The accurate prediction of geometric state evolution in complex systems is critical for advancing scientific domains such as quantum chemistry and material modeling. Traditional experimental and computational methods face challenges in terms of environmental constraints and computational demands, while current deep learning approaches still fall short in terms of precision and generality. In this work, we introduce the Geometric Diffusion Bridge (GDB), a novel generative modeling framework that accurately bridges initial and target geometric states. GDB leverages a probabilistic approach to evolve geometric state distributions, employing an equivariant diffusion bridge derived by a modified version of Doob's $h$-transform for connecting geometric states. This tailored diffusion process is anchored by initial and target geometric states as fixed endpoints and governed by equivariant transition kernels. Moreover, trajectory data can be seamlessly leveraged in our GDB framework by using a chain of equivariant diffusion bridges, providing a more detailed and accurate characterization of evolution dynamics. Theoretically, we conduct a thorough examination to confirm our framework's ability to preserve joint distributions of geometric states and capability to completely model the underlying dynamics inducing trajectory distributions with negligible error. Experimental evaluations across various real-world scenarios show that GDB surpasses existing state-of-the-art approaches, opening up a new pathway for accurately bridging geometric states and tackling crucial scientific challenges with improved accuracy and applicability.

Transformers have become the predominant architecture in foundation models due to their excellent performance across various domains. However, the substantial cost of scaling these models remains a significant concern. This problem arises primarily from their dependence on a fixed number of parameters within linear projections. When architectural modifications (e.g., channel dimensions) are introduced, the entire model typically requires retraining from scratch. As model sizes continue growing, this strategy results in increasingly high computational costs and becomes unsustainable. To overcome this problem, we introduce Tokenformer, a natively scalable architecture that leverages the attention mechanism not only for computations among input tokens but also for interactions between tokens and model parameters, thereby enhancing architectural flexibility. By treating model parameters as tokens, we replace all the linear projections in Transformers with our token-parameter attention layer, where input tokens act as queries and model parameters as keys and values. This reformulation allows for progressive and efficient scaling without necessitating retraining from scratch. Our model scales from 124M to 1.4B parameters by incrementally adding new key-value parameter pairs, achieving performance comparable to Transformers trained from scratch while greatly reducing training costs.

Despite the remarkable success of Transformer-based Large Language Models (LLMs) across various domains, understanding and enhancing their mathematical capabilities remains a significant challenge. In this paper, we conduct a rigorous theoretical analysis of LLMs' mathematical abilities, with a specific focus on their arithmetic performances. We identify numerical precision as a key factor that influences their effectiveness in mathematical tasks. Our results show that Transformers operating with low numerical precision fail to address arithmetic tasks, such as iterated addition and integer multiplication, unless the model size grows super-polynomially with respect to the input length. In contrast, Transformers with standard numerical precision can efficiently handle these tasks with significantly smaller model sizes. We further support our theoretical findings through empirical experiments that explore the impact of varying numerical precision on arithmetic tasks, providing valuable insights for improving the mathematical reasoning capabilities of LLMs.

Video Large Language Models (Video LLMs) have achieved impressive performance on video-and-language tasks, such as video question answering. However, most existing Video LLMs neglect temporal information in video data, leading to struggles with temporal-aware video understanding. To address this gap, we propose a Time Gating Video LLM (TG-Vid) designed to enhance temporal modeling through a novel Time Gating module (TG). The TG module employs a time gating mechanism on its sub-modules, comprising gating spatial attention, gating temporal attention, and gating MLP. This architecture enables our model to achieve a robust understanding of temporal information within videos. Extensive evaluation of temporal-sensitive video benchmarks (i.e., MVBench, TempCompass, and NExT-QA) demonstrates that our TG-Vid model significantly outperforms the existing Video LLMs. Further, comprehensive ablation studies validate that the performance gains are attributed to the designs of our TG module. Our code is available at https://github.com/LaVi-Lab/TG-Vid.

Large Language Models (LLMs) have revolutionized various sectors, including healthcare where they are employed in diverse applications. Their utility is particularly significant in the context of rare diseases, where data scarcity, complexity, and specificity pose considerable challenges. In the clinical domain, Named Entity Recognition (NER) stands out as an essential task and it plays a crucial role in extracting relevant information from clinical texts. Despite the promise of LLMs, current research mostly concentrates on document-level NER, identifying entities in a more general context across entire documents, without extracting their precise location. Additionally, efforts have been directed towards adapting ChatGPT for token-level NER. However, there is a significant research gap when it comes to employing token-level NER for clinical texts, especially with the use of local open-source LLMs. This study aims to bridge this gap by investigating the effectiveness of both proprietary and local LLMs in token-level clinical NER. Essentially, we delve into the capabilities of these models through a series of experiments involving zero-shot prompting, few-shot prompting, retrieval-augmented generation (RAG), and instruction-fine-tuning. Our exploration reveals the inherent challenges LLMs face in token-level NER, particularly in the context of rare diseases, and suggests possible improvements for their application in healthcare. This research contributes to narrowing a significant gap in healthcare informatics and offers insights that could lead to a more refined application of LLMs in the healthcare sector.

