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Daniel Freedman

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12 papers

2 author rows

TMLR Journal 2026 Journal Article

Neural Fourier Transform for Multiple Time Series Prediction

Noam Koren
Kira Radinsky
Daniel Freedman

Multivariate time series forecasting is an important task in various fields such as economic planning, healthcare management, and environmental monitoring. In this work, we present a novel methodology for improving multivariate forecasting, particularly, in data sets with strong seasonality. We frame the forecasting task as a Multi-Dimensional Fourier Transform (MFT) problem and propose the Neural Fourier Transform (NFT) that leverages a deep learning model to predict future time series values by learning the MFT coefficients. The efficacy of NFT is empirically validated on 7 diverse datasets, demonstrating improvements over multiple forecasting horizons and lookbacks, thereby establishing new state-of-the-art results. Our contributions advance the field of multivariate time series forecasting by providing a model that excels in predictive accuracy. The code of this study is publicly available.

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AAAI Conference 2026 Conference Paper

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

Noam Koren
Ralf J. J. Mackenbach
Ruud J. G. van Sloun
Kira Radinsky
Daniel Freedman

Neural operators have emerged as a promising paradigm for learning solution operators of partial differential equations (PDEs) directly from data. Existing methods, such as those based on Fourier or graph techniques, make strong assumptions about the structure of the kernel integral operator, 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 functions, 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 degree of expressivity. Furthermore, due to its low-rank structure the computational complexity of applying the operator remains reasonable, leading to a practical system. In extensive 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.

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AAAI Conference 2025 Conference Paper

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

Daniel Freedman
Eyal Rozenberg
Alex Bronstein

A central problem in quantum mechanics involves solving the Electronic Schrödinger 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 Schrödinger Equation.

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TMLR Journal 2025 Journal Article

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

Tomer Borreda
Daniel Freedman
Or Litany

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 long-range graph benchmarks indicate a consistent improvement in results over the base method, Neural Atoms, while maintaining a linear complexity instead of $O(n^{3/2})$. Remarkably, our sparse model achieves performance on par with its non-sparse counterpart. Furthermore, ReHub outperforms competitive baselines and consistently ranks among the top performers across various benchmarks.

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ICML Conference 2024 Conference Paper

Early Time Classification with Accumulated Accuracy Gap Control

Liran Ringel
Regev Cohen
Daniel Freedman
Michael Elad
Yaniv Romano

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.

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NeurIPS Conference 2024 Conference Paper

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

Regev Cohen
Idan Kligvasser
Ehud Rivlin
Daniel Freedman

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.

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TMLR Journal 2024 Journal Article

Overcoming Order in Autoregressive Graph Generation for Molecule Generation

Edo Cohen-Karlik
Eyal Rozenberg
Daniel Freedman

Graph generation is a fundamental problem in various domains, and is of particular interest in chemistry where graphs may be used to represent molecules. 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 the chemistry setting, molecular graphs commonly have multiple SMILES strings corresponding to the same molecule. Inspired by the use case of molecular graph generation, 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 molecular 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.

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ICML Conference 2021 Conference Paper

12-Lead ECG Reconstruction via Koopman Operators

Tomer Golany
Kira Radinsky
Daniel Freedman
Saar Minha

32% of all global deaths in the world are caused by cardiovascular diseases. Early detection, especially for patients with ischemia or cardiac arrhythmia, is crucial. To reduce the time between symptoms onset and treatment, wearable ECG sensors were developed to allow for the recording of the full 12-lead ECG signal at home. However, if even a single lead is not correctly positioned on the body that lead becomes corrupted, making automatic diagnosis on the basis of the full signal impossible. In this work, we present a methodology to reconstruct missing or noisy leads using the theory of Koopman Operators. Given a dataset consisting of full 12-lead ECGs, we learn a dynamical system describing the evolution of the 12 individual signals together in time. The Koopman theory indicates that there exists a high-dimensional embedding space in which the operator which propagates from one time instant to the next is linear. We therefore learn both the mapping to this embedding space, as well as the corresponding linear operator. Armed with this representation, we are able to impute missing leads by solving a least squares system in the embedding space, which can be achieved efficiently due to the sparse structure of the system. We perform an empirical evaluation using 12-lead ECG signals from thousands of patients, and show that we are able to reconstruct the signals in such way that enables accurate clinical diagnosis.

