Entropy Minimization (EM) is beneficial to reducing class overlap, bridging domain gap, and restricting uncertainty for various tasks in machine learning, yet its potential is limited. To study the internal mechanism of EM, we reformulate and decouple the classical EM into two parts with opposite effects: cluster aggregation driving factor (CADF) rewards dominant classes and prompts a peaked output distribution, while gradient mitigation calibrator (GMC) penalizes high-confidence classes based on predicted probabilities. Furthermore, we reveal the limitations of classical EM caused by its coupled formulation: 1) reward collapse impedes the contribution of high-certainty samples in the learning process, and 2) easy-class bias induces misalignment between output distribution and label distribution. To address these issues, we propose Adaptive Decoupled Entropy Minimization (AdaDEM), which normalizes the reward brought from CADF and employs a marginal entropy calibrator (MEC) to replace GMC. AdaDEM outperforms DEM*, an upper-bound variant of classical EM, and achieves superior performance across various imperfectly supervised learning tasks in noisy and dynamic environments.

Computational modeling of single-cell gene expression is crucial for understanding cellular processes, but generating realistic expression profiles remains a major challenge. This difficulty arises from the count nature of gene expression data and complex latent dependencies among genes. Existing generative models often impose artificial gene orderings or rely on shallow neural network architectures. We introduce a scalable latent diffusion model for single-cell gene expression data, which we refer to as scLDM, that respects the fundamental exchangeability property of the data. Our VAE uses fixed-size latent variables leveraging a unified Multi-head Cross-Attention Block (MCAB) architecture, which serves dual roles: permutation-invariant pooling in the encoder and permutation-equivariant unpooling in the decoder. We enhance this framework by replacing the Gaussian prior with a latent diffusion model using Diffusion Transformers and linear interpolants, enabling high-quality generation with multi-conditional classifier-free guidance. We show its superior performance in a variety of experiments for both observational and perturbational single-cell data, as well as downstream tasks like cell-level classification.

This paper introduces a theoretical framework to resolve a central paradox in modern machine learning: When is it better to use less data? This question has become critical as classical scaling laws suggesting ``more is more'' (Sun et al., 2025) are challenged by methods like LIMO (``less is more'') and s1 (Ye et al., 2025; Muenighoff et al., 2025), which achieve superior performance with small, aggressively curated datasets. Here, we study data curation strategies where an imperfect oracle selects the training examples according to their difficulty and correctness. Our results provide exact scaling law curves for test error under both label-agnostic and label-aware curation rules, revealing when and why keeping only a subset of data can improve generalization. In contrast to classical scaling laws, we show that under certain conditions, small curated datasets can outperform full datasets, and we provide analytical conditions for this by deriving precise phase transition curves tied to data size and quality. We validate these theoretical claims with empirical results on ImageNet, confirming our predictions about when curation improves accuracy and can even mitigate model collapse. Furthermore, our framework provides a principled explanation for the contradictory curation strategies recently observed in LLM mathematical reasoning.

Shortcuts, spurious rules that perform well during training but fail to generalize, present a major challenge to the reliability of deep networks (Geirhos et al., 2020). However, the impact of shortcuts on feature representations remains understudied, obstructing the design of principled shortcut-mitigation methods. To overcome this limitation, we investigate the layer-wise localization of shortcuts in deep models. Our novel experiment design quantifies the layer-wise contribution to accuracy degradation caused by a shortcut-inducing skew by counterfactual training on clean and skewed datasets. We employ our design to study shortcuts on CIFAR-10, Waterbirds, and CelebA datasets across VGG, ResNet, DeiT, and ConvNeXt architectures. We find that shortcut learning is not localized in specific layers but distributed throughout the network. Different network parts play different roles in this process: shallow layers predominantly encode spurious features, while deeper layers predominantly forget core features that are predictive on clean data. We also analyze the differences in localization and describe its principal axes of variation. Finally, our analysis of layer-wise shortcut-mitigation strategies suggests the hardness of designing general methods, supporting dataset- and architecture-specific approaches instead.

Gradient information is widely useful and available in applications, and is therefore natural to include in the training of neural networks. Yet little is known theoretically about the impact of Sobolev training -- regression with both function and gradient data -- on the generalization error of highly overparameterized predictive models in high dimensions. In this paper, we obtain a precise characterization of this training modality for random feature (RF) models in the limit where the number of trainable parameters, input dimensions, and training data tend proportionally to infinity. Our model for Sobolev training reflects practical implementations by sketching gradient data onto finite dimensional subspaces. By combining the replica method from statistical physics with linearizations in operator-valued free probability theory, we derive a closed-form description for the generalization errors of the trained RF models. For target functions described by single-index models, we demonstrate that supplementing function data with additional gradient data does not universally improve predictive performance. Rather, the degree of overparameterization should inform the choice of training method. More broadly, our results identify settings where models perform optimally by interpolating noisy function and gradient data.

Various data modalities are common in real-world applications (e.g., electronic health records, medical images and clinical notes in healthcare). It is essential to develop multimodal learning methods to aggregate various information from multiple modalities. The main challenge is how to appropriately align and fuse the representations of different modalities into a joint distribution. Existing methods mainly rely on concatenation or the Kronecker product, oversimplifying the interaction structure between modalities and indicating a need to model more complex interactions. Additionally, the joint distribution of latent representations with higher-order interactions is underexplored. Copula is a powerful statistical structure for modelling the interactions among variables, as it naturally bridges the joint distribution and marginal distributions of multiple variables. We propose a novel copula-driven multimodal learning framework, which focuses on learning the joint distribution of various modalities to capture the complex interactions among them. The key idea is to interpret the copula model as a tool to align the marginal distributions of the modalities efficiently. By assuming a Gaussian mixture distribution for each modality and a copula model on the joint distribution, our model can generate accurate representations for missing modalities. Extensive experiments on public MIMIC datasets demonstrate the superior performance of our model over other competitors. The code is available at https://github.com/HKU-MedAI/CMCM.

