arXiv subjects

Michael Arbel

Publications and source records attributed to Michael Arbel.

At least 19 recordsLinked to original sources

arXiv2026

Functional Bilevel Optimization for Predictive Fairness

When sensitive attributes are continuous and high-dimensional $-$ demographic score vectors, posteriors over attributes, age or income profiles $-$ enforcing full statistical independence is often too restrictive, and existing relaxations rely on indirect dependence penalties or adversarial schemes that do not directly target the fairness-accuracy trade-off. We instead consider mean demographic parity through DPVar, the variance of the conditional-mean prediction given the sensitive attribute, and show that optimizing it yields a functional bilevel problem. We propose two algorithms for this problem: FBO, which uses a closed-form adjoint we derive for the squared-loss case to obtain an exact hypergradient, and ITD, which differentiates through unrolled inner steps and extends beyond squared loss. On synthetic data and a new semi-synthetic benchmark built from 60 tabular regression datasets, both methods achieve the lowest or near-lowest aggregate fairness-accuracy regret, and consistently match or outperform strong HSIC, adversarial, linear-dependence, and generalized-DP baselines.

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arXiv2026

Semiparametric Efficient Bilevel Gradient Estimation

Functional bilevel methods estimate a lower-level function and plug it into a hypergradient, but this plug-in gradient can retain first-order bias when the lower-level problem is learned nonparametrically. To remove this bias, we develop a semiparametric debiasing theory for population bilevel gradients based on the efficient influence function. This perspective leads to a cross-fitted orthogonal hypergradient estimator for which we establish asymptotic normality together with uniform control over the outer parameter. Under quadratic losses, the estimator reduces to a simple doubly robust score based on conditional mean nuisances. On synthetic bilevel benchmarks with known ground truth, the method tracks the oracle efficient-gradient benchmark and improves over plug-in functional hypergradients and regularized kernel bilevel baselines.

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arXiv2026

$\textit{BlockFormer}$ : Transformer-based inference from interaction maps

Inference from interaction maps, such as centromere identification from genome-wide chromosome conformation capture techniques -- notably Hi-C -- can be formulated as a generic inverse problem: infer a set of parameters given a map summarizing pairwise interactions between entities through blocks of variable numbers and sizes. In this work, we introduce a data-driven approach that leverages shared structure between these maps, such as global alignment between localized patterns, while handling the variability in number and size of entities arising in real-world data. Our approach relies on a transformer architecture capable of handling such variability and a custom simulator to generate abundant, yet computationally cheap synthetic data for training. Applied to the problem of centromere localization, the method accurately recovers their genomic positions across a wide range of species of various genome sizes.

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arXiv2026

PEIRA: Learning Predictive Encoders through Inter-View Regressor Alignment

Non-contrastive self-supervised learning (SSL) is an effective framework for predictive representation learning, but popular (and in practice effective) methods such as SimSiam, BYOL, I-JEPA or DINO, which rely on a form of self-distillation to train a teacher-student network, remain poorly understood as they typically do not minimize a well-defined objective. We analyze the dynamics of a variant of the Joint Embedding Predictive Architecture (JEPA) using a regularized linear regressor to predict the learned representations of two views of the data from one another, and fully characterize its stability: non-collapsed stable equilibria align with leading nonlinear canonical correlation subspaces, while collapsed equilibria may also be stable attractors. Motivated by this result, we introduce PEIRA, a non-contrastive SSL method with an explicit objective defined through the trace of the optimal linear regressor. We show that its only stable equilibria are nontrivial global minimizers and recover the same canonical correlation subspaces, with regularization selecting the effective dimension. Experiments on ImageNet-1K and CIFAR-10 show PEIRA is competitive with VICReg and LeJEPA baselines, and qualitative empirical results support the theory.

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arXiv2026

Beyond MMSE: Enhancing PnP Restoration with ProxiMAP

Plug-and-Play (PnP) methods have become standard tools for solving imaging inverse problems by replacing the intractable maximum a posteriori (MAP) denoiser with the MMSE one. While this mismatch has been widely treated as unavoidable, recent works have sought to close this gap by targeting the MAP with diffusion-model scores. We show this is problematic in practice: learned scores do not match the true ones, so MAP-targeting iterations converge to cartoon-like images rather than realistic ones, and better results are obtained by stopping short of convergence. We turn this observation into a design principle and introduce ProxiMAP, an iterative MAP approximation whose noise schedule keeps the iterate's residual noise matched to the denoiser's training noise. This keeps the denoiser in-distribution where its score is reliable, and yields implicit early stopping that avoids the failure mode above. ProxiMAP is a modular drop-in replacement for MMSE denoisers in standard PnP algorithms and consistently sharpens reconstructions across deblurring, inpainting, super-resolution, and phase retrieval. Building on the same principle, we propose a hybrid variant that applies ProxiMAP only in the late iterations of PnP, where the denoiser is most reliable -- matching or exceeding the full-replacement variant at a fraction of the cost.

