arXiv subjects

Tom Tirer

Publications and source records attributed to Tom Tirer.

At least 19 recordsLinked to original sources

arXiv2026

Reducing Diffusion Model Memorization with Higher Order Langevin Dynamics

Diffusion/score-based models have emerged as powerful generative models, capable of generating high-quality samples that mimic the training data distribution. However, it has been observed that they are prone to reproducing training samples-known as "memorization"-potentially violating copyright and privacy. In this paper, we study the effect of Higher-Order Langevin Dynamics (HOLD) on this phenomenon. HOLD diffusion processes introduce auxiliary variables; if the data variable is interpreted as "position," then the auxiliary variables can be interpreted as "velocity" and "acceleration," depending on the chosen order of the model. They were originally proposed based on the intuition that they regularize the trajectories of the data variable by implicitly imposing additional dynamical constraints. Our work provides, to our knowledge, the first theoretical characterization of the regularization effect of HOLD. Specifically, we show that in HOLD, the dynamics of the data variable are governed by a low-pass-filtered version of the learned score function, with smoothness increasing with the order of HOLD. We then analyze the optimal empirical score and the possibility of distribution collapse. Together, our results explain the mitigation of memorization as the model order increases. Finally, we present an empirical study on real-world data that supports our theory and highlights this distinct advantage of HOLD over standard diffusion in practice.

stat.ML↗

arXiv2025

Does the Data Processing Inequality Reflect Practice? On the Utility of Low-Level Tasks

The data processing inequality is an information-theoretic principle stating that the information content of a signal cannot be increased by processing the observations. In particular, it suggests that there is no benefit in enhancing the signal or encoding it before addressing a classification problem. This assertion can be proven to be true for the case of the optimal Bayes classifier. However, in practice, it is common to perform "low-level" tasks before "high-level" downstream tasks despite the overwhelming capabilities of modern deep neural networks. In this paper, we aim to understand when and why low-level processing can be beneficial for classification. We present a comprehensive theoretical study of a binary classification setup, where we consider a classifier that is tightly connected to the optimal Bayes classifier and converges to it as the number of training samples increases. We prove that for any finite number of training samples, there exists a pre-classification processing that improves the classification accuracy. We also explore the effect of class separation, training set size, and class balance on the relative gain from this procedure. We support our theory with an empirical investigation of the theoretical setup. Finally, we conduct an empirical study where we investigate the effect of denoising and encoding on the performance of practical deep classifiers on benchmark datasets. Specifically, we vary the size and class distribution of the training set, and the noise level, and demonstrate trends that are consistent with our theoretical results.

cs.LG↗

arXiv2025

Enhancing Conformal Prediction via Class Similarity

Conformal Prediction (CP) has emerged as a powerful statistical framework for high-stakes classification applications. Instead of predicting a single class, CP generates a prediction set, guaranteed to include the true label with a pre-specified probability. The performance of different CP methods is typically assessed by their average prediction set size. In setups where the classes can be partitioned into semantic groups, e.g., diseases that require similar treatment, users can benefit from prediction sets that are not only small on average, but also contain a small number of semantically different groups. This paper begins by addressing this problem and ultimately offers a widely applicable tool for boosting any CP method on any dataset. First, given a class partition, we propose augmenting the CP score function with a term that penalizes predictions with out-of-group errors. We theoretically analyze this strategy and prove its advantages for group-related metrics. Surprisingly, we show mathematically that, for common class partitions, it can also reduce the average set size of any CP score function. Our analysis reveals the class-similarity factors behind this improvement and motivates a variant that can further reduce prediction set size by leveraging the model's embeddings, without requiring any human semantic partition. Finally, we present an extensive empirical study, encompassing prominent CP methods, multiple models, and several datasets, which demonstrates that our class-similarity-based approach consistently enhances CP methods.

