arXiv subjects

Zhenliang Zhang

Publications and source records attributed to Zhenliang Zhang.

At least 37 records · Page 2Linked to original sources

arXiv2025

Convergence exponent of Dirichlet non-improvable numbers in the theory of continued fractions

Let $x \in [0,1)$ be an irrational number with continued fraction expansion $[a_1(x),a_2(x), \cdots,a_n(x),\cdots]$ and $q_n(x)$ be the denominator of its $n$-th convergent. We establish, for any $α,β$ in $[0,+\infty]$, the Hausdorff dimension formula of the intersections of the sets of Dirichlet non-improvable numbers and the level set of convergent exponent, i.e. $$ G(α,β): =\left\{x\in[0,1)\colon τ(x)=α,\,\,\text{and} \,\, \limsup_{n\to\infty}\frac{\log (a_n(x)a_{n+1}(x))}{\log q_n(x)}\geqβ\right\}, $$ and $$ E(α,β): =\left\{x\in[0,1)\colon τ(x)=α,\,\,\text{and} \,\, \limsup_{n\to\infty}\frac{\log (a_n(x)a_{n+1}(x))}{\log q_n(x)}=β\right\}, $$ where $$ τ(x):= \inf\Big\{s \geq 0: \sum_{n \geq 1} a^{-s}_n(x)<\infty\Big\}. $$

math.NT↗

arXiv2025

On Domain-Adaptive Post-Training for Multimodal Large Language Models

Adapting general multimodal large language models (MLLMs) to specific domains, such as scientific and industrial fields, is highly significant in promoting their practical applications. This paper systematically investigates domain adaptation of MLLMs via post-training, focusing on data synthesis, training pipeline, and task evaluation. (1) Data Synthesis: Using only open-source models, we develop a generate-then-filter pipeline that curates diverse visual instruction tasks based on domain-specific image-caption pairs. The resulting data surpass the data synthesized by manual rules or strong closed-source models in enhancing domain-specific performance. (2) Training Pipeline: Unlike general MLLMs that typically adopt a two-stage training paradigm, we find that a single-stage approach is more effective for domain adaptation. (3) Task Evaluation: We conduct extensive experiments in high-impact domains such as biomedicine, food, and remote sensing, by post-training a variety of MLLMs and then evaluating MLLM performance on various domain-specific tasks. Finally, we fully open-source our models, code, and data to encourage future research in this area.

cs.CL↗

arXiv2025

Exploring Causal Effect of Social Bias on Faithfulness Hallucinations in Large Language Models

Large language models (LLMs) have achieved remarkable success in various tasks, yet they remain vulnerable to faithfulness hallucinations, where the output does not align with the input. In this study, we investigate whether social bias contributes to these hallucinations, a causal relationship that has not been explored. A key challenge is controlling confounders within the context, which complicates the isolation of causality between bias states and hallucinations. To address this, we utilize the Structural Causal Model (SCM) to establish and validate the causality and design bias interventions to control confounders. In addition, we develop the Bias Intervention Dataset (BID), which includes various social biases, enabling precise measurement of causal effects. Experiments on mainstream LLMs reveal that biases are significant causes of faithfulness hallucinations, and the effect of each bias state differs in direction. We further analyze the scope of these causal effects across various models, specifically focusing on unfairness hallucinations, which are primarily targeted by social bias, revealing the subtle yet significant causal effect of bias on hallucination generation.

cs.CL↗

arXiv2025

ICR Probe: Tracking Hidden State Dynamics for Reliable Hallucination Detection in LLMs

Large language models (LLMs) excel at various natural language processing tasks, but their tendency to generate hallucinations undermines their reliability. Existing hallucination detection methods leveraging hidden states predominantly focus on static and isolated representations, overlooking their dynamic evolution across layers, which limits efficacy. To address this limitation, we shift the focus to the hidden state update process and introduce a novel metric, the ICR Score (Information Contribution to Residual Stream), which quantifies the contribution of modules to the hidden states' update. We empirically validate that the ICR Score is effective and reliable in distinguishing hallucinations. Building on these insights, we propose a hallucination detection method, the ICR Probe, which captures the cross-layer evolution of hidden states. Experimental results show that the ICR Probe achieves superior performance with significantly fewer parameters. Furthermore, ablation studies and case analyses offer deeper insights into the underlying mechanism of this method, improving its interpretability.

