arXiv subjects

Teng Fang

Publications and source records attributed to Teng Fang.

9 recordsLinked to original sources

arXiv2026

Practical Lossless Volumetric Medical Image Compression via Tri-plane Context Tree Learning

Lossless compression of volumetric medical images is of paramount importance for clinical and research applications where data fidelity is essential. Traditional compression methods are often limited in efficiency due to rigid, handcrafted models. Conversely, deep neural network (DNN)-based compression methods, while effective, demand substantial computational resources, hindering deployment in resource-constrained settings. To address these challenges, we propose a novel tri-plane context tree (TCT)-based method for lossless volumetric medical image compression that delivers high performance without relying on DNNs or external training data. To exploit intra-slice and inter-slice redundancies, we introduce a compact tri-plane context representation that decomposes complex 3D context modeling into efficient 2D modeling on three orthogonal planes. By integrating this representation with a context tree framework, we develop an input-specific TCT model employing an adaptive binary tree structure. At each tree node, the model dynamically selects from a suite of tri-plane based predictors and contextual feature extractors, enabling data-adaptive context modeling tailored to local structural characteristics. Instead of offline training, we sample a subset of the input volume to learn the TCT model by optimizing the minimum description length (MDL) through iterative construction and pruning. With the learned TCT model, each pixel retrieves its corresponding context, computes the prediction residual using the predictor dictated by the context, and performs entropy encoding based on the associated histograms. Experimental results demonstrate that the proposed method achieves compression performance on par with recent DNN-based methods on multiple datasets, while maintaining low computational cost and fast coding speeds, making it highly applicable in practice.

eess.IV↗

arXiv2026

Best-of-Evidence: Best-of-N Selection under Partial Verification

BoN improves model outputs by sampling several candidates and selecting one with a proxy score, but it assumes that complete candidates can be evaluated reliably. Many vision-language tasks instead provide only partial verification: a finding, span, value, region, or relation may be checkable even when no dependable whole-response verifier exists. Moreover, the same claim may recur across candidates with opposing stances, allowing one observation to support part of the pool and contradict another. We introduce Best-of-Evidence (BoE), an inference-time selection framework that keeps the BoN candidate pool fixed, represents reusable claims with a signed candidate--factor graph, and allocates a limited budget to evidence actions that can change the final choice. BoE formalizes selection under partial verification and provides a practical score-based controller, with the zero-budget case recovering the underlying BoN decision. Theoretically, we show that residual evidence capacity limits any evidence-driven improvement and that shared factor queries can achieve an O(log K) versus {\Theta}(K) query separation in a factor-code model. Common-ledger experiments on four medical VQA settings show that BoE can improve fixed-pool selection and rescue some BoN failures when evidence is reliable, contrastive, and decision-relevant, while also revealing the channel-quality and candidate-generation limits that prevent universal gains.

cs.LG↗

arXiv2025

Fleming-R1: Toward Expert-Level Medical Reasoning via Reinforcement Learning

While large language models show promise in medical applications, achieving expert-level clinical reasoning remains challenging due to the need for both accurate answers and transparent reasoning processes. To address this challenge, we introduce Fleming-R1, a model designed for verifiable medical reasoning through three complementary innovations. First, our Reasoning-Oriented Data Strategy (RODS) combines curated medical QA datasets with knowledge-graph-guided synthesis to improve coverage of underrepresented diseases, drugs, and multi-hop reasoning chains. Second, we employ Chain-of-Thought (CoT) cold start to distill high-quality reasoning trajectories from teacher models, establishing robust inference priors. Third, we implement a two-stage Reinforcement Learning from Verifiable Rewards (RLVR) framework using Group Relative Policy Optimization, which consolidates core reasoning skills while targeting persistent failure modes through adaptive hard-sample mining. Across diverse medical benchmarks, Fleming-R1 delivers substantial parameter-efficient improvements: the 7B variant surpasses much larger baselines, while the 32B model achieves near-parity with GPT-4o and consistently outperforms strong open-source alternatives. These results demonstrate that structured data design, reasoning-oriented initialization, and verifiable reinforcement learning can advance clinical reasoning beyond simple accuracy optimization. We release Fleming-R1 publicly to promote transparent, reproducible, and auditable progress in medical AI, enabling safer deployment in high-stakes clinical environments.

cs.LG↗

arXiv2025

Tiling the symmetric group by transpositions

For nonempty subsets $X$ and $Y$ of a group $G$, we say that $(X,Y)$ is a tiling of $G$ if every element of $G$ can be uniquely expressed as $xy$ for some $x\in X$ and $y\in Y$. In 1966, Rothaus and Thompson studied whether the symmetric group $S_n$ with $n\geq3$ admits a tiling $(T_n,Y)$, where $T_n$ consists of the identity and all the transpositions in $S_n$. They showed that no such tiling exists if $1+n(n-1)/2$ is divisible by a prime number at least $\sqrt{n}+2$. In this paper, we establish a new necessary condition for the existence of such a tiling: the subset $Y$ must be partition-transitive with respect to certain partitions of $n$. This generalizes the result of Rothaus and Thompson, as well as a result of Nomura in 1985. We also study whether $S_n$ can be tiled by the set $T_n^*$ of all the transpositions, which finally leads us to conjecture that neither $T_n$ nor $T_n^*$ tiles $S_n$ for any $n\geq4$.