cs.LG↗

arXiv2025

Jacobian-Aware Posterior Sampling for Inverse Problems

Diffusion models provide powerful generative priors for solving inverse problems by sampling from a posterior distribution conditioned on corrupted measurements. Existing methods primarily follow two paradigms: direct methods, which approximate the likelihood term, and proximal methods, which incorporate intermediate solutions satisfying measurement constraints into the sampling process. Under standard Gaussian approximations and locally-linear measurements, we demonstrate that these approaches differ fundamentally in their treatment of the diffusion denoiser's Jacobian within the likelihood term. While this Jacobian encodes critical prior knowledge of the data distribution, training-induced non-idealities can degrade performance in zero-shot settings. In this work, we bridge direct and proximal approaches by proposing a principled Jacobian-Aware Posterior Sampler (JAPS). JAPS leverages the Jacobian's prior knowledge while mitigating its detrimental effects through a corresponding proximal solution, requiring no additional computational cost. Additionally, we integrate our guidance into DDIM sampling, with a corrected conditional factor that has been missing in previous works. Our method enhances reconstruction quality across diverse linear and nonlinear noisy imaging tasks, outperforming existing diffusion-based baselines in perceptual quality while maintaining or improving distortion metrics.

cs.CV↗

arXiv2025

SUMO: Subspace-Aware Moment-Orthogonalization for Accelerating Memory-Efficient LLM Training

Low-rank gradient-based optimization methods have significantly improved memory efficiency during the training of large language models (LLMs), enabling operations within constrained hardware without sacrificing performance. However, these methods primarily emphasize memory savings, often overlooking potential acceleration in convergence due to their reliance on standard isotropic steepest descent techniques, which can perform suboptimally in the highly anisotropic landscapes typical of deep networks, particularly LLMs. In this paper, we propose SUMO (Subspace-Aware Moment-Orthogonalization), an optimizer that employs exact singular value decomposition (SVD) for moment orthogonalization within a dynamically adapted low-dimensional subspace, enabling norm-inducing steepest descent optimization steps. By explicitly aligning optimization steps with the spectral characteristics of the loss landscape, SUMO effectively mitigates approximation errors associated with commonly used methods like Newton-Schulz orthogonalization approximation. We theoretically establish an upper bound on these approximation errors, proving their dependence on the condition numbers of moments, conditions we analytically demonstrate are encountered during LLM training. Furthermore, we both theoretically and empirically illustrate that exact orthogonalization via SVD substantially improves convergence rates while reducing overall complexity. Empirical evaluations confirm that SUMO accelerates convergence, enhances stability, improves performance, and reduces memory requirements by up to 20% compared to state-of-the-art methods.

cs.LG↗

arXiv2025

Efficient Conformal Prediction for Regression Models under Label Noise

In high-stakes scenarios, such as medical imaging applications, it is critical to equip the predictions of a regression model with reliable confidence intervals. Recently, Conformal Prediction (CP) has emerged as a powerful statistical framework that, based on a labeled calibration set, generates intervals that include the true labels with a pre-specified probability. In this paper, we address the problem of applying CP for regression models when the calibration set contains noisy labels. We begin by establishing a mathematically grounded procedure for estimating the noise-free CP threshold. Then, we turn it into a practical algorithm that overcomes the challenges arising from the continuous nature of the regression problem. We evaluate the proposed method on two medical imaging regression datasets with Gaussian label noise. Our method significantly outperforms the existing alternative, achieving performance close to the clean-label setting.

cs.LG↗

arXiv2025

(SP)$^2$-Net: A Neural Spatial Spectrum Method for DOA Estimation

We consider the problem of estimating the directions of arrival (DOAs) of multiple sources from a single snapshot of an antenna array, a task with many practical applications. In such settings, the classical Bartlett beamformer is commonly used, as maximum likelihood estimation becomes impractical when the number of sources is unknown or large, and spectral methods based on the sample covariance are not applicable due to the lack of multiple snapshots. However, the accuracy and resolution of the Bartlett beamformer are fundamentally limited by the array aperture. In this paper, we propose a deep learning technique, comprising a novel architecture and training strategy, for generating a high-resolution spatial spectrum from a single snapshot. Specifically, we train a deep neural network that takes the measurements and a hypothesis angle as input and learns to output a score consistent with the capabilities of a much wider array. At inference time, a heatmap can be produced by scanning an arbitrary set of angles. We demonstrate the advantages of our trained model, named (SP)$^2$-Net, over the Bartlett beamformer and sparsity-based DOA estimation methods.

