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Han Feng

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math.FA Machine Learning Computer Vision math.CA Artificial Intelligence eess.SP math.PR physics.ins-det physics.soc-ph q-fin.EC q-fin.PM

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preprint2026arXiv

CRAFT: Clinical Reward-Aligned Finetuning for Medical Image Synthesis

Foundation diffusion models can generate photorealistic natural images, but adapting them to medical imaging remains challenging. In medical adaptation, limited labeled data can exacerbate hallucination-like and clinically implausible synthesis, while existing metrics such as FID or Inception Score do not quantify per-image alignment with pathology-relevant criteria. We introduce the Clinical Alignment Score (CAS), a foundation-model-based proxy for clinical alignment that evaluates generated images along four complementary dimensions beyond visual fidelity. Building on CAS, we propose Clinical Reward-Aligned Finetuning (CRAFT), a reward-based adaptation framework that transfers medical knowledge from multimodal large language models and vision-language models through label-conditioned prompt enrichment, clinical checklists, and differentiable reward optimization. Across four diverse modalities, CRAFT improves CAS and downstream classification performance over strong adaptation baselines. Beyond average CAS gains, CRAFT reduces the empirical low-alignment tail below a real-image reference threshold by 5.5-34.7% points relative to the strongest baseline, corresponding to a 20.4% average relative reduction across datasets. These results indicate fewer hallucination-like generations under CAS, and are corroborated by out-of-family evaluator evaluation, structured checklist auditing, memorization analysis, and a blinded physician preference study on CheXpert.

preprint2024arXiv

Approximation analysis of CNNs from a feature extraction view

Deep learning based on deep neural networks has been very successful in many practical applications, but it lacks enough theoretical understanding due to the network architectures and structures. In this paper we establish some analysis for linear feature extraction by a deep multi-channel convolutional neural networks (CNNs), which demonstrates the power of deep learning over traditional linear transformations, like Fourier, wavelets, redundant dictionary coding methods. Moreover, we give an exact construction presenting how linear features extraction can be conducted efficiently with multi-channel CNNs. It can be applied to lower the essential dimension for approximating a high dimensional function. Rates of function approximation by such deep networks implemented with channels and followed by fully-connected layers are investigated as well. Harmonic analysis for factorizing linear features into multi-resolution convolutions plays an essential role in our work. Nevertheless, a dedicate vectorization of matrices is constructed, which bridges 1D CNN and 2D CNN and allows us to have corresponding 2D analysis.

preprint2022arXiv

Convolutional Neural Networks for Spherical Signal Processing via Spherical Haar Tight Framelets

In this paper, we develop a general theoretical framework for constructing Haar-type tight framelets on any compact set with a hierarchical partition. In particular, we construct a novel area-regular hierarchical partition on the 2-sphere and establish its corresponding spherical Haar tight framelets with directionality. We conclude by evaluating and illustrating the effectiveness of our area-regular spherical Haar tight framelets in several denoising experiments. Furthermore, we propose a convolutional neural network (CNN) model for spherical signal denoising which employs the fast framelet decomposition and reconstruction algorithms. Experiment results show that our proposed CNN model outperforms threshold methods, and processes strong generalization and robustness properties.

preprint2021arXiv

First Application of Large Reactivity Measurement through Rod Drop Based on Three-Dimensional Space-Time Dynamics

Reactivity measurement is an essential part of a zero-power physics test, which is critical to reactor design and development. The rod drop experimental technique is used to measure the control rod worth in a zero-power physics test. The conventional rod drop experimental technique is limited by the spatial effect and the difference between the calculated static reactivity and measured dynamic reactivity; thus, the method must be improved. In this study, a modified rod drop experimental technique that constrains the detector neutron flux shape function based on three-dimensional space-time dynamics to reduce the reactivity perturbation and a new method for calculating the detector neutron flux shape function are proposed. Correction factors were determined using Monte Carlo N-Particle transport code and transient analysis code for a pressurized water reactor at the Ulsan National Institute of Science and Technology and Xi'an Jiaotong University, and a large reactivity of over 2000 pcm was measured using the modified technique. This research evaluated the modified technique accuracy, studied the influence of the correction factors on the modification, and investigated the effect of constraining the shape function on the reactivity perturbation reduction caused by the difference between the calculated neutron flux and true value, using the new method to calculate the shape function of the detector neutron flux and avoiding the neutron detector response function (weighting factor) calculation.

preprint2020arXiv

Mathematical Modeling of Business Reopening when Facing SARS-CoV-2 Pandemic: Protection, Cost and Risk

