamic real-world environments. Subsequently, we incorporate this refined baseline into a tag-propagation framework for real-time detection. Our evaluation demonstrates the method's accuracy and adaptability in anomaly path mining, significantly advancing the state-of-the-art in handling and analyzing provenance graphs for anomaly detection.

Deep Learning · Robustness

Woohyun Lee, Hogun Park

Defending Graph Neural Networks (GNNs) against adversarial attacks requires balancing accuracy and robustness, a trade-off often mishandled by traditional methods like adversarial training that intertwine these conflicting objectives within a single classifier. To overcome this limitation, we propose a self-supervised adversarial purification framework. We separate robustness from the classifier by introducing a dedicated purifier, which cleanses the input data before classification. In contrast to prior adversarial purification methods, we propose GPR-GAE, a novel graph auto-encoder (GAE), as a specialized purifier trained with a self-supervised strategy, adapting to diverse graph structures in a data-driven manner. Utilizing multiple Generalized PageRank (GPR) filters, GPR-GAE captures diverse structural representations for robust and effective purification. Our multi-step purification process further facilitates GPR-GAE to achieve precise graph recovery and robust defense against structural perturbations. Experiments across diverse datasets and attack scenarios demonstrate the state-of-the-art robustness of GPR-GAE, showcasing it as an independent plug-and-play purifier for GNN classifiers. Our code can be found in https://github.com/woodavid31/GPR-GAE.

Reinforcement Learning · Multi-agent

Seth Karten, Andy Nguyen, Chi Jin

We introduce PokéChamp, a minimax agent powered by Large Language Models (LLMs) for Pokémon battles. Built on a general framework for two-player competitive games, PokéChamp leverages the generalist capabilities of LLMs to enhance minimax tree search. Specifically, LLMs replace three key modules: (1) player action sampling, (2) opponent modeling, and (3) value function estimation, enabling the agent to effectively utilize gameplay history and human knowledge to reduce the search space and address partial observability. Notably, our framework requires no additional LLM training. We evaluate PokéChamp in the popular Gen 9 OU format. When powered by GPT-4o, it achieves a win rate of 76\% against the best existing LLM-based bot and 84\% against the strongest rule-based bot, demonstrating its superior performance. Even with an open-source 8-billion-parameter Llama 3.1 model, PokéChamp consistently outperforms the previous best LLM-based bot, Pokéllmon powered by GPT-4o, with a 64\% win rate. PokéChamp attains a projected Elo of 1300-1500 on the Pokémon Showdown online ladder, placing it among the top 30\%-10\% of human players. In addition, this work compiles the largest real-player Pokémon battle dataset, featuring over 3 million games, including more than 500k high-Elo matches. Based on this dataset, we establish a series of battle benchmarks and puzzles to evaluate specific battling skills. We further provide key updates to the local game engine. This work establishes Pokémon as a benchmark to integrate LLM technologies with game-theoretic algorithms addressing general multi-agent problems. Videos, code, and dataset are available online.

Reinforcement Learning · Batch/Offline

Han Wang, Yang Xu, Wenbin Lu, Rui Song

Off-Policy Evaluation (OPE) aims to estimate the value of a target policy using offline data collected from potentially different policies. In real-world applications, however, logged data often suffers from missingness. While OPE has been extensively studied in the literature, a theoretical understanding of how missing data affects OPE results remains unclear. In this paper, we investigate OPE in the presence of monotone missingness and theoretically demonstrate that the value estimates remain unbiased under ignorable missingness but can be biased under nonignorable (informative) missingness. To retain the consistency of value estimation, we propose an inverse probability weighting value estimator and conduct statistical inference to quantify the uncertainty of the estimates. Through a series of numerical experiments, we empirically demonstrate that our proposed estimator yields a more reliable value inference under missing data.

Deep Learning · Generative Models and Autoencoders

JINHAO LIANG, Jacob Christopher, Sven Koenig, Ferdinando Fioretto

Recent advances in diffusion models hold significant potential in robotics, enabling the generation of diverse and smooth trajectories directly from raw representations of the environment. Despite this promise, applying diffusion models to motion planning remains challenging due to their difficulty in enforcing critical constraints, such as collision avoidance and kinematic feasibility. These limitations become even more pronounced in Multi-Robot Motion Planning (MRMP), where multiple robots must coordinate in shared spaces. To address these challenges, this work proposes **S**imultaneous **M**RMP **D**iffusion (SMD), a novel approach integrating constrained optimization into the diffusion sampling process to produce collision-free, kinematically feasible trajectories. Additionally, the paper introduces a comprehensive MRMP benchmark to evaluate trajectory planning algorithms across scenarios with varying robot densities, obstacle complexities, and motion constraints. Experimental results show SMD consistently outperforms classical and other learning-based motion planners, achieving higher success rates and efficiency in complex multi-robot environments. The code and implementation are available at https://github.com/RAISELab-atUVA/Diffusion-MRMP.

