arXiv subjects

Daniel Freedman

Publications and source records attributed to Daniel Freedman.

At least 19 recordsLinked to original sources

arXiv2026

Using Diffusion Models to Estimate Uncertainties in Analytic Continuation

Inverse problems are ubiquitous in physics, chemistry, and engineering, arising when reconstructing hidden quantities from indirect measurements. A key example is the analytic continuation of imaginary-time correlation functions (iTCFs) to the real-frequency domain. This process requires an inverse Laplace transform, which is inherently ill-posed and highly sensitive to small input variations. Recent neural network (NN)-based methods have shown promising results by learning mappings from imaginary-time to real-frequency spectra, often outperforming traditional techniques such as maximum entropy. However, because the problem is ill-posed, many spectra fit the same iTCF. Regression-based approaches output a single solution, which approximates an average over the true solution space, and therefore fail to capture the full distribution of plausible power spectra. To address this issue, we introduce a diffusion-based framework for analytic continuation that learns the distribution of spectra consistent with a given iTCF. It offers two key advantages. First, it quantifies uncertainty directly from the learned distribution. Second, by analyzing the spread and structure of this distribution, we can quantitatively assess the intrinsic hardness of each inversion problem. We measure this hardness with a new metric, the uncertainty pseudo-volume. Applying the framework to an iTCF from a path-integral molecular dynamics simulation of liquid parahydrogen, we obtain the self-diffusion coefficient with an error bar and flag a secondary high-frequency peak as a possible spurious artifact. In contrast to previous attempts at uncertainty quantification, our generative approach rests on a concrete probabilistic basis, providing a more theoretically grounded measure of confidence in the reconstructed power spectra.

physics.comp-ph↗

arXiv2025

SVD-NO: Learning PDE Solution Operators with SVD Integral Kernels

Neural operators have emerged as a promising paradigm for learning solution operators of partial differential equa- tions (PDEs) directly from data. Existing methods, such as those based on Fourier or graph techniques, make strong as- sumptions about the structure of the kernel integral opera- tor, assumptions which may limit expressivity. We present SVD-NO, a neural operator that explicitly parameterizes the kernel by its singular-value decomposition (SVD) and then carries out the integral directly in the low-rank basis. Two lightweight networks learn the left and right singular func- tions, a diagonal parameter matrix learns the singular values, and a Gram-matrix regularizer enforces orthonormality. As SVD-NO approximates the full kernel, it obtains a high de- gree of expressivity. Furthermore, due to its low-rank struc- ture the computational complexity of applying the operator remains reasonable, leading to a practical system. In exten- sive evaluations on five diverse benchmark equations, SVD- NO achieves a new state of the art. In particular, SVD-NO provides greater performance gains on PDEs whose solutions are highly spatially variable. The code of this work is publicly available at https://github.com/2noamk/SVDNO.git.

cs.LG↗

arXiv2025

Clinically Grounded Agent-based Report Evaluation: An Interpretable Metric for Radiology Report Generation

Radiological imaging is central to diagnosis, treatment planning, and clinical decision-making. Vision-language foundation models have spurred interest in automated radiology report generation (RRG), but safe deployment requires reliable clinical evaluation of generated reports. Existing metrics often rely on surface-level similarity or behave as black boxes, lacking interpretability. We introduce ICARE (Interpretable and Clinically-grounded Agent-based Report Evaluation), an interpretable evaluation framework leveraging large language model agents and dynamic multiple-choice question answering (MCQA). Two agents, each with either the ground-truth or generated report, generate clinically meaningful questions and quiz each other. Agreement on answers captures preservation and consistency of findings, serving as interpretable proxies for clinical precision and recall. By linking scores to question-answer pairs, ICARE enables transparent, and interpretable assessment. Clinician studies show ICARE aligns significantly more with expert judgment than prior metrics. Perturbation analyses confirm sensitivity to clinical content and reproducibility, while model comparisons reveal interpretable error patterns.

