arXiv subjects

Zhegong Shangguan

Publications and source records attributed to Zhegong Shangguan.

4 recordsLinked to original sources

arXiv2026

PHIRL: Aligning Learned Rewards with Task Progress for Inverse Reinforcement Learning

Human demonstrations provide dense policy-level information but sometimes lack local precision. Human feedback presents accurate local critiques, but offers sparse evaluations rather than direct policy guidance. We propose Progress-Heuristicized Inverse Reinforcement Learning (PHIRL), a data-efficient framework that learns robust reward functions by jointly leveraging demonstrations and feedback. Specifically, we use progress, a feedback modality that describes cumulative task completion. PHIRL iteratively infers a reward function from demonstrations via inverse reinforcement learning, calculates the learned rewards over the progress-annotated demonstrations, and aligns the rewards with progress annotations over four dimensions. We evaluate PHIRL on real and simulated robot tasks, with additional exploration using a fine-tuned vision-language model to provide progress feedback. Results demonstrate that PHIRL significantly outperforms the baselines, achieving substantially higher environmental return rewards and task success with only twenty percent of demonstrations annotated. Analysis of reward-hacking scenarios demonstrates that PHIRL learned reward functions are reliable against exploitation.

cs.RO↗

arXiv2026

NumerosityVLM: A Cognitively Inspired Benchmark for Interpreting Numerosity Representations in Vision-Language Models

Vision-language models (VLMs) achieve strong performance on high-level multimodal tasks, yet numerosity perception, a cognitive ability that emerges in human infants before language acquisition, remains poorly understood in current models, as existing counting benchmarks entangle numerosity with correlated visual factors. We introduce a cognitively inspired diagnostic benchmark, NumerosityVLM, comprising 10,800 synthetic images across six controlled conditions. The benchmark orthogonally manipulates object size, spatial arrangement, and numerosity, while progressively ablating texture, shape, and color. Evaluating seven VLMs in a zero-shot setting, multi-factor analysis reveals that model architecture explains the largest proportion of performance variance (partial $ω^{2}=0.325$), far exceeding visual conditions. Layer-wise probing further shows that linearly separable numerosity signals consistently emerge at early stages of the vision encoder, while performance differences across evaluated models are primarily associated with the language model component. Code and data are publicly available at https://github.com/fuy3/NumerosityVLM-Benchmark, and https://huggingface.co/datasets/fuy3/NumerosityVLM.

cs.CV↗

arXiv2026

Minimal Embodiment Enables Efficient Learning of Number Concepts in Robot

Robots are increasingly entering human-interactive scenarios that require understanding of quantity. How intelligent systems acquire abstract numerical concepts from sensorimotor experience remains a fundamental challenge in cognitive science and artificial intelligence. Here we investigate embodied numerical learning using a neural network model trained to perform sequential counting through naturalistic robotic interaction with a Franka Panda manipulator. We demonstrate that embodied models achieve 96.8\% counting accuracy with only 10\% of training data, compared to 60.6\% for vision-only baselines. This advantage persists when visual-motor correspondences are randomized, indicating that embodiment functions as a structural prior that regularizes learning rather than as an information source. The model spontaneously develops biologically plausible representations: number-selective units with logarithmic tuning, mental number line organization, Weber-law scaling, and rotational dynamics encoding numerical magnitude ($r = 0.97$, slope $= 30.6°$/count). The learning trajectory parallels children's developmental progression from subset-knowers to cardinal-principle knowers. These findings demonstrate that minimal embodiment can ground abstract concepts, improve data efficiency, and yield interpretable representations aligned with biological cognition, which may contribute to embodied mathematics tutoring and safety-critical industrial applications.

cs.RO↗

arXiv2025

Rethinking RoPE: A Mathematical Blueprint for N-dimensional Positional Embedding

Rotary Position Embedding (RoPE) is widely adopted in large language models (LLMs) due to its efficient encoding of relative positions with strong extrapolation capabilities. However, while its application in higher-dimensional input domains, such as 2D images, have been explored in several attempts, a unified theoretical framework is still lacking. To address this, we propose a systematic mathematical framework for RoPE grounded in Lie group and Lie algebra theory. We derive the necessary and sufficient conditions for any valid $N$-dimensional RoPE based on two core properties of RoPE - relativity and reversibility. We demonstrate that RoPE can be characterized as a basis of a maximal abelian subalgebra (MASA) in the special orthogonal Lie algebra, and that the commonly used axis-aligned block-diagonal RoPE, where each input axis is encoded by an independent 2x2 rotation block, corresponds to the maximal toral subalgebra. Furthermore, we reduce spatial inter-dimensional interactions to a change of basis, resolved by learning an orthogonal transformation. Our experiment results suggest that inter-dimensional interactions should be balanced with local structure preservation. Overall, our framework unifies and explains existing RoPE designs while enabling principled extensions to higher-dimensional modalities and tasks.

cs.LG↗