arXiv subjects

Yibo Gao

Publications and source records attributed to Yibo Gao.

At least 37 records · Page 2Linked to original sources

arXiv2025

Learning Concept-Driven Logical Rules for Interpretable and Generalizable Medical Image Classification

The pursuit of decision safety in clinical applications highlights the potential of concept-based methods in medical imaging. While these models offer active interpretability, they often suffer from concept leakages, where unintended information within soft concept representations undermines both interpretability and generalizability. Moreover, most concept-based models focus solely on local explanations (instance-level), neglecting the global decision logic (dataset-level). To address these limitations, we propose Concept Rule Learner (CRL), a novel framework to learn Boolean logical rules from binarized visual concepts. CRL employs logical layers to capture concept correlations and extract clinically meaningful rules, thereby providing both local and global interpretability. Experiments on two medical image classification tasks show that CRL achieves competitive performance with existing methods while significantly improving generalizability to out-of-distribution data. The code of our work is available at https://github.com/obiyoag/crl.

cs.CV↗

arXiv2025

Interlacing triangles, Schubert puzzles, and graph colorings

We show that interlacing triangular arrays, introduced by Aggarwal-Borodin-Wheeler to study certain probability measures, can be used to compute structure constants for multiplying Schubert classes in the $K$-theory of Grassmannians, in the cohomology of their cotangent bundles, and in the cohomology of partial flag varieties. Our results are achieved by establishing a splitting lemma, allowing for interlacing triangular arrays of high rank to be decomposed into arrays of lower rank, and by constructing a bijection between interlacing triangular arrays of rank 3 with certain proper vertex colorings of the triangular grid graph that factors through generalizations of Knutson-Tao puzzles. Along the way, we prove one enumerative conjecture of Aggarwal-Borodin-Wheeler and disprove another.

math.CO↗

arXiv2025

Empowering Medical Multi-Agents with Clinical Consultation Flow for Dynamic Diagnosis

Traditional AI-based healthcare systems often rely on single-modal data, limiting diagnostic accuracy due to incomplete information. However, recent advancements in foundation models show promising potential for enhancing diagnosis combining multi-modal information. While these models excel in static tasks, they struggle with dynamic diagnosis, failing to manage multi-turn interactions and often making premature diagnostic decisions due to insufficient persistence in information collection.To address this, we propose a multi-agent framework inspired by consultation flow and reinforcement learning (RL) to simulate the entire consultation process, integrating multiple clinical information for effective diagnosis. Our approach incorporates a hierarchical action set, structured from clinic consultation flow and medical textbook, to effectively guide the decision-making process. This strategy improves agent interactions, enabling them to adapt and optimize actions based on the dynamic state. We evaluated our framework on a public dynamic diagnosis benchmark. The proposed framework evidentially improves the baseline methods and achieves state-of-the-art performance compared to existing foundation model-based methods.

cs.AI↗

arXiv2024

Dual Mixed Volume

We define and study the dual mixed volume rational function of a sequence of polytopes, a dual version of the mixed volume polynomial. This concept has direct relations to the adjoint polynomials and the canonical forms of polytopes. We show that dual mixed volume is additive under mixed subdivisions, and is related by a change of variables to the dual volume of the Cayley polytope. We study dual mixed volume of zonotopes, generalized permutohedra, and associahedra. The latter reproduces the planar $ϕ^3$-scalar amplitude at tree level.

math.CO↗

arXiv2024

On the minimal power of $q$ in a Kazhdan-Lusztig polynomial

For $w$ in the symmetric group, we provide an exact formula for the smallest positive power $q^{h(w)}$ appearing in the Kazhdan-Lusztig polynomial $P_{e,w}(q)$. We also provide a tight upper bound on $h(w)$ in simply-laced types, resolving a conjecture of Billey-Postnikov from 2002.