cs.CL↗

arXiv2024

ReHub: Linear Complexity Graph Transformers with Adaptive Hub-Spoke Reassignment

We present ReHub, a novel graph transformer architecture that achieves linear complexity through an efficient reassignment technique between nodes and virtual nodes. Graph transformers have become increasingly important in graph learning for their ability to utilize long-range node communication explicitly, addressing limitations such as oversmoothing and oversquashing found in message-passing graph networks. However, their dense attention mechanism scales quadratically with the number of nodes, limiting their applicability to large-scale graphs. ReHub draws inspiration from the airline industry's hub-and-spoke model, where flights are assigned to optimize operational efficiency. In our approach, graph nodes (spokes) are dynamically reassigned to a fixed number of virtual nodes (hubs) at each model layer. Recent work, Neural Atoms (Li et al., 2024), has demonstrated impressive and consistent improvements over GNN baselines by utilizing such virtual nodes; their findings suggest that the number of hubs strongly influences performance. However, increasing the number of hubs typically raises complexity, requiring a trade-off to maintain linear complexity. Our key insight is that each node only needs to interact with a small subset of hubs to achieve linear complexity, even when the total number of hubs is large. To leverage all hubs without incurring additional computational costs, we propose a simple yet effective adaptive reassignment technique based on hub-hub similarity scores, eliminating the need for expensive node-hub computations. Our experiments on LRGB indicate a consistent improvement in results over the base method, Neural Atoms, while maintaining a linear complexity. Remarkably, our sparse model achieves performance on par with its non-sparse counterpart. Furthermore, ReHub outperforms competitive baselines and consistently ranks among top performers across various benchmarks.

cs.LG↗

arXiv2024

Streamlining Conformal Information Retrieval via Score Refinement

Information retrieval (IR) methods, like retrieval augmented generation, are fundamental to modern applications but often lack statistical guarantees. Conformal prediction addresses this by retrieving sets guaranteed to include relevant information, yet existing approaches produce large-sized sets, incurring high computational costs and slow response times. In this work, we introduce a score refinement method that applies a simple monotone transformation to retrieval scores, leading to significantly smaller conformal sets while maintaining their statistical guarantees. Experiments on various BEIR benchmarks validate the effectiveness of our approach in producing compact sets containing relevant information.

cs.IR↗

arXiv2024

Molecular Diffusion Models with Virtual Receptors

Machine learning approaches to Structure-Based Drug Design (SBDD) have proven quite fertile over the last few years. In particular, diffusion-based approaches to SBDD have shown great promise. We present a technique which expands on this diffusion approach in two crucial ways. First, we address the size disparity between the drug molecule and the target/receptor, which makes learning more challenging and inference slower. We do so through the notion of a Virtual Receptor, which is a compressed version of the receptor; it is learned so as to preserve key aspects of the structural information of the original receptor, while respecting the relevant group equivariance. Second, we incorporate a protein language embedding used originally in the context of protein folding. We experimentally demonstrate the contributions of both the virtual receptors and the protein embeddings: in practice, they lead to both better performance, as well as significantly faster computations.

cs.LG↗

arXiv2024

A Theoretical Framework for an Efficient Normalizing Flow-Based Solution to the Electronic Schrodinger Equation

A central problem in quantum mechanics involves solving the Electronic Schrodinger Equation for a molecule or material. The Variational Monte Carlo approach to this problem approximates a particular variational objective via sampling, and then optimizes this approximated objective over a chosen parameterized family of wavefunctions, known as the ansatz. Recently neural networks have been used as the ansatz, with accompanying success. However, sampling from such wavefunctions has required the use of a Markov Chain Monte Carlo approach, which is inherently inefficient. In this work, we propose a solution to this problem via an ansatz which is cheap to sample from, yet satisfies the requisite quantum mechanical properties. We prove that a normalizing flow using the following two essential ingredients satisfies our requirements: (a) a base distribution which is constructed from Determinantal Point Processes; (b) flow layers which are equivariant to a particular subgroup of the permutation group. We then show how to construct both continuous and discrete normalizing flows which satisfy the requisite equivariance. We further demonstrate the manner in which the non-smooth nature ("cusps") of the wavefunction may be captured, and how the framework may be generalized to provide induction across multiple molecules. The resulting theoretical framework entails an efficient approach to solving the Electronic Schrodinger Equation.

physics.chem-ph↗

arXiv2024

Looks Too Good To Be True: An Information-Theoretic Analysis of Hallucinations in Generative Restoration Models

The pursuit of high perceptual quality in image restoration has driven the development of revolutionary generative models, capable of producing results often visually indistinguishable from real data. However, as their perceptual quality continues to improve, these models also exhibit a growing tendency to generate hallucinations - realistic-looking details that do not exist in the ground truth images. Hallucinations in these models create uncertainty about their reliability, raising major concerns about their practical application. This paper investigates this phenomenon through the lens of information theory, revealing a fundamental tradeoff between uncertainty and perception. We rigorously analyze the relationship between these two factors, proving that the global minimal uncertainty in generative models grows in tandem with perception. In particular, we define the inherent uncertainty of the restoration problem and show that attaining perfect perceptual quality entails at least twice this uncertainty. Additionally, we establish a relation between distortion, uncertainty and perception, through which we prove the aforementioned uncertainly-perception tradeoff induces the well-known perception-distortion tradeoff. We demonstrate our theoretical findings through experiments with super-resolution and inpainting algorithms. This work uncovers fundamental limitations of generative models in achieving both high perceptual quality and reliable predictions for image restoration. Thus, we aim to raise awareness among practitioners about this inherent tradeoff, empowering them to make informed decisions and potentially prioritize safety over perceptual performance.

