arXiv subjects

Sixin Zhang

Publications and source records attributed to Sixin Zhang.

At least 19 recordsLinked to original sources

arXiv2026

SeqGPT: A Constrained Transformer Agent for the Inverse Design of Multi-Panel Composite Structures

Optimizing composite stacking sequences to match continuous targets (e.g., Lamination or Buckling Parameters) with discrete manufacturing constraints represents a challenging combinatorial inverse problem that regularly occurs in composite design especially when numerical optimization approaches are used (bi-step, bi-level configurations). In multipanel configurations, this complexity is further intensified by blending, a global compatibility/continuity requirement between the different panel stackings. This study presents SeqGPT, a conditional Transformer agent developed to replace computationally expensive iterative methods. To ensure both global continuity and manufacturing feasibility by construction, we implemented a hybrid neurosymbolic decoding strategy. SeqGPT predicts a conditional distribution that guides a Constrained Beam Search, where any branch violating blending rules is strictly pruned. Numerical experiments on the 18-panel horseshoe benchmark demonstrate that SeqGPT generates solutions near-instantaneously with buckling performance comparable to evolutionary methods, offering a significant speed-up compared to the state of the art.

cs.NE↗

arXiv2026

Lipschitz bounds for integral kernels

Feature maps associated with positive definite kernels play a central role in kernel methods and learning theory, where regularity properties such as Lipschitz continuity are closely related to robustness and stability guarantees. Despite their importance, explicit characterizations of the Lipschitz constant of kernel feature maps are available only in a limited number of cases. In this paper, we study the Lipschitz regularity of feature maps associated with integral kernels under differentiability assumptions. We first provide sufficient conditions ensuring Lipschitz continuity and derive explicit formulas for the corresponding Lipschitz constants. We then identify a condition under which the feature map fails to be Lipschitz continuous and apply these results to several important classes of kernels. For infinite width two-layer neural network with isotropic Gaussian weight distributions, we show that the Lipschitz constant of the associated kernel can be expressed as the supremum of a two-dimensional integral, leading to an explicit characterization for the Gaussian kernel and the ReLU random neural network kernel. We also study continuous and shift-invariant kernels such as Gaussian, Laplace, and Matérn kernels, which admit an interpretation as neural network with cosine activation function. In this setting, we prove that the feature map is Lipschitz continuous if and only if the weight distribution has a finite second-order moment, and we then derive its Lipschitz constant. Finally, we raise an open question concerning the asymptotic behavior of the convergence of the Lipschitz constant in finite width neural networks. Numerical experiments are provided to support this behavior.

stat.ML↗

arXiv2026

Feature Representation Transferring to Lightweight Models via Perception Coherence

In this paper, we propose a method for transferring feature representation to lightweight student models from larger teacher models. We mathematically define a new notion called \textit{perception coherence}. Based on this notion, we propose a loss function, which takes into account the dissimilarities between data points in feature space through their ranking. At a high level, by minimizing this loss function, the student model learns to mimic how the teacher model \textit{perceives} inputs. More precisely, our method is motivated by the fact that the representational capacity of the student model is weaker than the teacher model. Hence, we aim to develop a new method allowing for a better relaxation. This means that, the student model does not need to preserve the absolute geometry of the teacher one, while preserving global coherence through dissimilarity ranking. Importantly, while rankings are defined only on finite sets, our notion of \textit{perception coherence} extends them into a probabilistic form. This formulation depends on the input distribution and applies to general dissimilarity metrics. Our theoretical insights provide a probabilistic perspective on the process of feature representation transfer. Our experiments results show that our method outperforms or achieves on-par performance compared to strong baseline methods for representation transferring.

stat.ML↗

arXiv2026

Training More Robust Classification Model via Discriminative Loss and Gaussian Noise Injection

Robustness of deep neural networks to input noise remains a critical challenge, as naive noise injection often degrades accuracy on clean (uncorrupted) data. We propose a novel training framework that addresses this trade-off through two complementary objectives. First, we introduce a loss function applied at the penultimate layer that explicitly enforces intra-class compactness and increases the margin to analytically defined decision boundaries. This enhances feature discriminativeness and class separability for clean data. Second, we propose a class-wise feature alignment mechanism that brings noisy data clusters closer to their clean counterparts. Furthermore, we provide a theoretical analysis demonstrating that improving feature stability under additive Gaussian noise implicitly reduces the curvature of the softmax loss landscape in input space, as measured by Hessian eigenvalues.This thus naturally enhances robustness without explicit curvature penalties. Conversely, we also theoretically show that lower curvatures lead to more robust models. We validate the effectiveness of our method on standard benchmarks and our custom dataset. Our approach significantly reinforces model robustness to various perturbations while maintaining high accuracy on clean data, advancing the understanding and practice of noise-robust deep learning.

