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Yijian Zhang

Publications and source records attributed to Yijian Zhang.

9 recordsLinked to original sources

On questions of Pogorelov and Toponogov

We give explicit counterexamples to two questions. One is asked by Pogorelov and the other is by Toponogov. These questions concern the existence of closed asymptotic curves in a saddle surface, namely a complete immersed regular surface in $\mathbb{R}^3$ with nonpositive Gaussian/sectional curvature, and its geometric consequences under some topological conditions. We also modify the statements and prove a corrected version. In the appendix we include an example clarifying a conjecture of Milnor.

math.DG

CoreMem: Riemannian Retrieval and Fisher-Guided Distillation for Long-Term Memory in Dialogue Agents

Personalized dialogue agents require continuous long-term memory to maintain coherent interactions across multiple sessions. However, deploying these capabilities on consumer-grade hardware (e.g., 8 GB VRAM edge devices) introduces severe memory and compute bottlenecks. Existing systems typically rely on isotropic cosine similarity for retrieval and heuristic rules for context compression. These approaches lack a unified theoretical foundation, frequently suffering from the hubness problem in high-dimensional retrieval and syntactic fragmentation during compression. To overcome these limitations, we propose CoreMem, a resource-efficient edge-cloud memory architecture fundamentally unified by information geometry. First, Riemannian retrieval replaces cosine matching with a locally adaptive Fisher-Rao metric, effectively penalizing hub memories via Mahalanobis distance with O(Ndr) Woodbury acceleration for real-time search. Second, Fisher-guided discrete token distillation (FDTD) introduces a hierarchical sentence-to-token compression mechanism. It derives sensitivity scores from Fisher information traces, providing a principled compression-KL tradeoff augmented with explicit structural syntax protection. Evaluated on the LOCOMO and LongMemEval-S benchmarks, CoreMem achieves strong accuracy improvements, yielding substantial gains in Open-domain (+4.51 pp) and Temporal (+4.17 pp) reasoning. Extensive profiling confirms that CoreMem operates seamlessly within a strict 8 GB VRAM budget, successfully bridging the gap between resource-constrained edge devices and the demand for theoretically grounded, lifelong memory agents.

cs.CL

Dynamics of the Morse vector field

The (negative) gradient vector fields of Morse functions on a compact manifold provide an important example in dynamical system. In this note we prove two important properties of this kind of vector field: Connectedness of critical points through orbits and exponential shrinkage of the flow on stable submanifolds. We also find applications in showing some vanishing results of maps or curvature operators.

math.DG

Universality of the Divergence

Algebraists asked whether or not an operator on the module of smooth sections of the tangent bundle over the commutative ring of smooth functions of a smooth (orientable) manifold (can be any piece of a compact or a complete manifold) can be characterized by two axioms. In this note we confirm this for any smooth manifold M under the assumption that H^1(M, R) = {0}.

math.DG

ChemBART: A Pre-trained BART Model Assisting Organic Chemistry Analysis

Recent advances in large language models (LLMs) have demonstrated transformative potential across diverse fields. While LLMs have been applied to molecular simplified molecular input line entry system (SMILES) in computer-aided synthesis planning (CASP), existing methodologies typically address single tasks, such as precursor prediction. We introduce ChemBART, a SMILES-based LLM pre-trained on chemical reactions, which enables a unified model for multiple downstream chemical tasks--achieving the paradigm of "one model, one pre-training, multiple tasks." By leveraging outputs from a mask-filling pre-training task on reaction expressions, ChemBART effectively solves a variety of chemical problems, including precursor/reagent generation, temperature-yield regression, molecular property classification, and optimizing the policy and value functions within a reinforcement learning framework, integrated with Monte Carlo tree search for multi-step synthesis route design. Unlike single-molecule pre-trained LLMs constrained to specific applications, ChemBART addresses broader chemical challenges and integrates them for comprehensive synthesis planning. Crucially, ChemBART-designed multi-step synthesis routes and reaction conditions directly inspired wet-lab validation, which confirmed shorter pathways with ~30% yield improvement over literature benchmarks. Our work validates the power of reaction-focused pre-training and showcases the broad utility of ChemBART in advancing the complete synthesis planning cycle.

