Daily Papers

Policy mirror descent (PMD) provides a principled framework for reinforcement learning (RL) by iteratively solving KL-regularized policy improvement subproblems. While this approach has been adopted in training advanced LLMs such as Kimi K1.5/K2, the ideal closed-form PMD updates require reliable partition function estimation, a significant challenge when working with limited rollouts in the vast action spaces of LLMs. We investigate a practical algorithm, termed PMD-mean, that approximates the log-partition term with the mean reward under the sampling policy and performs regression in log-policy space. Specifically, we characterize the population solution of PMD-mean and demonstrate that it implicitly optimizes mirror descent subproblems with an adaptive mixed KL--χ^2 regularizer. This additional χ^2 regularization constrains large probability changes, producing more conservative updates when expected rewards are low and enhancing robustness against finite-sample estimation errors. Experiments on math reasoning tasks show that PMD-mean achieves superior performance with improved stability and time efficiency. These findings deepen our understanding of PMD-mean and illuminate pathways toward principled improvements in RL algorithms for LLMs. Code is available at https://github.com/horizon-rl/OpenKimi.

Linear attention reduces the quadratic cost of softmax attention by maintaining a recurrent fast-weight state, but it consistently lags on in-context retrieval and long-context tasks. Existing remedies act on the write side of memory through gating, delta updates, or kernel feature maps, but the read step is left unchanged: every past key contributes additively to the output, so useful targets are diluted by the bulk of stored vectors. We borrow one specific piece of softmax's geometry to construct a cheap read-time contraction of the query. A second-order Taylor expansion of the softmax log-partition at the isotropic-attention point gives a local quadratic model whose curvature coincides with the running key covariance, a quantity that can be maintained with the same recurrent/chunkwise mechanism as the linear-attention state. The associated linear operator contracts the query along the high-density directions of memory before it reads the state. We call this mechanism Curvature-Conditioned Query (CCQ). CCQ modifies only the read step and is composable with any linear-attention backbone. Attached to GLA and Gated DeltaNet, it improves perplexity, zero-shot downstream accuracy, S-NIAH retrieval at and beyond the training context, length-extrapolation perplexity from 4K to 20K, and LongBench accuracy, at small extra cost.

Learning unnormalized statistical models (e.g., energy-based models) is computationally challenging due to the complexity of handling the partition function. To eschew this complexity, noise-contrastive estimation~(NCE) has been proposed by formulating the objective as the logistic loss of the real data and the artificial noise. However, as found in previous works, NCE may perform poorly in many tasks due to its flat loss landscape and slow convergence. In this paper, we study it a direct approach for optimizing the negative log-likelihood of unnormalized models from the perspective of compositional optimization. To tackle the partition function, a noise distribution is introduced such that the log partition function can be written as a compositional function whose inner function can be estimated with stochastic samples. Hence, the objective can be optimized by stochastic compositional optimization algorithms. Despite being a simple method, we demonstrate that it is more favorable than NCE by (1) establishing a fast convergence rate and quantifying its dependence on the noise distribution through the variance of stochastic estimators; (2) developing better results for one-dimensional Gaussian mean estimation by showing our objective has a much favorable loss landscape and hence our method enjoys faster convergence; (3) demonstrating better performance on multiple applications, including density estimation, out-of-distribution detection, and real image generation.

Many problems in machine learning are naturally expressed in the language of undirected graphical models. Here, we propose black-box learning and inference algorithms for undirected models that optimize a variational approximation to the log-likelihood of the model. Central to our approach is an upper bound on the log-partition function parametrized by a function q that we express as a flexible neural network. Our bound makes it possible to track the partition function during learning, to speed-up sampling, and to train a broad class of hybrid directed/undirected models via a unified variational inference framework. We empirically demonstrate the effectiveness of our method on several popular generative modeling datasets.