cs.CL↗

arXiv2025

Learning Long Short-Term Intention within Human Daily Behaviors

In the domain of autonomous household robots, it is of utmost importance for robots to understand human behaviors and provide appropriate services. This requires the robots to possess the capability to analyze complex human behaviors and predict the true intentions of humans. Traditionally, humans are perceived as flawless, with their decisions acting as the standards that robots should strive to align with. However, this raises a pertinent question: What if humans make mistakes? In this research, we present a unique task, termed "long short-term intention prediction". This task requires robots can predict the long-term intention of humans, which aligns with human values, and the short term intention of humans, which reflects the immediate action intention. Meanwhile, the robots need to detect the potential non-consistency between the short-term and long-term intentions, and provide necessary warnings and suggestions. To facilitate this task, we propose a long short-term intention model to represent the complex intention states, and build a dataset to train this intention model. Then we propose a two-stage method to integrate the intention model for robots: i) predicting human intentions of both value-based long-term intentions and action-based short-term intentions; and 2) analyzing the consistency between the long-term and short-term intentions. Experimental results indicate that the proposed long short-term intention model can assist robots in comprehending human behavioral patterns over both long-term and short-term durations, which helps determine the consistency between long-term and short-term intentions of humans.

cs.RO↗

arXiv2025

Body Discovery of Embodied AI

In the pursuit of realizing artificial general intelligence (AGI), the importance of embodied artificial intelligence (AI) becomes increasingly apparent. Following this trend, research integrating robots with AGI has become prominent. As various kinds of embodiments have been designed, adaptability to diverse embodiments will become important to AGI. We introduce a new challenge, termed "Body Discovery of Embodied AI", focusing on tasks of recognizing embodiments and summarizing neural signal functionality. The challenge encompasses the precise definition of an AI body and the intricate task of identifying embodiments in dynamic environments, where conventional approaches often prove inadequate. To address these challenges, we apply causal inference method and evaluate it by developing a simulator tailored for testing algorithms with virtual environments. Finally, we validate the efficacy of our algorithms through empirical testing, demonstrating their robust performance in various scenarios based on virtual environments.

cs.RO↗

arXiv2025

ValuePilot: A Two-Phase Framework for Value-Driven Decision-Making

Despite recent advances in artificial intelligence (AI), it poses challenges to ensure personalized decision-making in tasks that are not considered in training datasets. To address this issue, we propose ValuePilot, a two-phase value-driven decision-making framework comprising a dataset generation toolkit DGT and a decision-making module DMM trained on the generated data. DGT is capable of generating scenarios based on value dimensions and closely mirroring real-world tasks, with automated filtering techniques and human curation to ensure the validity of the dataset. In the generated dataset, DMM learns to recognize the inherent values of scenarios, computes action feasibility and navigates the trade-offs between multiple value dimensions to make personalized decisions. Extensive experiments demonstrate that, given human value preferences, our DMM most closely aligns with human decisions, outperforming Claude-3.5-Sonnet, Gemini-2-flash, Llama-3.1-405b and GPT-4o. This research is a preliminary exploration of value-driven decision-making. We hope it will stimulate interest in value-driven decision-making and personalized decision-making within the community.

cs.AI↗

arXiv2025

Bongard-OpenWorld: Few-Shot Reasoning for Free-form Visual Concepts in the Real World

We introduce Bongard-OpenWorld, a new benchmark for evaluating real-world few-shot reasoning for machine vision. It originates from the classical Bongard Problems (BPs): Given two sets of images (positive and negative), the model needs to identify the set that query images belong to by inducing the visual concepts, which is exclusively depicted by images from the positive set. Our benchmark inherits the few-shot concept induction of the original BPs while adding the two novel layers of challenge: 1) open-world free-form concepts, as the visual concepts in Bongard-OpenWorld are unique compositions of terms from an open vocabulary, ranging from object categories to abstract visual attributes and commonsense factual knowledge; 2) real-world images, as opposed to the synthetic diagrams used by many counterparts. In our exploration, Bongard-OpenWorld already imposes a significant challenge to current few-shot reasoning algorithms. We further investigate to which extent the recently introduced Large Language Models (LLMs) and Vision-Language Models (VLMs) can solve our task, by directly probing VLMs, and combining VLMs and LLMs in an interactive reasoning scheme. We even conceived a neuro-symbolic reasoning approach that reconciles LLMs & VLMs with logical reasoning to emulate the human problem-solving process for Bongard Problems. However, none of these approaches manage to close the human-machine gap, as the best learner achieves 64% accuracy while human participants easily reach 91%. We hope Bongard-OpenWorld can help us better understand the limitations of current visual intelligence and facilitate future research on visual agents with stronger few-shot visual reasoning capabilities.