cs.LG↗

arXiv2024

On the Semantic Latent Space of Diffusion-Based Text-to-Speech Models

The incorporation of Denoising Diffusion Models (DDMs) in the Text-to-Speech (TTS) domain is rising, providing great value in synthesizing high quality speech. Although they exhibit impressive audio quality, the extent of their semantic capabilities is unknown, and controlling their synthesized speech's vocal properties remains a challenge. Inspired by recent advances in image synthesis, we explore the latent space of frozen TTS models, which is composed of the latent bottleneck activations of the DDM's denoiser. We identify that this space contains rich semantic information, and outline several novel methods for finding semantic directions within it, both supervised and unsupervised. We then demonstrate how these enable off-the-shelf audio editing, without any further training, architectural changes or data requirements. We present evidence of the semantic and acoustic qualities of the edited audio, and provide supplemental samples: https://latent-analysis-grad-tts.github.io/speech-samples/.

cs.SD↗

arXiv2024

Overcoming Order in Autoregressive Graph Generation

Graph generation is a fundamental problem in various domains, including chemistry and social networks. Recent work has shown that molecular graph generation using recurrent neural networks (RNNs) is advantageous compared to traditional generative approaches which require converting continuous latent representations into graphs. One issue which arises when treating graph generation as sequential generation is the arbitrary order of the sequence which results from a particular choice of graph flattening method. In this work we propose using RNNs, taking into account the non-sequential nature of graphs by adding an Orderless Regularization (OLR) term that encourages the hidden state of the recurrent model to be invariant to different valid orderings present under the training distribution. We demonstrate that sequential graph generation models benefit from our proposed regularization scheme, especially when data is scarce. Our findings contribute to the growing body of research on graph generation and provide a valuable tool for various applications requiring the synthesis of realistic and diverse graph structures.

cs.SI↗

arXiv2024

Early Time Classification with Accumulated Accuracy Gap Control

Early time classification algorithms aim to label a stream of features without processing the full input stream, while maintaining accuracy comparable to that achieved by applying the classifier to the entire input. In this paper, we introduce a statistical framework that can be applied to any sequential classifier, formulating a calibrated stopping rule. This data-driven rule attains finite-sample, distribution-free control of the accuracy gap between full and early-time classification. We start by presenting a novel method that builds on the Learn-then-Test calibration framework to control this gap marginally, on average over i.i.d. instances. As this algorithm tends to yield an excessively high accuracy gap for early halt times, our main contribution is the proposal of a framework that controls a stronger notion of error, where the accuracy gap is controlled conditionally on the accumulated halt times. Numerical experiments demonstrate the effectiveness, applicability, and usefulness of our method. We show that our proposed early stopping mechanism reduces up to 94% of timesteps used for classification while achieving rigorous accuracy gap control.

cs.LG↗

arXiv2023

Weakly-Supervised Surgical Phase Recognition

A key element of computer-assisted surgery systems is phase recognition of surgical videos. Existing phase recognition algorithms require frame-wise annotation of a large number of videos, which is time and money consuming. In this work we join concepts of graph segmentation with self-supervised learning to derive a random-walk solution for per-frame phase prediction. Furthermore, we utilize within our method two forms of weak supervision: sparse timestamps or few-shot learning. The proposed algorithm enjoys low complexity and can operate in lowdata regimes. We validate our method by running experiments with the public Cholec80 dataset of laparoscopic cholecystectomy videos, demonstrating promising performance in multiple setups.

cs.CV↗

arXiv2023

Self-Supervised Learning for Endoscopic Video Analysis

Self-supervised learning (SSL) has led to important breakthroughs in computer vision by allowing learning from large amounts of unlabeled data. As such, it might have a pivotal role to play in biomedicine where annotating data requires a highly specialized expertise. Yet, there are many healthcare domains for which SSL has not been extensively explored. One such domain is endoscopy, minimally invasive procedures which are commonly used to detect and treat infections, chronic inflammatory diseases or cancer. In this work, we study the use of a leading SSL framework, namely Masked Siamese Networks (MSNs), for endoscopic video analysis such as colonoscopy and laparoscopy. To fully exploit the power of SSL, we create sizable unlabeled endoscopic video datasets for training MSNs. These strong image representations serve as a foundation for secondary training with limited annotated datasets, resulting in state-of-the-art performance in endoscopic benchmarks like surgical phase recognition during laparoscopy and colonoscopic polyp characterization. Additionally, we achieve a 50% reduction in annotated data size without sacrificing performance. Thus, our work provides evidence that SSL can dramatically reduce the need of annotated data in endoscopy.