eess.SP↗

arXiv2025

Unveiling Multiple Descents in Unsupervised Autoencoders

The phenomenon of double descent has challenged the traditional bias-variance trade-off in supervised learning but remains unexplored in unsupervised learning, with some studies arguing for its absence. In this study, we first demonstrate analytically that double descent does not occur in linear unsupervised autoencoders (AEs). In contrast, we show for the first time that both double and triple descent can be observed with nonlinear AEs across various data models and architectural designs. We examine the effects of partial sample and feature noise and highlight the importance of bottleneck size in influencing the double descent curve. Through extensive experiments on both synthetic and real datasets, we uncover model-wise, epoch-wise, and sample-wise double descent across several data types and architectures. Our findings indicate that over-parameterized models not only improve reconstruction but also enhance performance in downstream tasks such as anomaly detection and domain adaptation, highlighting their practical value in complex real-world scenarios.

cs.LG↗

arXiv2025

ADIR: Adaptive Diffusion for Image Reconstruction

Denoising diffusion models have recently achieved remarkable success in image generation, capturing rich information about natural image statistics. This makes them highly promising for image reconstruction, where the goal is to recover a clean image from a degraded observation. In this work, we introduce a conditional sampling framework that leverages the powerful priors learned by diffusion models while enforcing consistency with the available measurements. To further adapt pre-trained diffusion models to the specific degradation at hand, we propose a novel fine-tuning strategy. In particular, we employ LoRA-based adaptation using images that are semantically and visually similar to the degraded input, efficiently retrieved from a large and diverse dataset via an off-the-shelf vision-language model. We evaluate our approach on two leading publicly available diffusion models--Stable Diffusion and Guided Diffusion--and demonstrate that our method, termed Adaptive Diffusion for Image Reconstruction (ADIR), yields substantial improvements across a range of image reconstruction tasks.

cs.CV↗

arXiv2025

Catastrophic Forgetting Mitigation Through Plateau Phase Activity Profiling

Catastrophic forgetting in deep neural networks occurs when learning new tasks degrades performance on previously learned tasks due to knowledge overwriting. Among the approaches to mitigate this issue, regularization techniques aim to identify and constrain "important" parameters to preserve previous knowledge. In the highly nonconvex optimization landscape of deep learning, we propose a novel perspective: tracking parameters during the final training plateau is more effective than monitoring them throughout the entire training process. We argue that parameters that exhibit higher activity (movement and variability) during this plateau reveal directions in the loss landscape that are relatively flat, making them suitable for adaptation to new tasks while preserving knowledge from previous ones. Our comprehensive experiments demonstrate that this approach achieves superior performance in balancing catastrophic forgetting mitigation with strong performance on newly learned tasks.

cs.LG↗

arXiv2025

On Temperature Scaling and Conformal Prediction of Deep Classifiers

In many classification applications, the prediction of a deep neural network (DNN) based classifier needs to be accompanied by some confidence indication. Two popular approaches for that aim are: 1) Calibration: modifies the classifier's softmax values such that the maximal value better estimates the correctness probability; and 2) Conformal Prediction (CP): produces a prediction set of candidate labels that contains the true label with a user-specified probability, guaranteeing marginal coverage but not, e.g., per class coverage. In practice, both types of indications are desirable, yet, so far the interplay between them has not been investigated. Focusing on the ubiquitous Temperature Scaling (TS) calibration, we start this paper with an extensive empirical study of its effect on prominent CP methods. We show that while TS calibration improves the class-conditional coverage of adaptive CP methods, surprisingly, it negatively affects their prediction set sizes. Motivated by this behavior, we explore the effect of TS on CP beyond its calibration application and reveal an intriguing trend under which it allows to trade prediction set size and conditional coverage of adaptive CP methods. Then, we establish a mathematical theory that explains the entire non-monotonic trend. Finally, based on our experiments and theory, we offer simple guidelines for practitioners to effectively combine adaptive CP with calibration, aligned with user-defined goals.

cs.LG↗

arXiv2025

Can Kernel Methods Explain How the Data Affects Neural Collapse?