math.CO↗

arXiv2024

Orbit structures and complexity in Schubert and Richardson Varieties

The goal of this paper is twofold. Firstly, we provide a type-uniform formula for the torus complexity of the usual torus action on a Richardson variety, by developing the notion of algebraic dimensions of Bruhat intervals, strengthening a type $A$ result by Donten-Bury, Escobar and Portakal. In the process, we give an explicit description of the torus action on any Deodhar component as well as describe the root subgroups that comprise the component. Secondly, when a Levi subgroup in a reductive algebraic group acts on a Schubert variety, we exhibit a codimension preserving bijection between the Levi-Borel subgroup (a Borel subgroup in the Levi subgroup) orbits in the big open cell of that Schubert variety and torus orbits in the big open cell of a distinguished Schubert subvariety. This bijection has many applications including a type-uniform formula for the Levi-Borel complexity of the usual Levi-Borel subgroup action on a Schubert variety. We conclude by extending the Levi-Borel complexity results to a large class of Schubert varieties in the partial flag variety.

math.CO↗

arXiv2024

Repeatable patterns and the maximum multiplicity of a generator in a reduced word

We study the maximum multiplicity $\mathcal{M}(k,n)$ of a simple transposition $s_k=(k \: k+1)$ in a reduced word for the longest permutation $w_0=n \: n-1 \: \cdots \: 2 \: 1$, a problem closely related to much previous work on sorting networks and on the "$k$-set" problem. After reinterpreting the problem in terms of monotone weakly separated paths, we show that, for fixed $k$ and sufficiently large $n$, the optimal density is realized by paths which are periodic in a precise sense, so that \[ \mathcal{M}(k,n)=c_k n + p_k(n) \] for a periodic function $p_k$ and constant $c_k$. In fact we show that $c_k$ is always rational, and compute several bounds and exact values for this quantity with "repeatable patterns", which we introduce.

math.CO↗

arXiv2024

Evidential Concept Embedding Models: Towards Reliable Concept Explanations for Skin Disease Diagnosis

Due to the high stakes in medical decision-making, there is a compelling demand for interpretable deep learning methods in medical image analysis. Concept Bottleneck Models (CBM) have emerged as an active interpretable framework incorporating human-interpretable concepts into decision-making. However, their concept predictions may lack reliability when applied to clinical diagnosis, impeding concept explanations' quality. To address this, we propose an evidential Concept Embedding Model (evi-CEM), which employs evidential learning to model the concept uncertainty. Additionally, we offer to leverage the concept uncertainty to rectify concept misalignments that arise when training CBMs using vision-language models without complete concept supervision. With the proposed methods, we can enhance concept explanations' reliability for both supervised and label-efficient settings. Furthermore, we introduce concept uncertainty for effective test-time intervention. Our evaluation demonstrates that evi-CEM achieves superior performance in terms of concept prediction, and the proposed concept rectification effectively mitigates concept misalignments for label-efficient training. Our code is available at https://github.com/obiyoag/evi-CEM.

cs.CV↗

arXiv2024

Multi-Center Fetal Brain Tissue Annotation (FeTA) Challenge 2022 Results

Segmentation is a critical step in analyzing the developing human fetal brain. There have been vast improvements in automatic segmentation methods in the past several years, and the Fetal Brain Tissue Annotation (FeTA) Challenge 2021 helped to establish an excellent standard of fetal brain segmentation. However, FeTA 2021 was a single center study, and the generalizability of algorithms across different imaging centers remains unsolved, limiting real-world clinical applicability. The multi-center FeTA Challenge 2022 focuses on advancing the generalizability of fetal brain segmentation algorithms for magnetic resonance imaging (MRI). In FeTA 2022, the training dataset contained images and corresponding manually annotated multi-class labels from two imaging centers, and the testing data contained images from these two imaging centers as well as two additional unseen centers. The data from different centers varied in many aspects, including scanners used, imaging parameters, and fetal brain super-resolution algorithms applied. 16 teams participated in the challenge, and 17 algorithms were evaluated. Here, a detailed overview and analysis of the challenge results are provided, focusing on the generalizability of the submissions. Both in- and out of domain, the white matter and ventricles were segmented with the highest accuracy, while the most challenging structure remains the cerebral cortex due to anatomical complexity. The FeTA Challenge 2022 was able to successfully evaluate and advance generalizability of multi-class fetal brain tissue segmentation algorithms for MRI and it continues to benchmark new algorithms. The resulting new methods contribute to improving the analysis of brain development in utero.