The sudden onset of the coronavirus (SARS-CoV-2) pandemic has resulted in tremendous loss of human life and economy in more than 210 countries and territories around the world. While self-protections such as wearing mask, sheltering in place and quarantine polices and strategies are necessary for containing virus transmission, tens of millions people in the U.S. have lost their jobs due to the shutdown of businesses. Therefore, how to reopen the economy safely while the virus is still circulating in population has become a problem of significant concern and importance to elected leaders and business executives. In this study, mathematical modeling is employed to quantify the profit generation and the infection risk simultaneously from the point of view of a business entity. Specifically, an ordinary differential equation model was developed to characterize disease transmission and infection risk. An algebraic equation is proposed to determine the net profit that a business entity can generate after reopening and take into account the costs associated of several protection/quarantine guidelines. All model parameters were calibrated based on various data and information sources. Sensitivity analyses and case studies were performed to illustrate the use of the model in practice.

preprint2020arXiv

Theory of Deep Convolutional Neural Networks II: Spherical Analysis

Deep learning based on deep neural networks of various structures and architectures has been powerful in many practical applications, but it lacks enough theoretical verifications. In this paper, we consider a family of deep convolutional neural networks applied to approximate functions on the unit sphere $\mathbb{S}^{d-1}$ of $\mathbb{R}^d$. Our analysis presents rates of uniform approximation when the approximated function lies in the Sobolev space $W^r_\infty (\mathbb{S}^{d-1})$ with $r>0$ or takes an additive ridge form. Our work verifies theoretically the modelling and approximation ability of deep convolutional neural networks followed by downsampling and one fully connected layer or two. The key idea of our spherical analysis is to use the inner product form of the reproducing kernels of the spaces of spherical harmonics and then to apply convolutional factorizations of filters to realize the generated linear features.

preprint2016arXiv

Gambling in contests with random initial law

This paper studies a variant of the contest model introduced in Seel and Strack [J. Econom. Theory 148 (2013) 2033-2048]. In the Seel-Strack contest, each agent or contestant privately observes a Brownian motion, absorbed at zero, and chooses when to stop it. The winner of the contest is the agent who stops at the highest value. The model assumes that all the processes start from a common value $x_0>0$ and the symmetric Nash equilibrium is for each agent to utilise a stopping rule which yields a randomised value for the stopped process. In the two-player contest, this randomised value has a uniform distribution on $[0,2x_0]$. In this paper, we consider a variant of the problem whereby the starting values of the Brownian motions are independent, nonnegative random variables that have a common law $μ$. We consider a two-player contest and prove the existence and uniqueness of a symmetric Nash equilibrium for the problem. The solution is that each agent should aim for the target law $ν$, where $ν$ is greater than or equal to $μ$ in convex order; $ν$ has an atom at zero of the same size as any atom of $μ$ at zero, and otherwise is atom free; on $(0,\infty)$ $ν$ has a decreasing density; and the density of $ν$ only decreases at points where the convex order constraint is binding.

preprint2015arXiv

Uncertainty Principles on weighted spheres, balls and simplexes

This paper studies the uncertainty principle for spherical $h$-harmonic expansions on the unit sphere of $\mathbb{R}^d$ associated with a weight function invariant under a general finite reflection group, which is in full analogy with the classical Heisenberg inequality. Our proof is motivated by a new decomposition of the Dunkl-Laplace-Beltrami operator on the weighted sphere.

preprint2014arXiv

Reverse Hölder's inequality for spherical harmonics

This paper determines the sharp asymptotic order of the following reverse Hölder inequality for spherical harmonics $Y_n$ of degree $n$ on the unit sphere $\mathbb{S}^{d-1}$ of $\mathbb{R}^d$ as $n\to \infty$: \[\|Y_n\|_{L^q(\mathbb{S}^{d-1})}\leq C n^{α(p,q)}\|Y_n\|_{L^p(\mathbb{S}^{d-1})},\quad 0<p<q\leq \infty.\] In many cases, these sharp estimates turn out to be significantly better than the corresponding estimates in the Nilkolskii inequality for spherical polynomials. Furthermore, they allow us to improve two recent results on the restriction conjecture and the sharp Pitt inequalities for the Fourier transform on $\mathbb{R}^d$.

preprint2013arXiv

Gambling in contests with regret

This paper discusses the gambling contest introduced in Seel & Strack (Gambling in contests, Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems 375, Mar 2012.) and considers the impact of adding a penalty associated with failure to follow a winning strategy. The Seel & Strack model consists of $n$-agents each of whom privately observes a transient diffusion process and chooses when to stop it. The player with the highest stopped value wins the contest, and each player's objective is to maximise their probability of winning the contest. We give a new derivation of the results of Seel & Strack based on a Lagrangian approach. Moreover, we consider an extension of the problem in which in the case when an agent is penalised when their strategy is suboptimal, in the sense that they do not win the contest, but there existed an alternative strategy which would have resulted in victory.