Numerous capability and safety techniques of Large Language Models (LLMs), including RLHF, automated red-teaming, prompt engineering, and infilling, can be cast as sampling from an unnormalized target distribution defined by a given reward or potential function over the full sequence. In this work, we leverage the rich toolkit of Sequential Monte Carlo (SMC) for these probabilistic inference problems. In particular, we use learned twist functions to estimate the expected future value of the potential at each timestep, which enables us to focus inference-time computation on promising partial sequences. We propose a novel contrastive method for learning the twist functions, and establish connections with the rich literature of soft reinforcement learning. As a complementary application of our twisted SMC framework, we present methods for evaluating the accuracy of language model inference techniques using novel bidirectional SMC bounds on the log partition function. These bounds can be used to estimate the KL divergence between the inference and target distributions in both directions. We apply our inference evaluation techniques to show that twisted SMC is effective for sampling undesirable outputs from a pretrained model (a useful component of harmlessness training and automated red-teaming), generating reviews with varied sentiment, and performing infilling tasks.

The notion of shortcut partition, introduced recently by Chang, Conroy, Le, Milenkovi\'c, Solomon, and Than [CCLMST23], is a new type of graph partition into low-diameter clusters. Roughly speaking, the shortcut partition guarantees that for every two vertices u and v in the graph, there exists a path between u and v that intersects only a few clusters. They proved that any planar graph admits a shortcut partition and gave several applications, including a construction of tree cover for arbitrary planar graphs with stretch 1+varepsilon and O(1) many trees for any fixed varepsilon in (0,1). However, the construction heavily exploits planarity in multiple steps, and is thus inherently limited to planar graphs. In this work, we breach the "planarity barrier" to construct a shortcut partition for K_r-minor-free graphs for any r. To this end, we take a completely different approach -- our key contribution is a novel deterministic variant of the cop decomposition in minor-free graphs [And86, AGG14]. Our shortcut partition for K_r-minor-free graphs yields several direct applications. Most notably, we construct the first optimal distance oracle for K_r-minor-free graphs, with 1+varepsilon stretch, linear space, and constant query time for any fixed varepsilon in (0,1). The previous best distance oracle [AG06] uses O(nlog n) space and O(log n) query time, and its construction relies on Robertson-Seymour structural theorem and other sophisticated tools. We also obtain the first tree cover of O(1) size for minor-free graphs with stretch 1+varepsilon, while the previous best (1+varepsilon)-tree cover has size O(log^2 n) [BFN19].

Generating high-fidelity 3D contents remains a fundamental challenge due to the complexity of representing arbitrary topologies-such as open surfaces and intricate internal structures-while preserving geometric details. Prevailing methods based on signed distance fields (SDFs) are hampered by costly watertight preprocessing and struggle with non-manifold geometries, while point-cloud representations often suffer from sampling artifacts and surface discontinuities. To overcome these limitations, we propose a novel 3D variational autoencoder (VAE) framework built upon unsigned distance fields (UDFs)-a more robust and computationally efficient representation that naturally handles complex and incomplete shapes. Our core innovation is a local-to-global (LoG) architecture that processes the UDF by partitioning it into uniform subvolumes, termed UBlocks. This architecture couples 3D convolutions for capturing local detail with sparse transformers for enforcing global coherence. A Pad-Average strategy further ensures smooth transitions at subvolume boundaries during reconstruction. This modular design enables seamless scaling to ultra-high resolutions up to 2048^3-a regime previously unattainable for 3D VAEs. Experiments demonstrate state-of-the-art performance in both reconstruction accuracy and generative quality, yielding superior surface smoothness and geometric flexibility.