stat.ML↗

arXiv2025

LSAM: Asynchronous Distributed Training with Landscape-Smoothed Sharpness-Aware Minimization

While Sharpness-Aware Minimization (SAM) improves generalization in deep neural networks by minimizing both loss and sharpness, it suffers from inefficiency in distributed large-batch training. We present Landscape-Smoothed SAM (LSAM), a novel optimizer that preserves SAM's generalization advantages while offering superior efficiency. LSAM integrates SAM's adversarial steps with an asynchronous distributed sampling strategy, generating an asynchronous distributed sampling scheme, producing a smoothed sharpness-aware loss landscape for optimization. This design eliminates synchronization bottlenecks, accelerates large-batch convergence, and delivers higher final accuracy compared to data-parallel SAM.

cs.LG↗

arXiv2025

Convolutional Rectangular Attention Module

In this paper, we introduce a novel spatial attention module that can be easily integrated to any convolutional network. This module guides the model to pay attention to the most discriminative part of an image. This enables the model to attain a better performance by an end-to-end training. In conventional approaches, a spatial attention map is typically generated in a position-wise manner. Thus, it is often resulting in irregular boundaries and so can hamper generalization to new samples. In our method, the attention region is constrained to be rectangular. This rectangle is parametrized by only 5 parameters, allowing for a better stability and generalization to new samples. In our experiments, our method systematically outperforms the position-wise counterpart. So that, we provide a novel useful spatial attention mechanism for convolutional models. Besides, our module also provides the interpretability regarding the \textit{where to look} question, as it helps to know the part of the input on which the model focuses to produce the prediction.

cs.CV↗

arXiv2025

Local convergence of simultaneous min-max algorithms to differential equilibrium on Riemannian manifold

We study min-max algorithms to solve zero-sum differential games on Riemannian manifold. Based on the notions of differential Stackelberg equilibrium and differential Nash equilibrium on Riemannian manifold, we analyze the local convergence of two representative deterministic simultaneous algorithms $τ$-GDA and $τ$-SGA to such equilibria. Sufficient conditions are obtained to establish the linear convergence rate of $τ$-GDA based on the Ostrowski theorem on manifold and spectral analysis. To avoid strong rotational dynamics in $τ$-GDA, $τ$-SGA is extended from the symplectic gradient-adjustment method in Euclidean space. We analyze an asymptotic approximation of $τ$-SGA when the learning rate ratio $τ$ is big. In some cases, it can achieve a faster convergence rate to differential Stackelberg equilibrium compared to $τ$-GDA. We show numerically how the insights obtained from the convergence analysis may improve the training of orthogonal Wasserstein GANs using stochastic $τ$-GDA and $τ$-SGA on simple benchmarks.

cs.LG↗

arXiv2024

CNN-based Compressor Mass Flow Estimator in Industrial Aircraft Vapor Cycle System

In Vapor Cycle Systems, the mass flow sensor playsa key role for different monitoring and control purposes. However,physical sensors can be inaccurate, heavy, cumbersome, expensive orhighly sensitive to vibrations, which is especially problematic whenembedded into an aircraft. The conception of a virtual sensor, basedon other standard sensors, is a good alternative. This paper has twomain objectives. Firstly, a data-driven model using a ConvolutionalNeural Network is proposed to estimate the mass flow of thecompressor. We show that it significantly outperforms the standardPolynomial Regression model (thermodynamic maps), in terms of thestandard MSE metric and Engineer Performance metrics. Secondly,a semi-automatic segmentation method is proposed to compute theEngineer Performance metrics for real datasets, as the standard MSEmetric may pose risks in analyzing the dynamic behavior of VaporCycle Systems.

