Recent studies have discovered that Chain-of-Thought prompting (CoT) can dramatically improve the performance of Large Language Models (LLMs), particularly when dealing with complex tasks involving mathematics or reasoning. Despite the enormous empirical success, the underlying mechanisms behind CoT and how it unlocks the potential of LLMs remain elusive. In this paper, we take a first step towards theoretically answering these questions. Specifically, we examine the expressivity of LLMs with CoT in solving fundamental mathematical and decisionmaking problems. By using circuit complexity theory, we first give impossibility results showing that bounded-depth Transformers are unable to directly produce correct answers for basic arithmetic/equation tasks unless the model size grows super-polynomially with respect to the input length. In contrast, we then prove by construction that autoregressive Transformers of constant size suffice to solve both tasks by generating CoT derivations using a commonly used math language format. Moreover, we show LLMs with CoT can handle a general class of decision-making problems known as Dynamic Programming, thus justifying their power in tackling complex real-world tasks. Finally, an extensive set of experiments show that, while Transformers always fail to directly predict the answers, they can consistently learn to generate correct solutions step-by-step given sufficient CoT demonstrations.

Aligning foundation models is essential for their safe and trustworthy deployment. However, traditional fine-tuning methods are computationally intensive and require updating billions of model parameters. A promising alternative, alignment via decoding, adjusts the response distribution directly without model updates to maximize a target reward r, thus providing a lightweight and adaptable framework for alignment. However, principled decoding methods rely on oracle access to an optimal Q-function (Q), which is often unavailable in practice. Hence, prior SoTA methods either approximate this Q using Qπsft (derived from the reference SFTmodel) or rely on short-term rewards, resulting in sub-optimal decoding performance. In this work, we propose Transfer Q, which implicitly estimates the optimal value function for a target reward r through a baseline model ρBL aligned with a baseline reward rBL (which can be different from the target reward r). Theoretical analyses of Transfer Q provide a rigorous characterization of its optimality, deriving an upper bound on the sub-optimality gap and identifying a hyperparameter to control the deviation from the pre-trained reference SFTmodel based on user needs. Our approach significantly reduces the sub-optimality gap observed in prior SoTA methods and demonstrates superior empirical performance across key metrics such as coherence, diversity, and quality in extensive tests on several synthetic and real datasets.

In this paper, we propose the Masked Space-Time Hash encoding (MSTH), a novel method for efficiently reconstructing dynamic 3D scenes from multi-view or monocular videos. Based on the observation that dynamic scenes often contain substantial static areas that result in redundancy in storage and computations, MSTH represents a dynamic scene as a weighted combination of a 3D hash encodingOurs and a 4DPlenoptic Dataset 30 hash encoding.

Traditional cameras produce desirable vision results but struggle with motion blur in high-speed scenes due to long exposure windows. Existing frame-based deblurring algorithms face challenges in extracting useful motion cues from severely blurred images. Recently, an emerging bio-inspired vision sensor known as the spike camera has achieved an extremely high frame rate while preserving rich spatial details, owing to its novel sampling mechanism. However, typical binary spike streams are relatively low-resolution, degraded image signals devoid of color information, making them unfriendly to human vision. In this paper, we propose a novel approach that integrates the two modalities from two branches, leveraging spike streams as auxiliary visual cues for guiding deblurring in high-speed motion scenes. We propose the first spike-based motion deblurring model with bidirectional information complementarity. We introduce a content-aware motion magnitude attention module that utilizes learnable mask to extract relevant information from blurry images effectively, and we incorporate a transposed cross-attention fusion module to efficiently combine features from both spike data and blurry RGB images. Furthermore, we build two extensive synthesized datasets for training and validation purposes, encompassing high-temporal-resolution spikes, blurry images, and corresponding sharp images. The experimental results demonstrate that our method effectively recovers clear RGB images from highly blurry scenes and outperforms state-of-the-art deblurring algorithms in multiple settings.

Furthermore, the large-scale vision and language models, which play a key role in the open vocabulary setting, struggle to recognize parts as effectively as objects. To comprehensively investigate and tackle these challenges, we propose an Open-Vocabulary Part Segmentation (OV-PARTS) benchmark. OV-PARTS includes refined versions of two publicly available datasets: Pascal-Part-116 and ADE20K-Part-234.

The health condition of components in civil infrastructures can be described by various discrete states according to their performance degradation. Inferring these states from measurable responses is typically an ill-posed inverse problem. Although Bayesian methods are well-suited to tackle such problems, computing the posterior probability density function (PDF) presents challenges. The likelihood function cannot be analytically formulated due to the unclear relationship between discrete states and structural responses, and the high-dimensional state parameters resulting from numerous components severely complicates the computation of the marginal likelihood function. To address these challenges, this study proposes a novel Bayesian inversion paradigm for discrete variables based on Probabilistic Graphical Models (PGMs). The Markov networks are employed as modeling tools, with model parameters learned from data and structural topology prior. It has been proved that inferring this PGM produces the same probabilistic estimation as the posterior PDF derived from Bayesian inference, which effectively solves the above challenges. The inference is accomplished by Graph Neural Networks (GNNs), and a graph property-based GNN training strategy is developed to enable accurate inference across varying graph scales, thereby significantly reducing the computational overhead in high-dimensional problems. Both synthetic and experimental data are used to validate the proposed framework