Modern vision-language models (VLMs) develop patch embedding and convolution backbone within vector space, especially Euclidean ones, at the very founding. When expanding VLMs to a galaxy scale for understanding astronomical phenomena, the integration of spherical space for planetary orbits and hyperbolic spaces for black holes raises two formidable challenges. a) The current pre-training model is confined to Euclidean space rather than a comprehensive geometric embedding. b) The predominant architecture lacks suitable backbones for anisotropic physical geometries. In this paper, we introduced Galaxy-Walker, a geometry-aware VLM, for the universe-level vision understanding tasks. We proposed the geometry prompt that generates geometry tokens by random walks across diverse spaces on a multi-scale physical graph, along with a geometry adapter that compresses and reshapes the space anisotropy in a mixture-of-experts manner. Extensive experiments demonstrate the effectiveness of our approach, with Galaxy-Walker achieving state-of-the-art performance in both galaxy property estimation ($R^2$ scores up to $0.91$) and morphology classification tasks (up to $+0.17$ F1 improvement in challenging features), significantly outperforming both domain-specific models and general-purpose VLMs.

Spatial-temporal sequence forecasting (STSF) is a long-standing research problem with widespread real-world applications. Neural architecture search (NAS), which automates the neural network design, has been shown effective in tackling the STSF problem. However, the existing NAS methods for STSF focus on generating architectures in a time-consuming data-driven fashion, which heavily limits their ability to use background knowledge and explore the complicated search trajectory. Large language models (LLMs) have shown remarkable ability in decision-making with comprehensive internal world knowledge, but how it could benefit NAS for STSF remains unexplored. In this paper, we propose a novel NAS method for STSF based on LLM. Instead of directly generate architectures with LLM, We inspire the LLM's capability with a multi-level enhancement mechanism. Specifically, on the step-level, we decompose the generation task into decision steps with powerful prompt engineering and inspire LLM to serve as instructor for architecture search based on its internal knowledge. On the instance-level, we utilize a one-step tuning framework to quickly evaluate the architecture instance and a memory bank to cumulate knowledge to improve LLM's search ability. On the task-level, we propose a two-stage architecture search, balancing the exploration stage and optimization stage, to reduce the possibility of being trapped in local optima. Extensive experimental results demonstrate that our method can achieve competitive effectiveness with superior efficiency against existing NAS methods for STSF.

Diffusion models have achieved remarkable success in generating high-resolution, realistic images across diverse natural distributions. However, their performance heavily relies on high-quality training data, making it challenging to learn meaningful distributions from corrupted samples. This limitation restricts their applicability in scientific domains where clean data is scarce or costly to obtain. In this work, we introduce denoising score distillation (DSD), a surprisingly effective and novel approach for training high-quality generative models from low-quality data. DSD first pretrains a diffusion model exclusively on noisy, corrupted samples and then distills it into a one-step generator capable of producing refined, clean outputs. While score distillation is traditionally viewed as a method to accelerate diffusion models, we show that it can also significantly enhance sample quality, particularly when starting from a degraded teacher model. Across varying noise levels and datasets, DSD consistently improves generative performance--we summarize our empirical evidence in Figure 1. Furthermore, we provide theoretical insights showing that, in a linear model setting, DSD identifies the eigenspace of the clean data distribution's covariance matrix, implicitly regularizing the generator. This perspective reframes score distillation as not only a tool for efficiency but also a mechanism for improving generative models, particularly in low-quality data settings.