A vast amount of literature has recently focused on the "Neural Collapse" (NC) phenomenon, which emerges when training neural network (NN) classifiers beyond the zero training error point. The core component of NC is the decrease in the within-class variability of the network's deepest features, dubbed as NC1. The theoretical works that study NC are typically based on simplified unconstrained features models (UFMs) that mask any effect of the data on the extent of collapse. To address this limitation of UFMs, this paper explores the possibility of analyzing NC1 using kernels associated with shallow NNs. We begin by formulating an NC1 metric as a function of the kernel. Then, we specialize it to the NN Gaussian Process kernel (NNGP) and the Neural Tangent Kernel (NTK), associated with wide networks at initialization and during gradient-based training with a small learning rate, respectively. As a key result, we show that the NTK does not represent more collapsed features than the NNGP for Gaussian data of arbitrary dimensions. This showcases the limitations of data-independent kernels such as NTK in approximating the NC behavior of NNs. As an alternative to NTK, we then empirically explore a recently proposed data-aware Gaussian Process kernel, which generalizes NNGP to model feature learning. We show that this kernel yields lower NC1 than NNGP but may not follow the trends of the shallow NN. Our study demonstrates that adaptivity to data may allow kernel-based analysis of NC, though further advancements in this area are still needed. A nice byproduct of our study is showing both theoretically and empirically that the choice of nonlinear activation function affects NC1 (with ERF yielding lower values than ReLU). The code is available at: https://github.com/kvignesh1420/shallow_nc1

cs.LG↗

arXiv2025

Zero-Shot Image Restoration Using Few-Step Guidance of Consistency Models (and Beyond)

In recent years, it has become popular to tackle image restoration tasks with a single pretrained diffusion model (DM) and data-fidelity guidance, instead of training a dedicated deep neural network per task. However, such "zero-shot" restoration schemes currently require many Neural Function Evaluations (NFEs) for performing well, which may be attributed to the many NFEs needed in the original generative functionality of the DMs. Recently, faster variants of DMs have been explored for image generation. These include Consistency Models (CMs), which can generate samples via a couple of NFEs. However, existing works that use guided CMs for restoration still require tens of NFEs or fine-tuning of the model per task that leads to performance drop if the assumptions during the fine-tuning are not accurate. In this paper, we propose a zero-shot restoration scheme that uses CMs and operates well with as little as 4 NFEs. It is based on a wise combination of several ingredients: better initialization, back-projection guidance, and above all a novel noise injection mechanism. We demonstrate the advantages of our approach for image super-resolution, deblurring and inpainting. Interestingly, we show that the usefulness of our noise injection technique goes beyond CMs: it can also mitigate the performance degradation of existing guided DM methods when reducing their NFE count.

cs.CV↗

arXiv2025

ConfIC-RCA: Statistically Grounded Efficient Estimation of Segmentation Quality

Assessing the quality of automatic image segmentation is crucial in clinical practice, but often very challenging due to the limited availability of ground truth annotations. Reverse Classification Accuracy (RCA) is an approach that estimates the quality of new predictions on unseen samples by training a segmenter on those predictions, and then evaluating it against existing annotated images. In this work we introduce ConfIC-RCA (Conformal In-Context RCA), a novel method for automatically estimating segmentation quality with statistical guarantees in the absence of ground-truth annotations, which consists of two main innovations. First, In-Context RCA, which leverages recent in-context learning models for image segmentation and incorporates retrieval-augmentation techniques to select the most relevant reference images. This approach enables efficient quality estimation with minimal reference data while avoiding the need of training additional models. Second, we introduce Conformal RCA, which extends both the original RCA framework and In-Context RCA to go beyond point estimation. Using tools from split conformal prediction, Conformal RCA produces prediction intervals for segmentation quality providing statistical guarantees that the true score lies within the estimated interval with a user-specified probability. Validated across 10 different medical imaging tasks in various organs and modalities, our methods demonstrate robust performance and computational efficiency, offering a promising solution for automated quality control in clinical workflows, where fast and reliable segmentation assessment is essential. The code is available at https://github.com/mcosarinsky/Conformal-In-Context-RCA

cs.CV↗

arXiv2025

LORENZA: Enhancing Generalization in Low-Rank Gradient LLM Training via Efficient Zeroth-Order Adaptive SAM