We study the Stochastic Boolean Function Certification (SBFC) problem, where we are given n Bernoulli random variables {X_e: e in U} on a ground set U of n elements with joint distribution p, a Boolean function f: 2^U to {0, 1}, and an (unknown) scenario S = {e in U: X_e = 1} of active elements sampled from p. We seek to probe the elements one-at-a-time to reveal if they are active until we can certify f(S) = 1, while minimizing the expected number of probes. Unlike most previous results that assume independence, we study correlated distributions p and give approximation algorithms for several classes of functions f. When f(S) is the indicator function for whether S is the spanning set of a given matroid, our problem reduces to finding a basis of active elements of a matroid by probing elements. We give a non-adaptive O(log n)-approximation algorithm for arbitrary distributions p, and show that this is tight up to constants unless P = NP, even for partition matroids. For uniform matroids, we give constant factor 4.642-approximation ([BBFT20]) that can be further improved to a 2-approximation if additionally the random variables are negatively correlated for the case of 1-uniform matroid. We also give an adaptive O(log k)-approximation algorithm for SBFC for k-uniform matroids for the Graph Probing problem, where we seek to probe the edges of a graph one-at-a-time until we find k active edges. The underlying distribution on edges arises from (hidden) independent vertex random variables, with an edge being active if at least one of its endpoints is active. This significantly improves over the information-theoretic lower bound on Ω(poly(n)) ([JGM19]) for adaptive algorithms for k-uniform matroids with arbitrary distributions.

We investigate the online bandit learning of the monotone multi-linear DR-submodular functions, designing the algorithm BanditMLSM that attains O(T^{2/3}log T) of (1-1/e)-regret. Then we reduce submodular bandit with partition matroid constraint and bandit sequential monotone maximization to the online bandit learning of the monotone multi-linear DR-submodular functions, attaining O(T^{2/3}log T) of (1-1/e)-regret in both problems, which improve the existing results. To the best of our knowledge, we are the first to give a sublinear regret algorithm for the submodular bandit with partition matroid constraint. A special case of this problem is studied by Streeter et al.(2009). They prove a O(T^{4/5}) (1-1/e)-regret upper bound. For the bandit sequential submodular maximization, the existing work proves an O(T^{2/3}) regret with a suboptimal 1/2 approximation ratio (Niazadeh et al. 2021).

A spanning tree T of graph G is a rho-approximate universal Steiner tree (UST) for root vertex r if, for any subset of vertices S containing r, the cost of the minimal subgraph of T connecting S is within a rho factor of the minimum cost tree connecting S in G. Busch et al. (FOCS 2012) showed that every graph admits 2^{O(log n)}-approximate USTs by showing that USTs are equivalent to strong sparse partition hierarchies (up to poly-logs). Further, they posed poly-logarithmic USTs and strong sparse partition hierarchies as open questions. We settle these open questions by giving polynomial-time algorithms for computing both O(log ^ 7 n)-approximate USTs and poly-logarithmic strong sparse partition hierarchies. For graphs with constant doubling dimension or constant pathwidth we improve this to O(log n)-approximate USTs and O(1) strong sparse partition hierarchies. Our doubling dimension result is tight up to second order terms. We reduce the existence of these objects to the previously studied cluster aggregation problem and what we call dangling nets.

The observations in many applications consist of counts of discrete events, such as photons hitting a detector, which cannot be effectively modeled using an additive bounded or Gaussian noise model, and instead require a Poisson noise model. As a result, accurate reconstruction of a spatially or temporally distributed phenomenon (f*) from Poisson data (y) cannot be effectively accomplished by minimizing a conventional penalized least-squares objective function. The problem addressed in this paper is the estimation of f* from y in an inverse problem setting, where (a) the number of unknowns may potentially be larger than the number of observations and (b) f* admits a sparse approximation. The optimization formulation considered in this paper uses a penalized negative Poisson log-likelihood objective function with nonnegativity constraints (since Poisson intensities are naturally nonnegative). In particular, the proposed approach incorporates key ideas of using separable quadratic approximations to the objective function at each iteration and penalization terms related to l1 norms of coefficient vectors, total variation seminorms, and partition-based multiscale estimation methods.

