arXiv subjects

Yuanrui Zhang

Publications and source records attributed to Yuanrui Zhang.

10 recordsLinked to original sources

arXiv2026

Labelled Process Logic

This paper develops a complete labelled proof-theoretic framework for process logic --- an extension of dynamic logic in which formulas specify properties of execution traces rather than only final states. The main difficulty is that first-order process logic must reason about concrete computations while preserving temporal information along regular-program traces. Existing compositional calculi cover important fragments but do not provide a complete treatment of full first-order process logic over regular programs. We address this difficulty by enriching process-logic formulas with labels that explicitly record trace and update information during derivations. Based on this construction, we define cyclic labelled proof systems for both propositional and first-order process logic, respectively denoted by \GiiiPPLcyc\ and \GiiiFOPLcyc. We study their soundness and completeness. Their soundness follows from a global progress condition: an invalid cyclic derivation would induce infinitely many strict decreases in a natural-valued counter-example measure. The completeness of \GiiiPPLcyc\ is established by deriving the axioms and rules of the Hilbert system for propositional process logic, while the completeness of \GiiiFOPLcyc\ is obtained relative to the underlying arithmetic theory through the standard arithmetical encoding used for first-order dynamic logic.

cs.LO↗

arXiv2026

Designing Reinforcement Learning for Diffusion Models: A Unified Path-Space View

Reinforcement learning (RL) post-training provides a direct way to align diffusion models with human preferences and task-specific rewards. However, current RL algorithms for diffusion models remain fragmented: reverse-trajectory methods rely on discretized likelihood ratios, whereas forward-matching methods train on reward-labeled noising versions of the rollout samples. This paper shows that these seemingly different losses arise from a single path-space principle. Starting from the regularized diffusion-RL objective, we use importance sampling between sampling SDEs to obtain an explicit policy-gradient estimator on trajectory space. The estimator contains the stochastic Itô integral underlying Flow-GRPO-type updates; we derive an equivalent variance-reduced value-gradient form that recovers the forward-matching structure of AWM and DiffusionNFT. This identifies the empirical gap between these method families as a variance-reduction effect rather than a difference in RL principle. The derivation yields a unified design space organized by value-gradient estimation, weight functions, and sampling choices. Within this space, we propose a multi-sample KDE value-gradient estimator that reuses rollout groups, together with scale-bounded weight families that retain stable existing recipes while excluding singular ones. Experiments on SD3.5-M and Qwen-Image models validate the variance-reduction explanation and show that the resulting recipe improves over prior diffusion-RL baselines.

cs.LG↗

arXiv2026

Ouroboros-Spatial: Closing the Data-Model Loop for Spatial Reasoning

Spatial reasoning remains a persistent challenge for multimodal large language models (MLLMs). Existing approaches largely rely on large-scale, statically curated datasets, where all training samples are treated uniformly regardless of the model's evolving capabilities. This static paradigm is inherently data-inefficient: training capacity is often spent on samples that are either trivial or overly difficult for the model at its current stage. To address this limitation, we propose Ouroboros-Spatial, a self-evolving training framework in which the model plays dual roles as a proposer and a solver. In each iteration, a frozen proposer generates spatial question-answer (QA) pairs from 3D scene metadata and raw video frames, together with executable code for deriving reliable ground truth. A learnable solver is then fine-tuned on the accepted samples, and its per-sample prediction confidence is used as a difficulty signal. This signal is fed back to the proposer in the next iteration, guiding it to generate questions better matched to the solver's current capabilities. Through this closed-loop design, the training distribution co-evolves with model ability, reducing redundant trivial examples while filtering out ambiguous or uninformative samples with limited learning value. Across six spatial reasoning benchmarks, Ouroboros-Spatial substantially improves Qwen3-VL-4B and Qwen3-VL-8B while using an order of magnitude fewer training examples than recent large-scale curated datasets. On VSI-Bench, it yields absolute gains of 9.9 and 6.8 points for the 4B and 8B models, respectively, enabling both to outperform a wide range of strong open-source and proprietary baselines.