eess.SY↗

arXiv2024

Combining Statistical Depth and Fermat Distance for Uncertainty Quantification

We measure the Out-of-domain uncertainty in the prediction of Neural Networks using a statistical notion called ``Lens Depth'' (LD) combined with Fermat Distance, which is able to capture precisely the ``depth'' of a point with respect to a distribution in feature space, without any assumption about the form of distribution. Our method has no trainable parameter. The method is applicable to any classification model as it is applied directly in feature space at test time and does not intervene in training process. As such, it does not impact the performance of the original model. The proposed method gives excellent qualitative result on toy datasets and can give competitive or better uncertainty estimation on standard deep learning datasets compared to strong baseline methods.

stat.ML↗

arXiv2023

Data Assimilation Networks

Data assimilation (DA) aims at forecasting the state of a dynamical system by combining a mathematical representation of the system with noisy observations taking into account their uncertainties. State of the art methods are based on the Gaussian error statistics and the linearization of the non-linear dynamics which may lead to sub-optimal methods. In this respect, there are still open questions how to improve these methods. In this paper, we propose a fully data driven deep learning architecture generalizing recurrent Elman networks and data assimilation algorithms which approximate a sequence of prior and posterior densities conditioned on noisy observations. By construction our approach can be used for general nonlinear dynamics and non-Gaussian densities. On numerical experiments based on the well-known Lorenz-95 system and with Gaussian error statistics, our architecture achieves comparable performance to EnKF on both the analysis and the propagation of probability density functions of the system state at a given time without using any explicit regularization technique.

cs.LG↗

arXiv2022

Leveraging Joint-Diagonalization in Transform-Learning NMF

Non-negative matrix factorization with transform learning (TL-NMF) is a recent idea that aims at learning data representations suited to NMF. In this work, we relate TL-NMF to the classical matrix joint-diagonalization (JD) problem. We show that, when the number of data realizations is sufficiently large, TL-NMF can be replaced by a two-step approach -- termed as JD+NMF -- that estimates the transform through JD, prior to NMF computation. In contrast, we found that when the number of data realizations is limited, not only is JD+NMF no longer equivalent to TL-NMF, but the inherent low-rank constraint of TL-NMF turns out to be an essential ingredient to learn meaningful transforms for NMF.

cs.LG↗

arXiv2022

Particle gradient descent model for point process generation

This paper presents a statistical model for stationary ergodic point processes, estimated from a single realization observed in a square window. With existing approaches in stochastic geometry, it is very difficult to model processes with complex geometries formed by a large number of particles. Inspired by recent works on gradient descent algorithms for sampling maximum-entropy models, we describe a model that allows for fast sampling of new configurations reproducing the statistics of the given observation. Starting from an initial random configuration, its particles are moved according to the gradient of an energy, in order to match a set of prescribed moments (functionals). Our moments are defined via a phase harmonic operator on the wavelet transform of point patterns. They allow one to capture multi-scale interactions between the particles, while controlling explicitly the number of moments by the scales of the structures to model. We present numerical experiments on point processes with various geometric structures, and assess the quality of the model by spectral and topological data analysis.

stat.ML↗

arXiv2022

On the Nash equilibrium of moment-matching GANs for stationary Gaussian processes

Generative Adversarial Networks (GANs) learn an implicit generative model from data samples through a two-player game. In this paper, we study the existence of Nash equilibrium of the game which is consistent as the number of data samples grows to infinity. In a realizable setting where the goal is to estimate the ground-truth generator of a stationary Gaussian process, we show that the existence of consistent Nash equilibrium depends crucially on the choice of the discriminator family. The discriminator defined from second-order statistical moments can result in non-existence of Nash equilibrium, existence of consistent non-Nash equilibrium, or existence and uniqueness of consistent Nash equilibrium, depending on whether symmetry properties of the generator family are respected. We further study empirically the local stability and global convergence of gradient descent-ascent methods towards consistent equilibrium.

stat.ML↗

arXiv2022

Generative Models of Multi-channel Data from a Single Example -- Application to Dust Emission