math.CO↗

arXiv2025

Proof of a conjecture of Green and Liebeck on codes in symmetric groups

Let $A$ and $B$ be subsets of a finite group $G$ and $r$ a positive integer. If for every $g\in G$, there are precisely $r$ pairs $(a,b)\in A\times B$ such that $g=ab$, then $B$ is called a code in $G$ with respect to $A$ and we write $r G=A\boldsymbol{\cdot}B$. If in addition $B$ is a subgroup of $G$, then we say that $B$ is a subgroup code in $G$. In this paper we resolve a conjecture by Green and Liebeck \cite[Conjecture 2.3]{Green20} on certain subgroup codes in the symmetric group $S_n$. Let $n>2k$ and let $j$ be such that $2^j\leqslant k<2^{j+1}$. Suppose that $X$ is a conjugacy class in $S_n$ containing $x$, and $Y_k$ is the subgroup $S_k\times S_{n-k}$ of $S_n$, where the factor $S_k$ permutes the subset $\{1,\ldots,k\}$ and the factor $S_{n-k}$ permutes the subset $\{k+1,\ldots,n\}$. We prove that $r S_n=X\boldsymbol{\cdot}Y_k$ for some positive integer $r$ if and only if the cycle type of $x$ has exactly one cycle of length $2^i$ for $0\leqslant i\leqslant j$ and all other cycles have length at least $k+1$. We also propose several problems concerning the existence of certain subgroup codes in a finite group $G$ with respect to a conjugation-closed subset in $G$.

math.CO↗

arXiv2024

A family of symmetric graphs in relation to 2-point-transitive linear spaces

A graph $\Gamma$ is $G$-symmetric if it admits $G$ as a group of automorphisms acting transitively on the set of arcs of $\Gamma$, where an arc is an ordered pair of adjacent vertices. Let $\Gamma$ be a $G$-symmetric graph such that its vertex set admits a nontrivial $G$-invariant partition ${\cal B}$, and let ${\cal D}(\Gamma, {\cal B})$ be the incidence structure with point set ${\cal B}$ and blocks $\{B\} \cup \Gamma_{\cal B}(\alpha)$, for $B \in {\cal B}$ and $\alpha \in B$, where $\Gamma_{\cal B}(\alpha)$ is the set of blocks of ${\cal B}$ containing at least one neighbour of $\alpha$ in $\Gamma$. In this paper we classify all $G$-symmetric graphs $\Gamma$ such that $\Gamma_{\cal B}(\alpha) \ne \Gamma_{\cal B}(\beta)$ for distinct $\alpha, \beta \in B$, the quotient graph of $\Gamma$ with respect to ${\cal B}$ is a complete graph, and ${\cal D}(\Gamma, {\cal B})$ is isomorphic to the complement of a $(G, 2)$-point-transitive linear space.

math.CO↗

arXiv2019

Affine flag graphs and classification of a family of symmetric graphs with complete quotients

A graph $Γ$ is $G$-symmetric if $G$ is a group of automorphisms of $Γ$ which is transitive on the set of ordered pairs of adjacent vertices of $Γ$. If $V(Γ)$ admits a nontrivial $G$-invariant partition ${\cal B}$ such that for blocks $B, C \in {\cal B}$ adjacent in the quotient graph $Γ_{\cal B}$ of $Γ$ relative to ${\cal B}$, exactly one vertex of $B$ has no neighbour in $C$, then $Γ$ is called an almost multicover of $Γ_{\cal B}$. In this case an incidence structure with point set ${\cal B}$ arises naturally, and it is a $(G, 2)$-point-transitive and $G$-block-transitive 2-design if in addition $Γ_{\cal B}$ is a complete graph. In this paper we classify all $G$-symmetric graphs $Γ$ such that (i) ${\cal B}$ has block size $|B| \ge 3$; (ii) $Γ_{\cal B}$ is complete and almost multi-covered by $Γ$; (iii) the incidence structure involved is a linear space; and (iv) $G$ contains a regular normal subgroup which is elementary abelian. This classification together with earlier results in [A. Gardiner and C. E. Praeger, Australas. J. Combin. 71 (2018) 403--426], [M.~Giulietti et al., J. Algebraic Combin. 38 (2013) 745--765] and [T. Fang et al., Electronic J. Combin. 23 (2) (2016) P2.27] completes the classification of symmetric graphs satisfying (i) and (ii).

math.CO↗

arXiv2017

Vertex-imprimitive symmetric graphs with exactly one edge between any two distinct blocks

A graph $Γ$ is called $G$-symmetric if it admits $G$ as a group of automorphisms acting transitively on the set of ordered pairs of adjacent vertices. We give a classification of $G$-symmetric graphs $Γ$ with $V(Γ)$ admitting a nontrivial $G$-invariant partition $\mathcal{B}$ such that there is exactly one edge of $Γ$ between any two distinct blocks of $\mathcal{B}$. This is achieved by giving a classification of $(G, 2)$-point-transitive and $G$-block-transitive designs $\mathcal{D}$ together with $G$-orbits $Ω$ on the flag set of $\mathcal{D}$ such that $G_{σ, L}$ is transitive on $L \setminus \{σ\}$ and $L \cap N = \{σ\}$ for distinct $(σ, L), (σ, N) \in Ω$, where $G_{σ, L}$ is the setwise stabilizer of $L$ in the stabilizer $G_σ$ of $σ$ in $G$. Along the way we determine all imprimitive blocks of $G_σ$ on $V \setminus \{σ\}$ for every $2$-transitive group $G$ on a set $V$, where $σ\in V$.

math.GR↗

arXiv2016

Cubic graphical regular representations of $PSL_2(q)$

We study cubic graphical regular representations of the finite simple groups $PSL_2(q)$. It is shown that such graphical regular representations exist if and only if $q\neq7$, and the generating set must consist of three involutions.

math.GR↗