Theory · Reinforcement Learning and Planning

Simone Drago, Marco Mussi, Alberto Maria Metelli

The success of sequential decision-making approaches, such as *reinforcement learning* (RL), is closely tied to the availability of a reward feedback. However, designing a reward function that encodes the desired objective is a challenging task. In this work, we address a more realistic scenario: sequential decision making with preference feedback provided, for instance, by a human expert. We aim to build a theoretical basis linking *preferences*, (non-Markovian) *utilities*, and (Markovian) *rewards*, and we study the connections between them. First, we model preference feedback using a partial (pre)order over trajectories, enabling the presence of incomparabilities that are common when preferences are provided by humans but are surprisingly overlooked in existing works. Second, to provide a theoretical justification for a common practice, we investigate how a preference relation can be approximated by a multi-objective utility. We introduce a notion of preference-utility compatibility and analyze the computational complexity of this transformation, showing that constructing the minimum-dimensional utility is NP-hard. Third, we propose a novel concept of preference-based policy dominance that does not rely on utilities or rewards and discuss the computational complexity of assessing it. Fourth, we develop a computationally efficient algorithm to approximate a utility using (Markovian) rewards and quantify the error in terms of the suboptimality of the optimal policy induced by the approximating reward. This work aims to lay the foundation for a principled approach to sequential decision making from preference feedback, with promising potential applications in RL from human feedback.

Deep Learning · Large Language Models

Kenneth Li, Yida Chen, Fernanda Viégas, Martin Wattenberg

In large language model (LLM) pretraining, data quality is believed to determine model quality. In this paper, we re-examine the notion of "quality" from the perspective of pre- and post-training co-design. Specifically, we explore the possibility that pre-training on more toxic data can lead to better control in post-training, ultimately decreasing a model's output toxicity. First, we use a toy experiment to study how data composition affects the geometry of features in the representation space. Next, through controlled experiments with Olmo-1B models trained on varying ratios of clean and toxic data, we find that the concept of toxicity enjoys a less entangled linear representation as the proportion of toxic data increases. Furthermore, we show that although toxic data increases the generational toxicity of the base model, it also makes the toxicity easier to remove. Evaluations on Toxigen and Real Toxicity Prompts demonstrate that models trained on toxic data achieve a better trade-off between reducing generational toxicity and preserving general capabilities when detoxifying techniques such as inference-time intervention (ITI) are applied. Our findings suggest that, with post-training taken into account, bad data may lead to good models.

Theory · Deep Learning

Viet Hoang Tran, Trang Pham, Tho Tran Huu, Minh-Khoi Nguyen-Nhat, Thanh Chu, Tam Le, Tan Nguyen

Many variants of Optimal Transport (OT) have been developed to address its heavy computation. Among them, notably, Sliced Wasserstein (SW) is widely used for application domains by projecting the OT problem onto one-dimensional lines, and leveraging the closed-form expression of the univariate OT to reduce the computational burden. However, projecting measures onto low-dimensional spaces can lead to a loss of topological information. To mitigate this issue, in this work, we propose to replace one-dimensional lines with a more intricate structure, called \emph{tree systems}. This structure is metrizable by a tree metric, which yields a closed-form expression for OT problems on tree systems. We provide an extensive theoretical analysis to formally define tree systems with their topological properties, introduce the concept of splitting maps, which operate as the projection mechanism onto these structures, then finally propose a novel variant of Radon transform for tree systems and verify its injectivity. This framework leads to an efficient metric between measures, termed Tree-Sliced Wasserstein distance on Systems of Lines (TSW-SL). By conducting a variety of experiments on gradient flows, image style transfer, and generative models, we illustrate that our proposed approach performs favorably compared to SW and its variants.

Deep Learning · Large Language Models

Ravi Ghadia, Avinash Kumar, Gaurav Jain, Prashant J. Nair, Poulami Das

Autoregressive Transformers rely on Key-Value (KV) caching to accelerate inference. However, the linear growth of the KV cache with context length leads to excessive memory consumption and bandwidth constraints. Existing methods drop distant tokens or compress states in a lossy manner, sacrificing accuracy by discarding vital context or introducing bias.We propose ${MorphKV}$, an inference-time technique that maintains a constant-sized KV cache while preserving accuracy. MorphKV balances long-range dependencies and local coherence during text generation. It eliminates early-token bias while retaining high-fidelity context by adaptively ranking tokens through correlation-aware selection. Unlike heuristic retention or lossy compression, MorphKV iteratively refines the KV cache via lightweight updates guided by attention patterns of recent tokens. This approach captures inter-token correlation with greater accuracy, which is crucial for tasks like content creation and code generation. Our studies on long-response tasks show 52.9\% memory savings and 18.2\% higher accuracy on average compared to state-of-the-art prior works, enabling efficient deployment.