eess.IV↗

arXiv2023

Levi-spherical Schubert varieties

We prove a short, root-system uniform, combinatorial classification of Levi-spherical Schubert varieties for any generalized flag variety $G/B$ of finite Lie type. We apply this to the study of multiplicity-free decompositions of a Demazure module into irreducible representations of a Levi subgroup.

math.RT↗

arXiv2023

Quantum Bruhat graphs and tilted Richardson varieties

Quantum Bruhat graph is a weighted directed graph on a finite Weyl group first defined by Brenti-Fomin-Postnikov. It encodes quantum Monk's rule and can be utilized to study the $3$-point Gromov-Witten invariants of the flag variety. In this paper, we provide an explicit formula for the minimal weights between any pair of permutations on the quantum Bruhat graph, and consequently obtain an Ehresmann-like characterization for the tilted Bruhat order. Moreover, for any ordered pair of permutations $u$ and $v$, we define the tilted Richardson variety $T_{u,v}$, with a stratification that gives a geometric meaning to intervals in the tilted Bruhat order. We provide a few equivalent definitions to this new family of varieties that include Richardson varieties, and establish some fundamental geometric properties including their dimensions and closure relations.

math.CO↗

arXiv2023

Single channel based interference-free and self-powered human-machine interactive interface using eigenfrequency-dominant mechanism

The recent development of wearable devices is revolutionizing the way of human-machine interaction (HMI). Nowadays, an interactive interface that carries more embedded information is desired to fulfil the increasing demand in era of Internet of Things. However, present approach normally relies on sensor arrays for memory expansion, which inevitably brings the concern of wiring complexity, signal differentiation, power consumption, and miniaturization. Herein, a one-channel based self-powered HMI interface, which uses the eigenfrequency of magnetized micropillar (MMP) as identification mechanism, is reported. When manually vibrated, the inherent recovery of the MMP caused a damped oscillation that generates current signals because of Faraday's Law of induction. The time-to-frequency conversion explores the MMP-related eigenfrequency, which provides a specific solution to allocate diverse commands in an interference-free behavior even with one electric channel. A cylindrical cantilever model was built to regulate the MMP eigenfrequencies via precisely designing the dimensional parameters and material properties. We show that using one device and two electrodes, high-capacity HMI interface can be realized when the MMPs with different eigenfrequencies have been integrated. This study provides the reference value to design the future HMI system especially for situations that require a more intuitive and intelligent communication experience with high-memory demand.

physics.app-ph↗

arXiv2023

Balance constants for Coxeter groups

The $1/3$-$2/3$ Conjecture, originally formulated in 1968, is one of the best-known open problems in the theory of posets, stating that the balance constant (a quantity determined by the linear extensions) of any non-total order is at least $1/3$. By reinterpreting balance constants of posets in terms of convex subsets of the symmetric group, we extend the study of balance constants to convex subsets $C$ of any Coxeter group. Remarkably, we conjecture that the lower bound of $1/3$ still applies in any finite Weyl group, with new and interesting equality cases appearing. We generalize several of the main results towards the $1/3$-$2/3$ Conjecture to this new setting: we prove our conjecture when $C$ is a weak order interval below a fully commutative element in any acyclic Coxeter group (an generalization of the case of width-two posets), we give a uniform lower bound for balance constants in all finite Weyl groups using a new generalization of order polytopes to this context, and we introduce generalized semiorders for which we resolve the conjecture. We hope this new perspective may shed light on the proper level of generality in which to consider the $1/3$-$2/3$ Conjecture, and therefore on which methods are likely to be successful in resolving it.

math.CO↗

arXiv2023

BayeSeg: Bayesian Modeling for Medical Image Segmentation with Interpretable Generalizability