cs.LG↗

arXiv2024

HabitAction: A Video Dataset for Human Habitual Behavior Recognition

Human Action Recognition (HAR) is a very crucial task in computer vision. It helps to carry out a series of downstream tasks, like understanding human behaviors. Due to the complexity of human behaviors, many highly valuable behaviors are not yet encompassed within the available datasets for HAR, e.g., human habitual behaviors (HHBs). HHBs hold significant importance for analyzing a person's personality, habits, and psychological changes. To solve these problems, in this work, we build a novel video dataset to demonstrate various HHBs. These behaviors in the proposed dataset are able to reflect internal mental states and specific emotions of the characters, e.g., crossing arms suggests to shield oneself from perceived threats. The dataset contains 30 categories of habitual behaviors including more than 300,000 frames and 6,899 action instances. Since these behaviors usually appear at small local parts of human action videos, it is difficult for existing action recognition methods to handle these local features. Therefore, we also propose a two-stream model using both human skeletons and RGB appearances. Experimental results demonstrate that our proposed method has much better performance in action recognition than the existing methods on the proposed dataset.

cs.CV↗

arXiv2024

Neighbor-Environment Observer: An Intelligent Agent for Immersive Working Companionship

Human-computer symbiosis is a crucial direction for the development of artificial intelligence. As intelligent systems become increasingly prevalent in our work and personal lives, it is important to develop strategies to support users across physical and virtual environments. While technological advances in personal digital devices, such as personal computers and virtual reality devices, can provide immersive experiences, they can also disrupt users' awareness of their surroundings and enhance the frustration caused by disturbances. In this paper, we propose a joint observation strategy for artificial agents to support users across virtual and physical environments. We introduce a prototype system, neighbor-environment observer (NEO), that utilizes non-invasive sensors to assist users in dealing with disruptions to their immersive experience. System experiments evaluate NEO from different perspectives and demonstrate the effectiveness of the joint observation strategy. A user study is conducted to evaluate its usability. The results show that NEO could lessen users' workload with the learned user preference. We suggest that the proposed strategy can be applied to various smart home scenarios.

cs.HC↗

arXiv2024

On the Emergence of Symmetrical Reality

Artificial intelligence (AI) has revolutionized human cognitive abilities and facilitated the development of new AI entities capable of interacting with humans in both physical and virtual environments. Despite the existence of virtual reality, mixed reality, and augmented reality for several years, integrating these technical fields remains a formidable challenge due to their disparate application directions. The advent of AI agents, capable of autonomous perception and action, further compounds this issue by exposing the limitations of traditional human-centered research approaches. It is imperative to establish a comprehensive framework that accommodates the dual perceptual centers of humans and AI agents in both physical and virtual worlds. In this paper, we introduce the symmetrical reality framework, which offers a unified representation encompassing various forms of physical-virtual amalgamations. This framework enables researchers to better comprehend how AI agents can collaborate with humans and how distinct technical pathways of physical-virtual integration can be consolidated from a broader perspective. We then delve into the coexistence of humans and AI, demonstrating a prototype system that exemplifies the operation of symmetrical reality systems for specific tasks, such as pouring water. Subsequently, we propose an instance of an AI-driven active assistance service that illustrates the potential applications of symmetrical reality. This paper aims to offer beneficial perspectives and guidance for researchers and practitioners in different fields, thus contributing to the ongoing research about human-AI coexistence in both physical and virtual environments.

cs.HC↗

arXiv2023

A Reconfigurable Data Glove for Reconstructing Physical and Virtual Grasps

In this work, we present a reconfigurable data glove design to capture different modes of human hand-object interactions, which are critical in training embodied artificial intelligence (AI) agents for fine manipulation tasks. To achieve various downstream tasks with distinct features, our reconfigurable data glove operates in three modes sharing a unified backbone design that reconstructs hand gestures in real time. In the tactile-sensing mode, the glove system aggregates manipulation force via customized force sensors made from a soft and thin piezoresistive material; this design minimizes interference during complex hand movements. The virtual reality (VR) mode enables real-time interaction in a physically plausible fashion: A caging-based approach is devised to determine stable grasps by detecting collision events. Leveraging a state-of-the-art finite element method (FEM), the simulation mode collects data on fine-grained 4D manipulation events comprising hand and object motions in 3D space and how the object's physical properties (e.g., stress and energy) change in accordance with manipulation over time. Notably, the glove system presented here is the first to use high-fidelity simulation to investigate the unobservable physical and causal factors behind manipulation actions. In a series of experiments, we characterize our data glove in terms of individual sensors and the overall system. More specifically, we evaluate the system's three modes by (i) recording hand gestures and associated forces, (ii) improving manipulation fluency in VR, and (iii) producing realistic simulation effects of various tool uses, respectively. Based on these three modes, our reconfigurable data glove collects and reconstructs fine-grained human grasp data in both physical and virtual environments, thereby opening up new avenues for the learning of manipulation skills for embodied AI agents.

