Searcharxiv⌕ Search

arXiv subjects

Michael Werman

Publications and source records attributed to Michael Werman.

At least 19 recordsLinked to original sources
arXiv2026

COMPOSE: Composing Future Theorems from Citations and Formal Structure

A plausible future mathematical claim must satisfy two constraints: it should follow the direction of prior work and respect the formal dependencies that constrain what can validly follow. Existing approaches typically model only one of these sources, producing claims that are either weakly grounded or insufficiently motivated. We introduce grounded future mathematical generation, where the goal is to generate a plausible future theorem-like claim for an anchor paper using two complementary sources of context: its scientific citation graph and aligned formal theorem dependency graph. To address this setting, we propose COMPOSE, a dual-graph framework that conditions a language model on both scientific citation context and formal theorem structure. To support this setting, we construct a dataset of 108K paired scientific-formal graph examples from arXiv and Mathlib, together with a benchmark of 47K future papers from 2024--2025. Experiments show that COMPOSE outperforms strong baselines on retrieval to real future papers and achieves the best overall performance under LLM-judge evaluation, producing more grounded and mathematically richer outputs. These results show that future mathematical generation benefits from combining scientific context with formal structure. Project page is available at https://david-busbib.github.io/COMPOSE-page/.

cs.CL↗
arXiv2026

Neural Global Optimization via Iterative Refinement from Noisy Samples

Global optimization of black-box functions from noisy samples is a fundamental challenge in machine learning and scientific computing. Traditional methods such as Bayesian Optimization often converge to local minima on multi-modal functions, while gradient-free methods require many function evaluations. We present a novel neural approach that learns to find global minima through iterative refinement. Our model takes noisy function samples and their fitted spline representation as input, then iteratively refines an initial guess toward the true global minimum. Trained on randomly generated functions with ground truth global minima obtained via exhaustive search, our method achieves a mean error of 8.05 percent on challenging multi-modal test functions, compared to 36.24 percent for the spline initialization, a 28.18 percent improvement. The model successfully finds global minima in 72 percent of test cases with error below 10 percent, demonstrating learned optimization principles rather than mere curve fitting. Our architecture combines encoding of multiple modalities including function values, derivatives, and spline coefficients with iterative position updates, enabling robust global optimization without requiring derivative information or multiple restarts.

cs.LG↗
arXiv2025

Exponential Convergence of Deep Composite Polynomial Approximation for Cusp-Type Functions

We investigate deep composite polynomial approximations of continuous but non-differentiable functions with algebraic cusp singularities. The functions in focus consist of finitely many cusp terms of the form $|x-a_j|^{\alpha_j}$ with rational exponents $\alpha_j\in(0,1)$ on a real-analytic background. We propose a constructive approximation scheme that combines a division-free polynomial iteration for fractional powers with an outer layer for the analytic polynomial fitting. Our main result shows that this composite structure achieves exponential convergence in the the number of scalar coefficients in the inner and outer polynomial layers. Specifically, the $L^p([-1,1])$ approximation error, decays exponentially with respect to the parameter budget, in contrast to the algebraic rates obtained by classical single-layer polynomial approximation for cusp-type functions. Numerical experiments for both single and multiple cusp configurations confirm the theoretical rates and demonstrate the parameter efficiency of deep composite polynomial constructions.

math.NA↗
arXiv2025

CanonNet: Canonical Ordering and Curvature Learning for Point Cloud Analysis

Point cloud processing poses two fundamental challenges: establishing consistent point ordering and effectively learning fine-grained geometric features. Current architectures rely on complex operations that limit expressivity while struggling to capture detailed surface geometry. We present CanonNet, a lightweight neural network composed of two complementary components: (1) a preprocessing pipeline that creates a canonical point ordering and orientation, and (2) a geometric learning framework where networks learn from synthetic surfaces with precise curvature values. This modular approach eliminates the need for complex transformation-invariant architectures while effectively capturing local geometric properties. Our experiments demonstrate state-of-the-art performance in curvature estimation and competitive results in geometric descriptor tasks with significantly fewer parameters (\textbf{100X}) than comparable methods. CanonNet's efficiency makes it particularly suitable for real-world applications where computational resources are limited, demonstrating that mathematical preprocessing can effectively complement neural architectures for point cloud analysis. The code for the project is publicly available \hyperlink{https://benjyfri.github.io/CanonNet/}{https://benjyfri.github.io/CanonNet/}.