cs.CV↗

arXiv2026

On A Parameterized Theory of Dynamic Logic for Operationally-based Programs

Applying dynamic logics to program verifications is a challenge, because their axiomatic rules for regular expressions can be difficult to be adapted to different program models. We present a novel dynamic logic, called DLp, which supports reasoning based on programs' operational semantics. For those programs whose transitional behaviours are their standard or natural semantics, DLp makes their verifications easier since one can directly apply the program transitions for reasoning, without the need of re-designing and validating new rules as in most other dynamic logics. DLp is parametric. It provides a model-independent framework consisting of a relatively small set of inference rules, which depends on a given set of trustworthy rules for the operational semantics. These features of DLp let multiple models easily compared in its framework and makes it compatible with existing dynamic-logic theories. DLp supports cyclic reasoning, providing an incremental derivation process for recursive programs, making it more convenient to reason about without prior program transformations. We analyze and prove the soundness and completeness of DLp under certain conditions. Several case studies illustrate the features of DLp and fully demonstrate its potential usage.

cs.LO↗

arXiv2026

Luminark: Training-free, Probabilistically-Certified Watermarking for General Vision Generative Models

In this paper, we introduce \emph{Luminark}, a training-free and probabilistically-certified watermarking method for general vision generative models. Our approach is built upon a novel watermark definition that leverages patch-level luminance statistics. Specifically, the service provider predefines a binary pattern together with corresponding patch-level thresholds. To detect a watermark in a given image, we evaluate whether the luminance of each patch surpasses its threshold and then verify whether the resulting binary pattern aligns with the target one. A simple statistical analysis demonstrates that the false positive rate of the proposed method can be effectively controlled, thereby ensuring certified detection. To enable seamless watermark injection across different paradigms, we leverage the widely adopted guidance technique as a plug-and-play mechanism and develop the \emph{watermark guidance}. This design enables Luminark to achieve generality across state-of-the-art generative models without compromising image quality. Empirically, we evaluate our approach on nine models spanning diffusion, autoregressive, and hybrid frameworks. Across all evaluations, Luminark consistently demonstrates high detection accuracy, strong robustness against common image transformations, and good performance on visual quality.

cs.CV↗

arXiv2025

Parameterized Dynamic Logic -- Towards A Cyclic Logical Framework for General Program Specification and Verification

We present a theory of parameterized dynamic logic, namely DLp, for specifying and reasoning about a rich set of program models based on their transitional behaviours. Different from most dynamic logics that deal with regular expressions or a particular type of formalisms, DLp introduces a type of labels called "program configurations" as explicit program status for symbolic executions, allowing programs and formulas to be of arbitrary forms according to interested domains. This characteristic empowers dynamic logical formulas with a direct support of symbolic-execution-based reasoning, while still maintaining reasoning based on syntactic structures in traditional dynamic logics through a rule-lifting process. We propose a proof system and build a cyclic preproof structure special for DLp, which guarantees the soundness of infinite proof trees induced by symbolically executing programs with explicit/implicit loop structures. The soundness of DLp is formally analyzed and proved. DLp provides a flexible verification framework based on the theories of dynamic logics. It helps reduce the burden of developing different dynamic-logic theories for different programs, and save the additional transformations in the derivations of non-compositional programs. We give some examples of instantiations of DLp in particular domains, showing the potential and advantages of using DLp in practical usage.

cs.LO↗

arXiv2024

Image Reflection on Process Graphs -- A Novel Approach for the Completeness of an Axiomatization of 1-Free Regular Expressions Modulo Bisimilarity

We analyze a phenomenon called ``image reflection'' on a type of characterization graphs -- LLEE charts -- of 1-free regular expressions. Due to the correspondence between 1-free regular expressions and the provable solutions of LEE/LLEE charts, this observation naturally leads to a new proof for the completeness of the proof system \MilIfree\ for 1-free regular expressions modulo bisimulation equivalence. The critical part of the previous proof is to show that bisimulation collapse, which plays the role in linking the provable solutions of two LLEE charts, is still an LLEE chart. The difference of our proof, compared to the previous one, is that we do not rely on the graph transformations from LLEE charts into their bisimulation collapses by merging two carefully-selected bisimilar nodes in each transformation step. Instead, we directly show that the bisimulation collapse of an LLEE chart possesses an LEE/LLEE structure based on its set of images mapped through the bisimulation function from the LLEE chart, and the constrained relation between the images and their so-called ``well-structured'' looping-back charts pre-images on the LLEE chart. Our approach provides a novel angle to look at this problem and related problems, and can also be used for simplifying the graph transformations in the proof of the completeness problem of the proof system \Mil\ for regular expressions modulo bisimulation equivalence, which had remained open until very recently.