The quest for primordial $B$-modes in the cosmic microwave background has emphasized the need for refined models of the Galactic dust foreground. Here, we aim at building a realistic statistical model of the multi-frequency dust emission from a single example. We introduce a generic methodology relying on microcanonical gradient descent models conditioned by an extended family of wavelet phase harmonic (WPH) statistics. To tackle the multi-channel aspect of the data, we define cross-WPH statistics, quantifying non-Gaussian correlations between maps. Our data-driven methodology could apply to various contexts, and we have updated the software PyWPH, on which this work relies, accordingly. Applying this to dust emission maps built from a magnetohydrodynamics simulation, we construct and assess two generative models of: 1) a $(I, E, B)$ multi-observable input, 2) a $\{I_ν\}_ν$ multi-frequency input. The samples exhibit consistent features compared to the original maps. A statistical analysis of 1) shows that the power spectra, distributions of pixels, and Minkowski functionals are captured to a good extent. We analyze 2) by fitting the spectral energy distribution (SED) of both the synthetic and original maps with a modified blackbody (MBB) law. The maps are equally well fitted, and a comparison of the MBB parameters shows that our model succeeds in capturing the spatial variations of the SED from the data. Besides the perspectives of this work for dust emission modeling, the introduction of cross-WPH statistics opens a new avenue to characterize non-Gaussian interactions across different maps, which we believe will be fruitful for astrophysics.

astro-ph.CO↗

arXiv2022

Kymatio: Scattering Transforms in Python

The wavelet scattering transform is an invariant signal representation suitable for many signal processing and machine learning applications. We present the Kymatio software package, an easy-to-use, high-performance Python implementation of the scattering transform in 1D, 2D, and 3D that is compatible with modern deep learning frameworks. All transforms may be executed on a GPU (in addition to CPU), offering a considerable speed up over CPU implementations. The package also has a small memory footprint, resulting inefficient memory usage. The source code, documentation, and examples are available undera BSD license at https://www.kymat.io/

cs.LG↗

arXiv2022

Generalized Rectifier Wavelet Covariance Models For Texture Synthesis

State-of-the-art maximum entropy models for texture synthesis are built from statistics relying on image representations defined by convolutional neural networks (CNN). Such representations capture rich structures in texture images, outperforming wavelet-based representations in this regard. However, conversely to neural networks, wavelets offer meaningful representations, as they are known to detect structures at multiple scales (e.g. edges) in images. In this work, we propose a family of statistics built upon non-linear wavelet based representations, that can be viewed as a particular instance of a one-layer CNN, using a generalized rectifier non-linearity. These statistics significantly improve the visual quality of previous classical wavelet-based models, and allow one to produce syntheses of similar quality to state-of-the-art models, on both gray-scale and color textures.

cs.CV↗

arXiv2021

Maximum Entropy Models from Phase Harmonic Covariances

The covariance of a stationary process $X$ is diagonalized by a Fourier transform. It does not take into account the complex Fourier phase and defines Gaussian maximum entropy models. We introduce a general family of phase harmonic covariance moments, which rely on complex phases to capture non-Gaussian properties. They are defined as the covariance of $\hat{H} (L X)$, where $L$ is a complex linear operator and $\hat{H} $ is a non-linear phase harmonic operator which multiplies the phase of each complex coefficient by integers. The operator $\hat{H} (L X)$ can also be calculated from rectifiers, which relates $\hat{H} (L X)$ to neural network coefficients. If $L$ is a Fourier transform then the covariance is a sparse matrix whose non-zero off-diagonal coefficients capture dependencies between frequencies. These coefficients have similarities with high order moment, but smaller statistical variabilities because $\hat{H} (L X)$ is Lipschitz. If $L$ is a complex wavelet transform then off-diagonal coefficients reveal dependencies across scales, which specify the geometry of local coherent structures. We introduce maximum entropy models conditioned by these wavelet phase harmonic covariances. The precision of these models is numerically evaluated to synthesize images of turbulent flows and other stationary processes.

eess.SP↗

arXiv2019

Phase Harmonic Correlations and Convolutional Neural Networks

A major issue in harmonic analysis is to capture the phase dependence of frequency representations, which carries important signal properties. It seems that convolutional neural networks have found a way. Over time-series and images, convolutional networks often learn a first layer of filters which are well localized in the frequency domain, with different phases. We show that a rectifier then acts as a filter on the phase of the resulting coefficients. It computes signal descriptors which are local in space, frequency and phase. The non-linear phase filter becomes a multiplicative operator over phase harmonics computed with a Fourier transform along the phase. We prove that it defines a bi-Lipschitz and invertible representation. The correlations of phase harmonics coefficients characterise coherent structures from their phase dependence across frequencies. For wavelet filters, we show numerically that signals having sparse wavelet coefficients can be recovered from few phase harmonic correlations, which provide a compressive representation

eess.SP↗