cs.CV↗
arXiv2024

The Fibonacci Network: A Simple Alternative for Positional Encoding

Coordinate-based Multi-Layer Perceptrons (MLPs) are known to have difficulty reconstructing high frequencies of the training data. A common solution to this problem is Positional Encoding (PE), which has become quite popular. However, PE has drawbacks. It has high-frequency artifacts and adds another hyper-hyperparameter, just like batch normalization and dropout do. We believe that under certain circumstances PE is not necessary, and a smarter construction of the network architecture together with a smart training method is sufficient to achieve similar results. In this paper, we show that very simple MLPs can quite easily output a frequency when given input of the half-frequency and quarter-frequency. Using this, we design a network architecture in blocks, where the input to each block is the output of the two previous blocks along with the original input. We call this a {\it Fibonacci Network}. By training each block on the corresponding frequencies of the signal, we show that Fibonacci Networks can reconstruct arbitrarily high frequencies.

cs.LG↗
arXiv2024

Camera Calibration and Stereo via a Single Image of a Spherical Mirror

This paper presents a novel technique for camera calibration using a single view that incorporates a spherical mirror. Leveraging the distinct characteristics of the sphere's contour visible in the image and its reflections, we showcase the effectiveness of our method in achieving precise calibration. Furthermore, the reflection from the mirrored surface provides additional information about the surrounding scene beyond the image frame. Our method paves the way for the development of simple catadioptric stereo systems. We explore the challenges and opportunities associated with employing a single mirrored sphere, highlighting the potential applications of this setup in practical scenarios. The paper delves into the intricacies of the geometry and calibration procedures involved in catadioptric stereo utilizing a spherical mirror. Experimental results, encompassing both synthetic and real-world data, are presented to illustrate the feasibility and accuracy of our approach.

cs.CV↗
arXiv2023

Beyond the Benchmark: Detecting Diverse Anomalies in Videos

Video Anomaly Detection (VAD) plays a crucial role in modern surveillance systems, aiming to identify various anomalies in real-world situations. However, current benchmark datasets predominantly emphasize simple, single-frame anomalies such as novel object detection. This narrow focus restricts the advancement of VAD models. In this research, we advocate for an expansion of VAD investigations to encompass intricate anomalies that extend beyond conventional benchmark boundaries. To facilitate this, we introduce two datasets, HMDB-AD and HMDB-Violence, to challenge models with diverse action-based anomalies. These datasets are derived from the HMDB51 action recognition dataset. We further present Multi-Frame Anomaly Detection (MFAD), a novel method built upon the AI-VAD framework. AI-VAD utilizes single-frame features such as pose estimation and deep image encoding, and two-frame features such as object velocity. They then apply a density estimation algorithm to compute anomaly scores. To address complex multi-frame anomalies, we add a deep video encoding features capturing long-range temporal dependencies, and logistic regression to enhance final score calculation. Experimental results confirm our assumptions, highlighting existing models limitations with new anomaly types. MFAD excels in both simple and complex anomaly detection scenarios.

cs.CV↗
arXiv2023

Robust affine point matching via quadratic assignment on Grassmannians

Robust Affine Matching with Grassmannians (RoAM) is a new algorithm to perform affine registration of point clouds. The algorithm is based on minimizing the Frobenius distance between two elements of the Grassmannian. For this purpose, an indefinite relaxation of the Quadratic Assignment Problem (QAP) is used, and several approaches to affine feature matching are studied and compared. Experiments demonstrate that RoAM is more robust to noise and point discrepancy than previous methods.

cs.CV↗
arXiv2022

An approach to robust ICP initialization

In this note, we propose an approach to initialize the Iterative Closest Point (ICP) algorithm to match unlabelled point clouds related by rigid transformations. The method is based on matching the ellipsoids defined by the points' covariance matrices and then testing the various principal half-axes matchings that differ by elements of a finite reflection group. We derive bounds on the robustness of our approach to noise and numerical experiments confirm our theoretical findings.

cs.CV↗
arXiv2022

DecisioNet: A Binary-Tree Structured Neural Network

Deep neural networks (DNNs) and decision trees (DTs) are both state-of-the-art classifiers. DNNs perform well due to their representational learning capabilities, while DTs are computationally efficient as they perform inference along one route (root-to-leaf) that is dependent on the input data. In this paper, we present DecisioNet (DN), a binary-tree structured neural network. We propose a systematic way to convert an existing DNN into a DN to create a lightweight version of the original model. DecisioNet takes the best of both worlds - it uses neural modules to perform representational learning and utilizes its tree structure to perform only a portion of the computations. We evaluate various DN architectures, along with their corresponding baseline models on the FashionMNIST, CIFAR10, and CIFAR100 datasets. We show that the DN variants achieve similar accuracy while significantly reducing the computational cost of the original network.