Due to the sheer size of software logs, developers rely on automated techniques for log analysis. One of the first and most important steps of automated log analysis is log abstraction, which parses the raw logs into a structured format. Prior log abstraction techniques aim to identify and abstract all the dynamic variables in logs and output a static log template for automated log analysis. However, these abstracted dynamic variables may also contain important information that is useful to different tasks in log analysis. In this paper, we investigate the characteristics of dynamic variables and their importance in practice, and explore the potential of a variable-aware log abstraction technique. Through manual investigations and surveys with practitioners, we find that different categories of dynamic variables record various information that can be important depending on the given tasks, the distinction of dynamic variables in log abstraction can further assist in log analysis. We then propose a deep learning based log abstraction approach, named VALB, which can identify different categories of dynamic variables and preserve the value of specified categories of dynamic variables along with the log templates (i.e., variable-aware log abstraction). Through the evaluation on a widely used log abstraction benchmark, we find that VALB outperforms other state-of-the-art log abstraction techniques on general log abstraction (i.e., when abstracting all the dynamic variables) and also achieves a high variable-aware log abstraction accuracy that further identifies the category of the dynamic variables. Our study highlights the potential of leveraging the important information recorded in the dynamic variables to further improve the process of log analysis.

Logs have been widely adopted in software system development and maintenance because of the rich runtime information they record. In recent years, the increase of software size and complexity leads to the rapid growth of the volume of logs. To handle these large volumes of logs efficiently and effectively, a line of research focuses on developing intelligent and automated log analysis techniques. However, only a few of these techniques have reached successful deployments in industry due to the lack of public log datasets and open benchmarking upon them. To fill this significant gap and facilitate more research on AI-driven log analytics, we have collected and released loghub, a large collection of system log datasets. In particular, loghub provides 19 real-world log datasets collected from a wide range of software systems, including distributed systems, supercomputers, operating systems, mobile systems, server applications, and standalone software. In this paper, we summarize the statistics of these datasets, introduce some practical usage scenarios of the loghub datasets, and present our benchmarking results on loghub to benefit the researchers and practitioners in this field. Up to the time of this paper writing, the loghub datasets have been downloaded for roughly 90,000 times in total by hundreds of organizations from both industry and academia. The loghub datasets are available at https://github.com/logpai/loghub.

Log analysis is crucial for ensuring the orderly and stable operation of information systems, particularly in the field of Artificial Intelligence for IT Operations (AIOps). Large Language Models (LLMs) have demonstrated significant potential in natural language processing tasks. In the AIOps domain, they excel in tasks such as anomaly detection, root cause analysis of faults, operations and maintenance script generation, and alert information summarization. However, the performance of current LLMs in log analysis tasks remains inadequately validated. To address this gap, we introduce LogEval, a comprehensive benchmark suite designed to evaluate the capabilities of LLMs in various log analysis tasks for the first time. This benchmark covers tasks such as log parsing, log anomaly detection, log fault diagnosis, and log summarization. LogEval evaluates each task using 4,000 publicly available log data entries and employs 15 different prompts for each task to ensure a thorough and fair assessment. By rigorously evaluating leading LLMs, we demonstrate the impact of various LLM technologies on log analysis performance, focusing on aspects such as self-consistency and few-shot contextual learning. We also discuss findings related to model quantification, Chinese-English question-answering evaluation, and prompt engineering. These findings provide insights into the strengths and weaknesses of LLMs in multilingual environments and the effectiveness of different prompt strategies. Various evaluation methods are employed for different tasks to accurately measure the performance of LLMs in log analysis, ensuring a comprehensive assessment. The insights gained from LogEvals evaluation reveal the strengths and limitations of LLMs in log analysis tasks, providing valuable guidance for researchers and practitioners.

We propose MCGrad, a novel and scalable multicalibration algorithm. Multicalibration - calibration in subgroups of the data - is an important property for the performance of machine learning-based systems. Existing multicalibration methods have thus far received limited traction in industry. We argue that this is because existing methods (1) require such subgroups to be manually specified, which ML practitioners often struggle with, (2) are not scalable, or (3) may harm other notions of model performance such as log loss and Area Under the Precision-Recall Curve (PRAUC). MCGrad does not require explicit specification of protected groups, is scalable, and often improves other ML evaluation metrics instead of harming them. MCGrad has been in production at Meta, and is now part of hundreds of production models. We present results from these deployments as well as results on public datasets. We provide an open source implementation of MCGrad at https://github.com/facebookincubator/MCGrad.