Diffusion models have recently demonstrated notable success in solving inverse problems. However, current diffusion model-based solutions typically require a large number of function evaluations (NFEs) to generate high-quality images conditioned on measurements, as they incorporate only limited information at each step. To accelerate the diffusion-based inverse problem-solving process, we introduce \textbf{M}easurements \textbf{O}ptimization (MO), a more efficient plug-and-play module for integrating measurement information at each step of the inverse problem-solving process. This method is comprehensively evaluated across eight diverse linear and nonlinear tasks on the FFHQ and ImageNet datasets. By using MO, we establish state-of-the-art (SOTA) performance across multiple tasks, with key advantages: (1) it operates with no more than 100 NFEs, with phase retrieval on ImageNet being the sole exception; (2) it achieves SOTA or near-SOTA results even at low NFE counts; and (3) it can be seamlessly integrated into existing diffusion model-based solutions for inverse problems, such as DPS \cite{chung2022diffusion} and Red-diff \cite{mardani2023variational}. For example, DPS-MO attains a peak signal-to-noise ratio (PSNR) of 28.71 dB on the FFHQ 256 dataset for high dynamic range imaging, setting a new SOTA benchmark with only 100 NFEs, whereas current methods require between 1000 and 4000 NFEs for comparable performance.

We consider the linear causal representation learning setting where we observe a linear mixing of $d$ unknown latent factors, which follow a linear structural causal model. Recent work has shown that it is possible to recover the latent factors as well as the underlying structural causal model over them, up to permutation and scaling, provided that we have at least $d$ environments, each of which corresponds to perfect interventions on a single latent node (factor). After this powerful result, a key open problem faced by the community has been to relax these conditions: allow for coarser than perfect single-node interventions, and allow for fewer than $d$ of them, since the number of latent factors $d$ could be very large. In this work, we consider precisely such a setting, where we allow a smaller than $d$ number of environments, and also allow for very coarse interventions that can very coarsely \textit{change the entire causal graph over the latent factors}. On the flip side, we relax what we wish to extract to simply the \textit{list of nodes that have shifted between one or more environments}. We provide a surprising identifiability result that it is indeed possible, under some very mild standard assumptions, to identify the set of shifted nodes. Our identifiability proof moreover is a constructive one: we explicitly provide necessary and sufficient conditions for a node to be a shifted node, and show that we can check these conditions given observed data. Our algorithm lends itself very naturally to the sample setting where instead of just interventional distributions, we are provided datasets of samples from each of these distributions. We corroborate our results on both synthetic experiments as well as an interesting psychometric dataset. The code can be found at https://github.com/TianyuCodings/iLCS.

Neural posterior estimation (NPE), a simulation-based computational approach for Bayesian inference, has shown great success in situations where posteriors are intractable or likelihood functions are treated as "black boxes." Existing NPE methods typically rely on normalizing flows, which transform a base distributions into a complex posterior by composing many simple, invertible transformations. But flow-based models, while state of the art for NPE, are known to suffer from several limitations, including training instability and sharp trade-offs between representational power and computational cost. In this work, we demonstrate the effectiveness of conditional diffusions as an alternative to normalizing flows for NPE. Conditional diffusions address many of the challenges faced by flow-based methods. Our results show that, across a highly varied suite of benchmarking problems for NPE architectures, diffusions offer improved stability, superior accuracy, and faster training times, even with simpler, shallower models. These gains persist across a variety of different encoder or "summary network" architectures, as well as in situations where no summary network is required.

Ensuring correctness is crucial for code generation. Formal verification offers a definitive assurance of correctness, but demands substantial human effort in proof construction and hence raises a pressing need for automation. The primary obstacle lies in the severe lack of data -- there is much less proof than code for LLMs to train upon. In this paper, we introduce SAFE, a novel framework that overcomes the lack of human-written proof to enable automated proof generation of Rust code. SAFE establishes a self-evolving cycle where data synthesis and fine-tuning collaborate to enhance the model capability, leveraging the definitive power of a symbolic verifier in telling correct proof from incorrect ones. SAFE also re-purposes the large number of synthesized incorrect proofs to train the selfdebugging capability of the fine-tuned models, empowering them to fix incorrect proofs based on the verifier's feedback. SAFE demonstrates superior efficiency and precision compared to GPT-4o. Through tens of thousands of synthesized proofs and the self-debugging mechanism, we improve the capability of opensource models, initially unacquainted with formal verification, to automatically write proof for Rust code. This advancement leads to a significant improvement in performance, achieving a 70.50% accuracy rate in a benchmark crafted by human experts, a significant leap over GPT-4o's performance of 24.46%. Large Language Models (LLMs) have recently exhibited impressive capabilities in code generation (Roziere et al., 2023; Guo et al., 2024; Lozhkov et al., 2024; Google, 2024). However, the correctness of generated code cannot be guaranteed. To tackle this issue, prior research (Chen et al., 2022; Zhang et al., 2024a; Huang et al., 2023) has explored assessing generated code by test cases, which sometimes are also generated by LLMs. Although helpful, testing cannot cover all possible program inputs; they can reveal the presence of bugs but cannot prove their absence (Dahl et al., 1972).