cs.CV↗
arXiv2022

On best uniform approximation of finite sets by linear combinations of real valued functions using linear programming

We study the best approximation problem: \[ \displaystyle \min_{\alpha\in \mathbb R^m}\max_{1\leq i\leq n}\left|y_i -\sum_{j=1}^m \alpha_j \Gamma_j ({\bf x}_i) \right|. \] Here: $\Gamma:=\left\{\Gamma_1,...,\Gamma_m\right\}$ is a list of functions where for each $1\leq j\leq m$, $\Gamma_j:\Delta \rightarrow \mathbb R$ with $\Delta$ a set of evaluation points $\left\{{\bf x_1},...,{\bf x_n}\right\}$. $\left\{y_1,...,y_n\right\}$ is a set of real values and $\mathbb R^m:=\left\{(\alpha_1,...,\alpha_m),\, \alpha_j\in \mathbb R,\, 1\leq j\leq m\right\}$.

math.OC↗
arXiv2022

Fully Convolutional Fractional Scaling

We introduce a fully convolutional fractional scaling component, FCFS. Fully convolutional networks can be applied to any size input and previously did not support non-integer scaling. Our architecture is simple with an efficient single layer implementation. Examples and code implementations of three common scaling methods are published.

cs.NE↗
arXiv2020

Using a Supervised Method without supervision for foreground segmentation

Neural networks are a powerful framework for foreground segmentation in video acquired by static cameras, segmenting moving objects from the background in a robust way in various challenging scenarios. The premier methods are those based on supervision requiring a final training stage on a database of tens to hundreds of manually segmented images from the specific static camera. In this work, we propose a method to automatically create an "artificial" database that is sufficient for training the supervised methods so that it performs better than current unsupervised methods. It is based on combining a weak foreground segmenter, compared to the supervised method, to extract suitable objects from the training images and randomly inserting these objects back into a background image. Test results are shown on the test sequences in CDnet.

cs.CV↗
arXiv2019

Cameras Viewing Cameras Geometry

A basic problem in computer vision is to understand the structure of a real-world scene given several images of it. Here we study several theoretical aspects of the intra multi-view geometry of calibrated cameras when all that they can reliably recognize is each other. With the proliferation of wearable cameras, autonomous vehicles and drones, the geometry of these multiple cameras is a timely and relevant problem to study.

cs.CV↗
arXiv2019

Clear Skies Ahead: Towards Real-Time Automatic Sky Replacement in Video

Digital videos such as those captured by a smartphone often exhibit exposure inconsistencies, a poorly exposed sky, or simply suffer from an uninteresting or plain looking sky. Professionals may edit these videos using advanced and time-consuming tools unavailable to most users, to replace the sky with a more expressive or imaginative sky. In this work, we propose an algorithm for automatic replacement of the sky region in a video with a different sky, providing nonprofessional users with a simple yet efficient tool to seamlessly replace the sky. The method is fast, achieving close to real-time performance on mobile devices and the user's involvement can remain as limited as simply selecting the replacement sky.

cs.CV↗
arXiv2018

Detection of distal radius fractures trained by a small set of X-ray images and Faster R-CNN

Distal radius fractures are the most common fractures of the upper extremity in humans. As such, they account for a significant portion of the injuries that present to emergency rooms and clinics throughout the world. We trained a Faster R-CNN, a machine vision neural network for object detection, to identify and locate distal radius fractures in anteroposterior X-ray images. We achieved an accuracy of 96\% in identifying fractures and mean Average Precision, mAP, of 0.866. This is significantly more accurate than the detection achieved by physicians and radiologists. These results were obtained by training the deep learning network with only 38 original images of anteroposterior hands X-ray images with fractures. This opens the possibility to detect with this type of neural network rare diseases or rare symptoms of common diseases , where only a small set of diagnosed X-ray images could be collected for each disease.

cs.CV↗
arXiv2018

On Min-Max affine approximants of convex or concave real valued functions from $\mathbb R^k$, Chebyshev equioscillation and graphics

We study Min-Max affine approximants of a continuous convex or concave function $f:\Delta\subset \mathbb R^k\xrightarrow{} \mathbb R$ where $\Delta$ is a convex compact subset of $\mathbb R^k$. In the case when $\Delta$ is a simplex we prove that there is a vertical translate of the supporting hyperplane in $\mathbb R^{k+1}$ of the graph of $f$ at the vertices which is the unique best affine approximant to $f$ on $\Delta$. For $k=1$, this result provides an extension of the Chebyshev equioscillation theorem for linear approximants. Our result has interesting connections to the computer graphics problem of rapid rendering of projective transformations.

math.OC↗