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AAAI Conference 2021 Conference Paper

ECG ODE-GAN: Learning Ordinary Differential Equations of ECG Dynamics via Generative Adversarial Learning

Tomer Golany
Daniel Freedman
Kira Radinsky

Understanding the dynamics of complex biological and physiological systems has been explored for many years in the form of physically-based mathematical simulators. The behavior of a physical system is often described via ordinary differential equations (ODE), referred to as the dynamics. In the standard case, the dynamics are derived from purely physical considerations. By contrast, in this work we study how the dynamics can be learned by a generative adversarial network which combines both physical and data considerations. As a use case, we focus on the dynamics of the heart signal electrocardiogram (ECG). We begin by introducing a new GAN framework, dubbed ODE-GAN, in which the generator learns the dynamics of a physical system in the form of an ordinary differential equation. Specifically, the generator network receives as input a value at a specific time step, and produces the derivative of the system at that time step. Thus, the ODE-GAN learns purely data-driven dynamics. We then show how to incorporate physical considerations into ODE- GAN. We achieve this through the introduction of an additional input to the ODE-GAN generator: physical parameters, which partially characterize the signal of interest. As we focus on ECG signals, we refer to this new framework as ECG- ODE-GAN. We perform an empirical evaluation and show that generating ECG heartbeats from our learned dynamics improves ECG heartbeat classification.

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NeurIPS Conference 2021 Conference Paper

It Has Potential: Gradient-Driven Denoisers for Convergent Solutions to Inverse Problems

Regev Cohen
Yochai Blau
Daniel Freedman
Ehud Rivlin

In recent years there has been increasing interest in leveraging denoisers for solving general inverse problems. Two leading frameworks are regularization-by-denoising (RED) and plug-and-play priors (PnP) which incorporate explicit likelihood functions with priors induced by denoising algorithms. RED and PnP have shown state-of-the-art performance in diverse imaging tasks when powerful denoisersare used, such as convolutional neural networks (CNNs). However, the study of their convergence remains an active line of research. Recent works derive the convergence of RED and PnP methods by treating CNN denoisers as approximations for maximum a posteriori (MAP) or minimum mean square error (MMSE) estimators. Yet, state-of-the-art denoisers cannot be interpreted as either MAPor MMSE estimators, since they typically do not exhibit symmetric Jacobians. Furthermore, obtaining stable inverse algorithms often requires controlling the Lipschitz constant of CNN denoisers during training. Precisely enforcing this constraint is impractical, hence, convergence cannot be completely guaranteed. In this work, we introduce image denoisers derived as the gradients of smooth scalar-valued deep neural networks, acting as potentials. This ensures two things: (1) the proposed denoisers display symmetric Jacobians, allowing for MAP and MMSE estimators interpretation; (2) the denoisers may be integrated into RED and PnP schemes with backtracking step size, removing the need for enforcing their Lipschitz constant. To show the latter, we develop a simple inversion method that utilizes the proposed denoisers. We theoretically establish its convergence to stationary points of an underlying objective function consisting of the learned potentials. We numerically validate our method through various imaging experiments, showing improved results compared to standard RED and PnP methods, and with additional provable stability.

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ICML Conference 2020 Conference Paper

SimGANs: Simulator-Based Generative Adversarial Networks for ECG Synthesis to Improve Deep ECG Classification

Tomer Golany
Kira Radinsky
Daniel Freedman

Generating training examples for supervised tasks is a long sought after goal in AI. We study the problem of heart signal electrocardiogram (ECG) synthesis for improved heartbeat classification. ECG synthesis is challenging: the generation of training examples for such biological-physiological systems is not straightforward, due to their dynamic nature in which the various parts of the system interact in complex ways. However, an understanding of these dynamics has been developed for years in the form of mathematical process simulators. We study how to incorporate this knowledge into the generative process by leveraging a biological simulator for the task of ECG classification. Specifically, we use a system of ordinary differential equations representing heart dynamics, and incorporate this ODE system into the optimization process of a generative adversarial network to create biologically plausible ECG training examples. We perform empirical evaluation and show that heart simulation knowledge during the generation process improves ECG classification.

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SODA Conference 2010 Conference Paper

Hardness Results for Homology Localization

Chao Chen 0012
Daniel Freedman

We address the problem of localizing homology classes, namely, finding the cycle representing a given class with the most concise geometric measure. We focus on the volume measure, that is, the 1-norm of a cycle. Two main results are presented. First, we prove the problem is NP-hard to approximate within any constant factor. Second, we prove that for homology of dimension two or higher, the problem is NP-hard to approximate even when the Betti number is O (1). A side effect is the inapproximability of the problem of computing the nonbounding cycle with the smallest volume, and computing cycles representing a homology basis with the minimal total volume. We also discuss other geometric measures (diameter and radius) and show their disadvantages in homology localization. Our work is restricted to homology over the ℤ 2 field.

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