cs.LG

Power Efficient Video Super-Resolution on Mobile NPUs with Deep Learning, Mobile AI & AIM 2022 challenge: Report

Video super-resolution is one of the most popular tasks on mobile devices, being widely used for an automatic improvement of low-bitrate and low-resolution video streams. While numerous solutions have been proposed for this problem, they are usually quite computationally demanding, demonstrating low FPS rates and power efficiency on mobile devices. In this Mobile AI challenge, we address this problem and propose the participants to design an end-to-end real-time video super-resolution solution for mobile NPUs optimized for low energy consumption. The participants were provided with the REDS training dataset containing video sequences for a 4X video upscaling task. The runtime and power efficiency of all models was evaluated on the powerful MediaTek Dimensity 9000 platform with a dedicated AI processing unit capable of accelerating floating-point and quantized neural networks. All proposed solutions are fully compatible with the above NPU, demonstrating an up to 500 FPS rate and 0.2 [Watt / 30 FPS] power consumption. A detailed description of all models developed in the challenge is provided in this paper.

eess.IV

ELSR: Extreme Low-Power Super Resolution Network For Mobile Devices

With the popularity of mobile devices, e.g., smartphone and wearable devices, lighter and faster model is crucial for the application of video super resolution. However, most previous lightweight models tend to concentrate on reducing lantency of model inference on desktop GPU, which may be not energy efficient in current mobile devices. In this paper, we proposed Extreme Low-Power Super Resolution (ELSR) network which only consumes a small amount of energy in mobile devices. Pretraining and finetuning methods are applied to boost the performance of the extremely tiny model. Extensive experiments show that our method achieves a excellent balance between restoration quality and power consumption. Finally, we achieve a competitive score of 90.9 with PSNR 27.34 dB and power 0.09 W/30FPS on the target MediaTek Dimensity 9000 plantform, ranking 1st place in the Mobile AI & AIM 2022 Real-Time Video Super-Resolution Challenge.

cs.CV

AIM 2022 Challenge on Super-Resolution of Compressed Image and Video: Dataset, Methods and Results

This paper reviews the Challenge on Super-Resolution of Compressed Image and Video at AIM 2022. This challenge includes two tracks. Track 1 aims at the super-resolution of compressed image, and Track~2 targets the super-resolution of compressed video. In Track 1, we use the popular dataset DIV2K as the training, validation and test sets. In Track 2, we propose the LDV 3.0 dataset, which contains 365 videos, including the LDV 2.0 dataset (335 videos) and 30 additional videos. In this challenge, there are 12 teams and 2 teams that submitted the final results to Track 1 and Track 2, respectively. The proposed methods and solutions gauge the state-of-the-art of super-resolution on compressed image and video. The proposed LDV 3.0 dataset is available at https://github.com/RenYang-home/LDV_dataset. The homepage of this challenge is at https://github.com/RenYang-home/AIM22_CompressSR.

eess.IV

Online Proximal-ADMM For Time-varying Constrained Convex Optimization

This paper considers a convex optimization problem with cost and constraints that evolve over time. The function to be minimized is strongly convex and possibly non-differentiable, and variables are coupled through linear constraints. In this setting, the paper proposes an online algorithm based on the alternating direction method of multipliers (ADMM), to track the optimal solution trajectory of the time-varying problem; in particular, the proposed algorithm consists of a primal proximal gradient descent step and an appropriately perturbed dual ascent step. The paper derives tracking results, asymptotic bounds, and linear convergence results. The proposed algorithm is then specialized to a multi-area power grid optimization problem, and our numerical results verify the desired properties.

eess.SY