cs.CV↗

arXiv2023

Principal Uncertainty Quantification with Spatial Correlation for Image Restoration Problems

Uncertainty quantification for inverse problems in imaging has drawn much attention lately. Existing approaches towards this task define uncertainty regions based on probable values per pixel, while ignoring spatial correlations within the image, resulting in an exaggerated volume of uncertainty. In this paper, we propose PUQ (Principal Uncertainty Quantification) -- a novel definition and corresponding analysis of uncertainty regions that takes into account spatial relationships within the image, thus providing reduced volume regions. Using recent advancements in generative models, we derive uncertainty intervals around principal components of the empirical posterior distribution, forming an ambiguity region that guarantees the inclusion of true unseen values with a user-defined confidence probability. To improve computational efficiency and interpretability, we also guarantee the recovery of true unseen values using only a few principal directions, resulting in more informative uncertainty regions. Our approach is verified through experiments on image colorization, super-resolution, and inpainting; its effectiveness is shown through comparison to baseline methods, demonstrating significantly tighter uncertainty regions.

cs.CV↗

arXiv2023

Semi-Equivariant Conditional Normalizing Flows

We study the problem of learning conditional distributions of the form $p(G | \hat G)$, where $G$ and $\hat G$ are two 3D graphs, using continuous normalizing flows. We derive a semi-equivariance condition on the flow which ensures that conditional invariance to rigid motions holds. We demonstrate the effectiveness of the technique in the molecular setting of receptor-aware ligand generation.

cs.LG↗

arXiv2023

Designing Nonlinear Photonic Crystals for High-Dimensional Quantum State Engineering

We propose a novel, physically-constrained and differentiable approach for the generation of D-dimensional qudit states via spontaneous parametric down-conversion (SPDC) in quantum optics. We circumvent any limitations imposed by the inherently stochastic nature of the physical process and incorporate a set of stochastic dynamical equations governing its evolution under the SPDC Hamiltonian. We demonstrate the effectiveness of our model through the design of structured nonlinear photonic crystals (NLPCs) and shaped pump beams; and show, theoretically and experimentally, how to generate maximally entangled states in the spatial degree of freedom. The learning of NLPC structures offers a promising new avenue for shaping and controlling arbitrary quantum states and enables all-optical coherent control of the generated states. We believe that this approach can readily be extended from bulky crystals to thin Metasurfaces and potentially applied to other quantum systems sharing a similar Hamiltonian structures, such as superfluids and superconductors.

quant-ph↗

arXiv2022

What's Behind the Mask: Estimating Uncertainty in Image-to-Image Problems

Estimating uncertainty in image-to-image networks is an important task, particularly as such networks are being increasingly deployed in the biological and medical imaging realms. In this paper, we introduce a new approach to this problem based on masking. Given an existing image-to-image network, our approach computes a mask such that the distance between the masked reconstructed image and the masked true image is guaranteed to be less than a specified threshold, with high probability. The mask thus identifies the more certain regions of the reconstructed image. Our approach is agnostic to the underlying image-to-image network, and only requires triples of the input (degraded), reconstructed and true images for training. Furthermore, our method is agnostic to the distance metric used. As a result, one can use $L_p$-style distances or perceptual distances like LPIPS, which contrasts with interval-based approaches to uncertainty. Our theoretical guarantees derive from a conformal calibration procedure. We evaluate our mask-based approach to uncertainty on image colorization, image completion, and super-resolution tasks, demonstrating high quality performance on each.

cs.CV↗

arXiv2022

Semi-Equivariant Continuous Normalizing Flows for Target-Aware Molecule Generation

We propose an algorithm for learning a conditional generative model of a molecule given a target. Specifically, given a receptor molecule that one wishes to bind to, the conditional model generates candidate ligand molecules that may bind to it. The distribution should be invariant to rigid body transformations that act $\textit{jointly}$ on the ligand and the receptor; it should also be invariant to permutations of either the ligand or receptor atoms. Our learning algorithm is based on a continuous normalizing flow. We establish semi-equivariance conditions on the flow which guarantee the aforementioned invariance conditions on the conditional distribution. We propose a graph neural network architecture which implements this flow, and which is designed to learn effectively despite the vast differences in size between the ligand and receptor. We evaluate our method on the CrossDocked2020 dataset, attaining a significant improvement in binding affinity over competing methods.

cs.LG↗