Learning complex functions that involve multi-step reasoning poses a significant challenge for standard supervised learning from input-output examples. Chainof-thought (CoT) supervision, which augments training data with intermediate reasoning steps to provide a richer learning signal, has driven recent advances in large language model reasoning. This paper develops a statistical theory of learning under CoT supervision. Central to the theory is the CoT information, which measures the additional discriminative power offered by the chain-of-thought for distinguishing hypotheses with different end-to-end behaviors. The main theoretical results demonstrate how CoT supervision can yield significantly faster learning rates compared to standard end-to-end supervision, with both upper bounds and information-theoretic lower bounds characterized by the CoT information.

Complex games have long been an important benchmark for testing the progress of artificial intelligence algorithms. AlphaGo, AlphaZero, and MuZero have defeated top human players in Go and Chess, garnering widespread societal attention towards artificial intelligence. Concurrently, large language models (LLMs) have exhibited remarkable capabilities across various tasks, raising the question of whether LLMs can achieve similar success in complex games. In this paper, we explore the potential of LLMs in mastering complex card games. We systematically assess the learning capabilities of LLMs across eight diverse card games, evaluating the impact of fine-tuning on high-quality gameplay data, and examining the models' ability to retain general capabilities while mastering these games. Our findings indicate that: (1) LLMs can approach the performance of strong game AIs through supervised fine-tuning on high-quality data, (2) LLMs can achieve a certain level of proficiency in multiple complex card games simultaneously, with performance augmentation for games with similar rules and conflicts for dissimilar ones, and (3) LLMs experience a decline in general capabilities when mastering complex games, but this decline can be mitigated by integrating a certain amount of general instruction data. The evaluation results demonstrate strong learning ability and versatility of LLMs. The code is available at https://github.com/THUDM/

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We study the implicit bias of flatness / low (loss) curvature and its effects on generalization in two-layer overparameterized ReLU networks with multivariate inputs--a problem well motivated by the minima stability and edge-of-stability phenomena in gradient-descent training. Existing work either requires interpolation or focuses only on univariate inputs. This paper presents new and somewhat surprising theoretical results for multivariate inputs. On two natural settings (1) generalization gap for flat solutions, and (2) mean-squared error (MSE) in nonparametric function estimation by stable minima, we prove upper and lower bounds, which establish that while flatness does imply generalization, the resulting rates of convergence necessarily deteriorate exponentially as the input dimension grows. This gives an exponential separation between the flat solutions compared to low-norm solutions (i.e., weight decay), which are known not to suffer from the curse of dimensionality. In particular, our minimax lower bound construction, based on a novel packing argument with boundary-localized ReLU neurons, reveals how flat solutions can exploit a kind of "neural shattering" where neurons rarely activate, but with high weight magnitudes. This leads to poor performance in high dimensions. We corroborate these theoretical findings with extensive numerical simulations. To the best of our knowledge, our analysis provides the first systematic explanation for why flat minima may fail to generalize in high dimensions.

Many real-world problems require reasoning across multiple scales, demanding models which operate not on single data points, but on entire distributions. We introduce generative distribution embeddings (GDE), a framework that lifts autoencoders to the space of distributions. In GDEs, an encoder acts on sets of samples, and the decoder is replaced by a generator which aims to match the input distribution. This framework enables learning representations of distributions by coupling conditional generative models with encoder networks which satisfy a criterion we call distributional invariance. We show that GDEs learn predictive sufficient statistics embedded in the Wasserstein space, such that latent GDE distances approximately recover the W2 distance, and latent interpolation approximately recovers optimal transport trajectories for Gaussian and Gaussian mixture distributions.

In order to enable fluid and natural human-machine speech interaction, existing full-duplex conversational systems often adopt modular architectures with auxiliary components such as voice activity detectors, interrupters, conversation state predictors, or multiple LLMs. These systems, however, suffer from error accumulation across modules and struggle with key challenges such as context-dependent bargein and echo cancellation. Recent approaches, most notably Moshi, simplify the pipeline by injecting audio codecs into the token space of a single LLM. However, such methods still incur significant performance degradation when operating on the speech rather than text modality. In this paper, we introduce SALMONN-omni, the first single, standalone full-duplex speech LLM that operates without audio codecs in its token space. It features a novel dynamic thinking mechanism within the LLM backbone, enabling the model to learn when to transition between speaking and listening states. Experiments on widely used benchmarks for spoken question answering and open-domain dialogue show that SALMONN-omni achieves at least 30% relative performance improvement over existing open-source fullduplex models and performs highly competitively to half-duplex and turn-based systems, despite using substantially less training data. Moreover, SALMONN-omni demonstrates strong performance in complex conversational scenarios, including turn-taking, backchanneling, echo cancellation and context-dependent barge-in, with further improvements achieved through reinforcement learning.

Reinforcement Learning (RL) has shown promising results in solving Job Scheduling Problems (JSPs), automatically deriving powerful dispatching rules from data without relying on expert knowledge. However, most RL-based methods train only a single decision-maker, which limits exploration capability and leaves significant room for performance improvement. Moreover, designing reward functions for different JSP variants remains a challenging and labor-intensive task. To address these limitations, we introduce a novel and generic learning framework that optimizes multiple policies sharing a common objective and a single neural network, while enabling each policy to learn specialized and diverse strategies. The model optimization process is fully guided by a self-labeling manner, eliminating the need for reward functions. In addition, we develop a training scheme that adaptively controls the imitation intensity to reflect the quality of self-labels. Experimental results show that our method effectively addresses the aforementioned challenges and significantly outperforms state-of-the-art RL methods across six JSP variants. Furthermore, our approach also demonstrates strong performance on other combinatorial optimization problems, highlighting its versatility beyond JSPs.

We propose a new calibration method for survival models based on the Kolmogorov-Smirnov (KS) metric. Existing approaches--including conformal prediction, D-calibration, and Kaplan-Meier (KM)-based methods--often rely on heuristic binning or additional nonparametric estimators, which undermine their adaptability to continuous-time settings and complex model outputs. To address these limitations, we introduce a streamlined KS metric-based post-processing framework (KSP) that calibrates survival predictions without relying on discretization or KM estimation. This design enhances flexibility and broad applicability. We conduct extensive experiments on diverse real-world datasets using a variety of survival models. Empirical results demonstrate that our method consistently improves calibration performance over existing methods while maintaining high predictive accuracy. We also provide a theoretical analysis of the KS metric and discuss extensions to in-processing settings.

In recent years, diffusion models trained on equilibrium molecular distributions have proven effective for sampling biomolecules. Beyond direct sampling, the score of such a model can also be used to derive the forces that act on molecular systems. However, while classical diffusion sampling usually recovers the training distribution, the corresponding energy-based interpretation of the learned score is often inconsistent with this distribution, even for low-dimensional toy systems. We trace this inconsistency to inaccuracies of the learned score at very small diffusion timesteps, where the model must capture the correct evolution of the data distribution. In this regime, diffusion models fail to satisfy the Fokker-Planck equation, which governs the evolution of the score. We interpret this deviation as one source of the observed inconsistencies and propose an energy-based diffusion model with a Fokker-Planck-derived regularization term to enforce consistency. We demonstrate our approach by sampling and simulating multiple biomolecular systems, including fast-folding proteins, and by introducing a state-of-the-art transferable Boltzmann emulator for dipeptides that supports simulation and achieves improved consistency and efficient sampling.