We study robust parameter-efficient fine-tuning (PEFT) techniques designed to improve accuracy and generalization while operating within strict computational and memory hardware constraints, specifically focusing on large-language models (LLMs). Existing PEFT methods often lack robustness and fail to generalize effectively across diverse tasks, leading to suboptimal performance in real-world scenarios. To address this, we present a new highly computationally efficient framework called AdaZo-SAM, combining Adam and Sharpness-Aware Minimization (SAM) while requiring only a single-gradient computation in every iteration. This is achieved using a stochastic zeroth-order estimation to find SAM's ascent perturbation. We provide a convergence guarantee for AdaZo-SAM and show that it improves the generalization ability of state-of-the-art PEFT methods. Additionally, we design a low-rank gradient optimization method named LORENZA, which is a memory-efficient version of AdaZo-SAM. LORENZA utilizes a randomized SVD scheme to efficiently compute the subspace projection matrix and apply optimization steps onto the selected subspace. This technique enables full-parameter fine-tuning with adaptive low-rank gradient updates, achieving the same reduced memory consumption as gradient-low-rank-projection methods. We provide a convergence analysis of LORENZA and demonstrate its merits for pre-training and fine-tuning LLMs.

cs.LG↗

arXiv2024

Denoiser-based projections for 2-D super-resolution multi-reference alignment

We study the 2-D super-resolution multi-reference alignment (SR-MRA) problem: estimating an image from its down-sampled, circularly-translated, and noisy copies. The SR-MRA problem serves as a mathematical abstraction of the structure determination problem for biological molecules. Since the SR-MRA problem is ill-posed without prior knowledge, accurate image estimation relies on designing priors that well-describe the statistics of the images of interest. In this work, we build on recent advances in image processing, and harness the power of denoisers as priors of images. In particular, we suggest to use denoisers as projections, and design two computational frameworks to estimate the image: projected expectation-maximization and projected method of moments. We provide an efficient GPU implementation, and demonstrate the effectiveness of these algorithms by extensive numerical experiments on a wide range of parameters and images.

eess.IV↗

arXiv2024

Image Restoration by Denoising Diffusion Models with Iteratively Preconditioned Guidance

Training deep neural networks has become a common approach for addressing image restoration problems. An alternative for training a "task-specific" network for each observation model is to use pretrained deep denoisers for imposing only the signal's prior within iterative algorithms, without additional training. Recently, a sampling-based variant of this approach has become popular with the rise of diffusion/score-based generative models. Using denoisers for general purpose restoration requires guiding the iterations to ensure agreement of the signal with the observations. In low-noise settings, guidance that is based on back-projection (BP) has been shown to be a promising strategy (used recently also under the names "pseudoinverse" or "range/null-space" guidance). However, the presence of noise in the observations hinders the gains from this approach. In this paper, we propose a novel guidance technique, based on preconditioning that allows traversing from BP-based guidance to least squares based guidance along the restoration scheme. The proposed approach is robust to noise while still having much simpler implementation than alternative methods (e.g., it does not require SVD or a large number of iterations). We use it within both an optimization scheme and a sampling-based scheme, and demonstrate its advantages over existing methods for image deblurring and super-resolution.

eess.IV↗

arXiv2024

Deep Internal Learning: Deep Learning from a Single Input

Deep learning, in general, focuses on training a neural network from large labeled datasets. Yet, in many cases there is value in training a network just from the input at hand. This is particularly relevant in many signal and image processing problems where training data is scarce and diversity is large on the one hand, and on the other, there is a lot of structure in the data that can be exploited. Using this information is the key to deep internal-learning strategies, which may involve training a network from scratch using a single input or adapting an already trained network to a provided input example at inference time. This survey paper aims at covering deep internal-learning techniques that have been proposed in the past few years for these two important directions. While our main focus will be on image processing problems, most of the approaches that we survey are derived for general signals (vectors with recurring patterns that can be distinguished from noise) and are therefore applicable to other modalities.

cs.LG↗