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Mengzhen Liu

Publications and source records attributed to Mengzhen Liu.

24 records · Page 2Linked to original sources

RoboMamba: Efficient Vision-Language-Action Model for Robotic Reasoning and Manipulation

A fundamental objective in robot manipulation is to enable models to comprehend visual scenes and execute actions. Although existing Vision-Language-Action (VLA) models for robots can handle a range of basic tasks, they still face challenges in two areas: (1) insufficient reasoning ability to tackle complex tasks, and (2) high computational costs for VLA model fine-tuning and inference. The recently proposed state space model (SSM) known as Mamba demonstrates promising capabilities in non-trivial sequence modeling with linear inference complexity. Inspired by this, we introduce RoboMamba, an end-to-end robotic VLA model that leverages Mamba to deliver both robotic reasoning and action capabilities, while maintaining efficient fine-tuning and inference. Specifically, we first integrate the vision encoder with Mamba, aligning visual tokens with language embedding through co-training, empowering our model with visual common sense and robotic-related reasoning. To further equip RoboMamba with SE(3) pose prediction abilities, we explore an efficient fine-tuning strategy with a simple policy head. We find that once RoboMamba possesses sufficient reasoning capability, it can acquire manipulation skills with minimal fine-tuning parameters (0.1\% of the model) and time. In experiments, RoboMamba demonstrates outstanding reasoning capabilities on general and robotic evaluation benchmarks. Meanwhile, our model showcases impressive pose prediction results in both simulation and real-world experiments, achieving inference speeds 3 times faster than existing VLA models. Our project web page: https://sites.google.com/view/robomamba-web

cs.CV↗

Minimisation of 2-coverings of genus 2 Jacobians

An important problem in computational arithmetic geometry is to find changes of coordinates to simplify a system of polynomial equations with rational coefficients. This is tackled by a combination of two techniques, called minimisation and reduction. We give an algorithm for minimising certain pairs of quadratic forms, subject to the constraint that the first quadratic form is fixed. This has applications to 2-descent on the Jacobian of a genus 2 curve.

math.NT↗

Tiling of rectangles with squares via Diophantine approximation

This article shines new light on the classical problem of tiling rectangles with squares efficiently with a novel method. With a twist on the traditional approach of resistor networks, we provide new and improved results on the matter using the theory of Diophantine Approximation, hence overcoming long-established difficulties, such as generalizations to higher-dimensional analogues. The universality of the method is demonstrated through its applications to different tiling problems. These include tiling rectangles with other rectangles, with their respective higher-dimensional counterparts, as well as tiling equilateral triangles, parallelograms, and trapezoids with equilateral triangles.

math.CO↗

Laplacian pretty good fractional revival

We develop the theory of pretty good fractional revival in quantum walks on graphs using their Laplacian matrices as the Hamiltonian. We classify the paths and the double stars that have Laplacian pretty good fractional revival.

math.CO↗

Laplacian Fractional Revival on Graphs

We develop the theory of fractional revival in the quantum walk on a graph using its Laplacian matrix as the Hamiltonian. We first give a spectral characterization of Laplacian fractional revival, which leads to a polynomial time algorithm to check this phenomenon and find the earliest time when it occurs. We then apply the characterization theorem to special families of graphs. In particular, we show that no tree admits Laplacian fractional revival except for the paths on two and three vertices, and the only graphs on a prime number of vertices that admit Laplacian fractional revival are double cones. Finally, we construct, through Cartesian products and joins, several infinite families of graphs that admit Laplacian fractional revival; some of these graphs exhibit polygamous fractional revival.

math.CO↗