Deep research systems, agentic AI that solve complex, multi-step tasks by coordinating reasoning, search across the open web and user files, and tool use, are moving toward hierarchical deployments with a Planner, Coordinator, and Executors. In practice, training entire stacks end-to-end remains impractical, so most work trains a single planner connected to core tools such as search, browsing, and code. While SFT imparts protocol fidelity, it suffers from imitation and exposure biases and underuses environment feedback. Preference alignment methods such as DPO are schema and proxy-dependent, off-policy, and weak for long-horizon credit assignment and multi-objective trade-offs. A further limitation of SFT and DPO is their reliance on human defined decision points and subskills through schema design and labeled comparisons. Reinforcement learning aligns with closed-loop, tool-interaction research by optimizing trajectory-level policies, enabling exploration, recovery behaviors, and principled credit assignment, and it reduces dependence on such human priors and rater biases. This survey is, to our knowledge, the first dedicated to the RL foundations of deep research systems. It systematizes recent work along three axes: (i) data synthesis and curation; (ii) RL methods for agentic research covering stability, sample efficiency, long context handling, reward and credit design, multi-objective optimization, and multimodal integration; and (iii) agentic RL training systems and frameworks. We also cover agent architecture and coordination, as well as evaluation and benchmarks, including recent QA, VQA, long-form synthesis, and domain-grounded, tool-interaction tasks. We distill recurring patterns, surface infrastructure bottlenecks, and offer practical guidance for training robust, transparent deep research agents with RL.

Large language models (LLMs) have shown remarkable multimodal information processing and reasoning ability. When equipped with tools through function calling and enhanced with retrieval-augmented techniques, compound LLM-based systems can access closed data sources and answer questions about them. However, they still struggle to process and reason over large-scale graph-structure data. We introduce the GDS (Graph Data Science) agent in this technical report. The GDS agent introduces a comprehensive set of graph algorithms as tools, together with preprocessing (retrieval) and postprocessing of algorithm results, in a model context protocol (MCP) server. The server can be used with any modern LLM out-of-the-box. GDS agent allows users to ask any question that implicitly and intrinsically requires graph algorithmic reasoning about their data, and quickly obtain accurate and grounded answers. We introduce new benchmarks that evaluate intermediate tool calls as well as final responses. The results indicate that GDS agent is able to solve a wide spectrum of graph tasks. We also provide detailed case studies for more open-ended tasks and study scenarios where the agent struggles. Finally, we discuss the remaining challenges and the future roadmap.

As artificial intelligence (AI) advances toward superhuman capabilities, aligning these systems with human values becomes increasingly critical. Current alignment strategies rely largely on externally specified constraints that may prove insufficient against future super-intelligent AI capable of circumventing top-down controls. This research investigates whether artificial neural networks (ANNs) can develop patterns analogous to biological mirror neurons cells that activate both when performing and observing actions, and how such patterns might contribute to intrinsic alignment in AI. Mirror neurons play a crucial role in empathy, imitation, and social cognition in humans. The study therefore asks: (1) Can simple ANNs develop mirror-neuron patterns? and (2) How might these patterns contribute to ethical and cooperative decision-making in AI systems? Using a novel Frog and Toad game framework designed to promote cooperative behaviors, we identify conditions under which mirror-neuron patterns emerge, evaluate their influence on action circuits, introduce the Checkpoint Mirror Neuron Index (CMNI) to quantify activation strength and consistency, and propose a theoretical framework for further study. Our findings indicate that appropriately scaled model capacities and self/other coupling foster shared neural representations in ANNs similar to biological mirror neurons. These empathy-like circuits support cooperative behavior and suggest that intrinsic motivations modeled through mirror-neuron dynamics could complement existing alignment techniques by embedding empathy-like mechanisms directly within AI architectures.

Developing efficient CUDA kernels is increasingly critical for AI applications such as large-scale LLM training. However, manual kernel design is both costly and time-consuming, motivating automatic approaches that leverage LLMs for code generation. Existing methods for automatic kernel generation, however, often produce low-efficiency kernels, incur high computational overhead, and fail to generalize across settings. In this work, we propose CudaForge, a training-free multi-agent workflow for CUDA kernel generation and optimization. Our workflow is inspired by the iterative workflow of human experts, which contains steps such as developing initial kernels, testing correctness, analyzing hardware feedback, and iterative improvement. More specifically, CudaForge employs two LLM agents: a Coder and a Judge, that iteratively generate, correct, and optimize CUDA kernels, while integrating hardware feedback such as Nsight Compute (NCU) metrics. In extensive evaluations, we show that CudaForge, by leveraging base models like OpenAI-o3, achieves 97.6\% correctness of generated kernels and an average 1.68$\times$ speedup over PyTorch baselines, substantially surpassing state-of-the-art models including OpenAI-o3 and Kevin on KernelBench.Beyond accuracy and speed, CudaForge demonstrates strong generalization across GPUs (A100, RTX 6000, 4090, 3090) and base models (OpenAI-o3, GPT-5, gpt-oss-120B, Claude-Sonnet-4, QwQ-32B), while maintaining high efficiency. In particular, generating an optimized kernel takes about 26.5 minutes on one RTX6000 and incurs about \$ 0.3 API cost, which is significantly cheaper than existing agentic work that costs 6 H100 hours and \$ 5 API cost per kernel. Our results highlight that multi-agent, training-free workflows can enable cost-effective, generalizable, and high-performance CUDA kernel optimization. Code available at https://github.com/OptimAI-Lab/CudaForge