Visual representation learning has been a cornerstone in computer vision, involving typical forms such as visual embeddings, structural symbols, and text-based representations. Despite the success of CLIP-type visual embeddings, they often lack access to world knowledge critical for visual reasoning. In this work, we propose Visual Table, a novel form of visual representation tailored for visual reasoning. Visual tables are constructed as hierarchical descriptions of visual scenes, featuring a scene description and multiple object-centric descriptions covering categories, attributes, and knowledge. Thanks to the structural and textual formats, visual tables offer unique advantages over mere visual embeddings, such as interpretability and controllable editing. Furthermore, they deliver instance-level world knowledge and detailed attributes that are essential for visual reasoning. To create visual tables, we develop a generator trained on the dataset with collected, small-scale annotations. Extensive results on 11 visual reasoning benchmarks demonstrate that the generated visual tables significantly outperform previous structural and text-based representations. Moreover, they consistently enhance state-of-the-art multimodal large language models across diverse benchmarks, showcasing their potential for advancing visual reasoning tasks. Our code is available at https://github.com/LaVi-Lab/Visual-Table.

We present Visual AutoRegressive modeling (VAR), a new generation paradigm that redefines the autoregressive learning on images as coarse-to-fine "next-scale prediction" or "next-resolution prediction", diverging from the standard raster-scan "next-token prediction". This simple, intuitive methodology allows autoregressive (AR) transformers to learn visual distributions fast and generalize well: VAR, for the first time, makes GPT-like AR models surpass diffusion transformers in image generation. On ImageNet 256x256 benchmark, VAR significantly improve AR baseline by improving Frechet inception distance (FID) from 18.65 to 1.73, inception score (IS) from 80.4 to 350.2, with around 20x faster inference speed. It is also empirically verified that VAR outperforms the Diffusion Transformer (DiT) in multiple dimensions including image quality, inference speed, data efficiency, and scalability. Scaling up VAR models exhibits clear power-law scaling laws similar to those observed in LLMs, with linear correlation coefficients near -0.998 as solid evidence. VAR further showcases zero-shot generalization ability in downstream tasks including image in-painting, out-painting, and editing. These results suggest VAR has initially emulated the two important properties of LLMs: Scaling Laws and zero-shot task generalization. We have released all models and codes to promote the exploration of AR/VAR models for visual generation and unified learning.

Finite-sum optimization has wide applications in machine learning, covering important problems such as support vector machines, regression, etc. In this paper, we initiate the study of solving finite-sum optimization problems by quantum computing. Specifically, let $f_1,\ldots,f_n\colon\mathbb{R}^d\to\mathbb{R}$ be $\ell$-smooth convex functions and $\psi\colon\mathbb{R}^d\to\mathbb{R}$ be a $\mu$-strongly convex proximal function. The goal is to find an $\epsilon$-optimal point for $F(\mathbf{x})=\frac{1}{n}\sum_{i=1}^n f_i(\mathbf{x})+\psi(\mathbf{x})$. We give a quantum algorithm with complexity $\tilde{O}\big(n+\sqrt{d}+\sqrt{\ell/\mu}\big(n^{1/3}d^{1/3}+n^{-2/3}d^{5/6}\big)\big)$, improving the classical tight bound $\tilde{\Theta}\big(n+\sqrt{n\ell/\mu}\big)$. We also prove a quantum lower bound $\tilde{\Omega}(n+n^{3/4}(\ell/\mu)^{1/4})$ when $d$ is large enough. Both our quantum upper and lower bounds can extend to the cases where $\psi$ is not necessarily strongly convex, or each $f_i$ is Lipschitz but not necessarily smooth. In addition, when $F$ is nonconvex, our quantum algorithm can find an $\epsilon$-critial point using $\tilde{O}(n+\ell(d^{1/3}n^{1/3}+\sqrt{d})/\epsilon^2)$ queries.

Reinforcement learning from human feedback (RLHF) has contributed to performance improvements in large language models. To tackle its reliance on substantial amounts of human-labeled data, a successful approach is multi-task representation learning, which involves learning a high-quality, low-dimensional representation from a wide range of source tasks. In this paper, we formulate RLHF as the contextual dueling bandit problem and assume a common linear representation. We demonstrate that the sample complexity of source tasks in multi-task RLHF can be reduced by considering task relevance and allocating different sample sizes to source tasks with varying task relevance. We further propose an algorithm to estimate task relevance by a small number of additional data and then learn a policy. We prove that to achieve $\varepsilon-$optimal, the sample complexity of the source tasks can be significantly reduced compared to uniform sampling. Additionally, the sample complexity of the target task is only linear in the dimension of the latent space, thanks to representation learning.

In the classical Reinforcement Learning from Human Feedback (RLHF) framework, Proximal Policy Optimization (PPO) is employed to learn from sparse, sentence-level rewards -- a challenging scenario in traditional deep reinforcement learning. Despite the great successes of PPO in the alignment of state-of-the-art closed-source large language models (LLMs), its open-source implementation is still largely sub-optimal, as widely reported by numerous research studies. To address these issues, we introduce a framework that models RLHF problems as a Markov decision process (MDP), enabling the capture of fine-grained token-wise information. Furthermore, we provide theoretical insights that demonstrate the superiority of our MDP framework over the previous sentence-level bandit formulation. Under this framework, we introduce an algorithm, dubbed as Reinforced Token Optimization (\texttt{RTO}), which learns the token-wise reward function from preference data and performs policy optimization based on this learned token-wise reward signal. Theoretically, \texttt{RTO} is proven to have the capability of finding the near-optimal policy sample-efficiently. For its practical implementation, \texttt{RTO} innovatively integrates Direct Preference Optimization (DPO) and PPO. DPO, originally derived from sparse sentence rewards, surprisingly provides us with a token-wise characterization of response quality, which is seamlessly incorporated into our subsequent PPO training stage. Extensive real-world alignment experiments verify the effectiveness of the proposed approach.