Offline reinforcement learning (RL) leverages pre-collected datasets to train optimal policies. Diffusion Q-Learning (DQL), introducing diffusion models as a powerful and expressive policy class, significantly boosts the performance of offline RL. However, its reliance on iterative denoising sampling to generate actions slows down both training and inference. While several recent attempts have tried to accelerate diffusion-QL, the improvement in training and/or inference speed often results in degraded performance. In this paper, we introduce a dual policy approach, Diffusion Trusted Q-Learning (DTQL), which comprises a diffusion policy for pure behavior cloning and a practical one-step policy. We bridge the two polices by a newly introduced diffusion trust region loss. The diffusion policy maintains expressiveness, while the trust region loss directs the one-step policy to explore freely and seek modes within the region defined by the diffusion policy. DTQL eliminates the need for iterative denoising sampling during both training and inference, making it remarkably computationally efficient. We evaluate its effectiveness and algorithmic characteristics against popular Kullback-Leibler (KL) based distillation methods in 2D bandit scenarios and gym tasks. We then show that DTQL could not only outperform other methods on the majority of the D4RL benchmark tasks but also demonstrate efficiency in training and inference speeds. The PyTorch implementation is available at https://github.com/TianyuCodings/Diffusion_Trusted_Q_Learning.

In this paper, we extend financial sentiment analysis~(FSA) to event-level since events usually serve as the subject of the sentiment in financial text. Though extracting events from the financial text may be conducive to accurate sentiment predictions, it has specialized challenges due to the lengthy and discontinuity of events in a financial text. To this end, we reconceptualize the event extraction as a classification task by designing a categorization comprising coarse-grained and fine-grained event categories. Under this setting, we formulate the \textbf{E}vent-Level \textbf{F}inancial \textbf{S}entiment \textbf{A}nalysis~(\textbf{EFSA} for short) task that outputs quintuples consisting of (company, industry, coarse-grained event, fine-grained event, sentiment) from financial text. A large-scale Chinese dataset containing $12,160$ news articles and $13,725$ quintuples is publicized as a brand new testbed for our task. A four-hop Chain-of-Thought LLM-based approach is devised for this task. Systematically investigations are conducted on our dataset, and the empirical results demonstrate the benchmarking scores of existing methods and our proposed method can reach the current state-of-the-art. Our dataset and framework implementation are available at https://anonymous.4open.science/r/EFSA-645E

Foundation models have revolutionized knowledge acquisition across domains, and our study introduces OmniArch, a paradigm-shifting approach designed for building foundation models in multi-physics scientific computing. OmniArch's pre-training involves a versatile pipeline that processes multi-physics spatio-temporal data, casting forward problem learning into scalable auto-regressive tasks, while our novel Physics-Informed Reinforcement Learning (PIRL) technique during fine-tuning ensures alignment with physical laws. Pre-trained on the comprehensive PDEBench dataset, OmniArch not only sets new performance benchmarks for 1D, 2D and 3D PDEs but also demonstrates exceptional adaptability to new physics via few-shot and zero-shot learning approaches. The model's representations further extend to inverse problem-solving, highlighting the transformative potential of AI-enabled Scientific Computing(AI4SC) foundation models for engineering applications and physics discovery.