Due to the cross-domain distribution shift aroused from diverse medical imaging systems, many deep learning segmentation methods fail to perform well on unseen data, which limits their real-world applicability. Recent works have shown the benefits of extracting domain-invariant representations on domain generalization. However, the interpretability of domain-invariant features remains a great challenge. To address this problem, we propose an interpretable Bayesian framework (BayeSeg) through Bayesian modeling of image and label statistics to enhance model generalizability for medical image segmentation. Specifically, we first decompose an image into a spatial-correlated variable and a spatial-variant variable, assigning hierarchical Bayesian priors to explicitly force them to model the domain-stable shape and domain-specific appearance information respectively. Then, we model the segmentation as a locally smooth variable only related to the shape. Finally, we develop a variational Bayesian framework to infer the posterior distributions of these explainable variables. The framework is implemented with neural networks, and thus is referred to as deep Bayesian segmentation. Quantitative and qualitative experimental results on prostate segmentation and cardiac segmentation tasks have shown the effectiveness of our proposed method. Moreover, we investigated the interpretability of BayeSeg by explaining the posteriors and analyzed certain factors that affect the generalization ability through further ablation studies. Our code will be released via https://zmiclab.github.io/projects.html, once the manuscript is accepted for publication.

cs.CV↗

arXiv2022

Degrees of the stretched Kostka quasi-polynomials

We provide a type-uniform formula for the degree of the stretched Kostka quasi-polynomial $K_{λ,μ}(N)$ in all classical types, improving a previous result by McAllister in $\mathfrak{sl}_r(\mathbb{C})$. Our proof relies on a combinatorial model for the weight multiplicity by Berenstein and Zelevinsky.

math.CO↗

arXiv2022

Electrical networks and the Grove algebra

We study the ring of regular functions on the space of planar electrical networks, which we coin the grove algebra. This algebra is an electrical analogue of the Plücker ring studied classically in invariant theory. We develop the combinatorics of double groves to study the grove algebra, and find a quadratic Gröbner basis for the grove ideal.

math.CO↗

arXiv2022

Joint Modeling of Image and Label Statistics for Enhancing Model Generalizability of Medical Image Segmentation

Although supervised deep-learning has achieved promising performance in medical image segmentation, many methods cannot generalize well on unseen data, limiting their real-world applicability. To address this problem, we propose a deep learning-based Bayesian framework, which jointly models image and label statistics, utilizing the domain-irrelevant contour of a medical image for segmentation. Specifically, we first decompose an image into components of contour and basis. Then, we model the expected label as a variable only related to the contour. Finally, we develop a variational Bayesian framework to infer the posterior distributions of these variables, including the contour, the basis, and the label. The framework is implemented with neural networks, thus is referred to as deep Bayesian segmentation. Results on the task of cross-sequence cardiac MRI segmentation show that our method set a new state of the art for model generalizability. Particularly, the BayeSeg model trained with LGE MRI generalized well on T2 images and outperformed other models with great margins, i.e., over 0.47 in terms of average Dice. Our code is available at https://zmiclab.github.io/projects.html.

eess.IV↗

arXiv2022

Towards Self-supervised and Weight-preserving Neural Architecture Search

Neural architecture search (NAS) algorithms save tremendous labor from human experts. Recent advancements further reduce the computational overhead to an affordable level. However, it is still cumbersome to deploy the NAS techniques in real-world applications due to the fussy procedures and the supervised learning paradigm. In this work, we propose the self-supervised and weight-preserving neural architecture search (SSWP-NAS) as an extension of the current NAS framework by allowing the self-supervision and retaining the concomitant weights discovered during the search stage. As such, we simplify the workflow of NAS to a one-stage and proxy-free procedure. Experiments show that the architectures searched by the proposed framework achieve state-of-the-art accuracy on CIFAR-10, CIFAR-100, and ImageNet datasets without using manual labels. Moreover, we show that employing the concomitant weights as initialization consistently outperforms the random initialization and the two-stage weight pre-training method by a clear margin under semi-supervised learning scenarios. Codes are publicly available at https://github.com/LzVv123456/SSWP-NAS.

cs.CV↗