cs.LO↗

arXiv2021

A Dynamic Logic for Verification of Synchronous Models based on Theorem Proving

Synchronous model is a type of formal models for modelling and specifying reactive systems. It has a great advantage over other real-time models that its modelling paradigm supports a deterministic concurrent behaviour of systems. Various approaches have been utilized for verification of synchronous models based on different techniques, such as model checking, SAT/SMT sovling, term rewriting, type inference and so on. In this paper, we propose a verification approach for synchronous models based on compositional reasoning and term rewriting. Specifically, we initially propose a variation of dynamic logic, called synchronous dynamic logic (SDL). SDL extends the regular program model of first-order dynamic logic (FODL) with necessary primitives to capture the notion of synchrony and synchronous communication between parallel programs, and enriches FODL formulas with temporal dynamic logical formulas to specify safety properties -- a type of properties mainly concerned in reactive systems. To rightly capture the synchronous communications, we define a constructive semantics for the program model of SDL. We build a sound and relatively complete proof system for SDL. Compared to previous verification approaches, SDL provides a divide and conquer way to analyze and verify synchronous models based on compositional reasoning of the syntactic structure of the programs of SDL. To illustrate the usefulness of SDL, we apply SDL to specify and verify a small example in the synchronous model SyncChart, which shows the potential of SDL to be used in practice.

cs.SE↗

arXiv2016

Wireless Security with Beamforming Technique

This thesis focuses on the wireless security in the physical layer with beamforming technique. One of the emerging areas is the security enhancement in the physical layer, which exploits the intrinsic properties of the wireless medium. Beamforming, which has been proved to have many advantages, can also be applied to enhance the wireless security. One of the most common threats, i.e., passive eavesdropping, is addressed in this thesis. To reduce the risk of leaking information to the eavesdroppers, the physical region where the transmission is exposed to eavesdropping has been studied. In this thesis, the exposure region based beamforming technique is proposed to combat the threat from the randomly located eavesdroppers in a fading channel. In this system model, the large-scale path loss and a general Rician fading channel model are considered. The exposure region is established to describe the secrecy performance of the system, based on which the probability that the secrecy outage event occurs is defined to evaluate the security level of the exposure region. The antenna array is one of the most important factors that affect the secrecy performance of the exposure region based beamforming technique. The potential of using different array geometry and array configuration to improve security is explored. In this thesis, two common arrays, i.e., linear and circular arrays, are considered.Analytic expressions for general array geometry and for the linear and circular arrays are derived. Based on the empirical results, numerical optimization algorithms are developed to exploit the array configuration to enhance the system security level. In addition, experiments are carried out to study the performance of the beamformer with linear and circular arrays. Especially, the impact of the mutual coupling on the security performance is investigated.

cs.IT↗

arXiv2016

Defining Spatial Security Outage Probability for Exposure Region Based Beamforming

With increasing number of antennae in base stations, there is considerable interest in using beamfomining to improve physical layer security, by creating an `exposure region' that enhances the received signal quality for a legitimate user and reduces the possibility of leaking information to a randomly located passive eavesdropper. The paper formalises this concept by proposing a novel definition for the security level of such a legitimate transmission, called the `Spatial Secrecy Outage Probability' (SSOP). By performing a theoretical and numerical analysis, it is shown how the antenna array parameters can affect the SSOP and its analytic upper bound. Whilst this approach may be applied to any array type and any fading channel model, it is shown here how the security performance of a uniform linear array varies in a Rician fading channel by examining the analytic SSOP upper bound.

cs.IT↗