cs.RO↗

arXiv2022

A One-bit, Comparison-Based Gradient Estimator

We study zeroth-order optimization for convex functions where we further assume that function evaluations are unavailable. Instead, one only has access to a $\textit{comparison oracle}$, which given two points $x$ and $y$ returns a single bit of information indicating which point has larger function value, $f(x)$ or $f(y)$. By treating the gradient as an unknown signal to be recovered, we show how one can use tools from one-bit compressed sensing to construct a robust and reliable estimator of the normalized gradient. We then propose an algorithm, coined SCOBO, that uses this estimator within a gradient descent scheme. We show that when $f(x)$ has some low dimensional structure that can be exploited, SCOBO outperforms the state-of-the-art in terms of query complexity. Our theoretical claims are verified by extensive numerical experiments.

math.OC↗

arXiv2021

Zeroth-Order Regularized Optimization (ZORO): Approximately Sparse Gradients and Adaptive Sampling

We consider the problem of minimizing a high-dimensional objective function, which may include a regularization term, using (possibly noisy) evaluations of the function. Such optimization is also called derivative-free, zeroth-order, or black-box optimization. We propose a new $\textbf{Z}$eroth-$\textbf{O}$rder $\textbf{R}$egularized $\textbf{O}$ptimization method, dubbed ZORO. When the underlying gradient is approximately sparse at an iterate, ZORO needs very few objective function evaluations to obtain a new iterate that decreases the objective function. We achieve this with an adaptive, randomized gradient estimator, followed by an inexact proximal-gradient scheme. Under a novel approximately sparse gradient assumption and various different convex settings, we show the (theoretical and empirical) convergence rate of ZORO is only logarithmically dependent on the problem dimension. Numerical experiments show that ZORO outperforms the existing methods with similar assumptions, on both synthetic and real datasets.

math.OC↗

arXiv2020

A General Framework for Bounding Approximate Dynamic Programming Schemes

For years, there has been interest in approximation methods for solving dynamic programming problems, because of the inherent complexity in computing optimal solutions characterized by Bellman's principle of optimality. A wide range of approximate dynamic programming (ADP) methods now exists. It is of great interest to guarantee that the performance of an ADP scheme be at least some known fraction, say $β$, of optimal. This paper introduces a general approach to bounding the performance of ADP methods, in this sense, in the stochastic setting. The approach is based on new results for bounding greedy solutions in string optimization problems, where one has to choose a string (ordered set) of actions to maximize an objective function. This bounding technique is inspired by submodularity theory, but submodularity is not required for establishing bounds. Instead, the bounding is based on quantifying certain notions of curvature of string functions; the smaller the curvatures the better the bound. The key insight is that any ADP scheme is a greedy scheme for some surrogate string objective function that coincides in its optimal solution and value with those of the original optimal control problem. The ADP scheme then yields to the bounding technique mentioned above, and the curvatures of the surrogate objective determine the value $β$ of the bound. The surrogate objective and its curvatures depend on the specific ADP.

math.OC↗

arXiv2019

Inhomogeneous Diophantine approximation over fields of formal power series

We prove a sharp analogue of Minkowski's inhomogeneous approximation theorem over fields of power series $\mathbb{F}_q((T^{-1}))$. Furthermore, we study the approximation to a given point $\underline{y}$ in $\mathbb{F}_q((T^{-1}))^2$ by the $SL_2(\mathbb{F}_q[T])$-orbit of a given point $\underline{x}$ in $\mathbb{F}_q((T^{-1}))^2$.

math.NT↗

arXiv2019

On homogeneous and inhomogeneous Diophantine approximation over the fields of formal power series

We prove over fields of power series the analogues of several Diophantine approximation results obtained over the field of real numbers. In particular we establish the power series analogue of Kronecker's theorem for matrices, together with a quantitative form of it, which can also be seen as a transference inequality between uniform approximation and inhomogeneous approximation. Special attention is devoted to the one dimensional case. Namely, we give a necessary and sufficient condition on an irrational power series $α$ which ensures that, for some positive $\eps$, the set $$ \liminf_{Q \in \mathbb{F}_q[z], \,\, °Q \to \infty} \| Q \| \cdot |\langle Q α- θ\rangle| \geq \eps $$ has full Hausdorff dimension.

math.NT↗

arXiv2019

Submodular Optimization Problems and Greedy Strategies: A Survey

The greedy strategy is an approximation algorithm to solve optimization problems arising in decision making with multiple actions. How good is the greedy strategy compared to the optimal solution? In this survey, we mainly consider two classes of optimization problems where the objective function is submodular. The first is set submodular optimization, which is to choose a set of actions to optimize a set submodular objective function, and the second is string submodular optimization, which is to choose an ordered set of actions to optimize a string submodular function. Our emphasis here is on performance bounds for the greedy strategy in submodular optimization problems. Specifically, we review performance bounds for the greedy strategy, more general and improved bounds in terms of curvature, performance bounds for the batched greedy strategy, and performance bounds for Nash equilibria.

math.OC↗