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arXiv2026

Non-Stationary Functional Bilevel Optimization

Functional bilevel optimization (FBO) provides a powerful framework for hierarchical learning in function spaces, yet current methods are limited to static offline settings and perform suboptimally in online, non-stationary scenarios. We propose SmoothFBO, the first algorithm for non-stationary FBO with both theoretical guarantees and practical scalability. SmoothFBO introduces a time-smoothed stochastic hypergradient estimator that reduces variance through a window parameter, enabling stable outer-loop updates with sublinear regret. Importantly, the classical parametric bilevel case is a special reduction of our framework, making SmoothFBO a natural extension to online, non-stationary settings. Empirically, SmoothFBO consistently outperforms existing FBO methods in non-stationary hyperparameter optimization and model-based reinforcement learning, demonstrating its practical effectiveness. Together, these results establish SmoothFBO as a general, theoretically grounded, and practically viable foundation for bilevel optimization in online, non-stationary scenarios.

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arXiv2025

Flow Matching Calibration for Simulation-Based Inference under Model Misspecification

Simulation-based inference (SBI) is transforming experimental sciences by enabling parameter estimation in complex non-linear models from simulated data. A persistent challenge, however, is model misspecification. In a Bayesian setting, targeting posterior distributions, errors may arise from the simulator, the noise or prior modelling. These model components are only approximations of reality, and severe mismatches can yield biased or overconfident posteriors. We address this issue by introducing Flow Matching Corrected Posterior Estimation (FMCPE), a framework that leverages the flow matching paradigm to refine simulation-trained posterior estimators using a small set of calibration samples. Our approach proceeds in two stages: first, a posterior approximator is trained on abundant simulated data; second, flow matching transports its predictions toward the true posterior supported by calibration observations. We rely on the later to guide the correction, without requiring explicit knowledge of the misspecification form or of which model components are affected. This design enables FMCPE to combine the scalability of SBI with robustness to distributional shift. Across synthetic benchmarks and real-world datasets, we show that our proposal consistently mitigates the effects of misspecification, delivering improved inference accuracy and uncertainty quantification compared to standard SBI baselines, while remaining computationally efficient.

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arXiv2025

Simulation-based inference of yeast centromeres

The chromatin folding and the spatial arrangement of chromosomes in the cell play a crucial role in DNA replication and genes expression. An improper chromatin folding could lead to malfunctions and, over time, diseases. For eukaryotes, centromeres are essential for proper chromosome segregation and folding. Despite extensive research using de novo sequencing of genomes and annotation analysis, centromere locations in yeasts remain difficult to infer and are still unknown in most species. Recently, genome-wide chromosome conformation capture coupled with next-generation sequencing (Hi-C) has become one of the leading methods to investigate chromosome structures. Some recent studies have used Hi-C data to give a point estimate of each centromere, but those approaches highly rely on a good pre-localization. Here, we present a novel approach that infers in a stochastic manner the locations of all centromeres in budding yeast based on both the experimental Hi-C map and simulated contact maps.

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arXiv2025

MAP Estimation with Denoisers: Convergence Rates and Guarantees

Denoiser models have become powerful tools for inverse problems, enabling the use of pretrained networks to approximate the score of a smoothed prior distribution. These models are often used in heuristic iterative schemes aimed at solving Maximum a Posteriori (MAP) optimisation problems, where the proximal operator of the negative log-prior plays a central role. In practice, this operator is intractable, and practitioners plug in a pretrained denoiser as a surrogate-despite the lack of general theoretical justification for this substitution. In this work, we show that a simple algorithm, closely related to several used in practice, provably converges to the proximal operator under a log-concavity assumption on the prior $p$. We show that this algorithm can be interpreted as a gradient descent on smoothed proximal objectives. Our analysis thus provides a theoretical foundation for a class of empirically successful but previously heuristic methods.

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arXiv2025

Dual Perspectives on Non-Contrastive Self-Supervised Learning

The {\em stop gradient} and {\em exponential moving average} iterative procedures are commonly used in non-contrastive approaches to self-supervised learning to avoid representation collapse, with excellent performance in downstream applications in practice. This presentation investigates these procedures from the dual viewpoints of optimization and dynamical systems. We show that, in general, although they {\em do not} optimize the original objective, or {\em any} other smooth function, they {\em do} avoid collapse Following~\citet{Tian21}, but without any of the extra assumptions used in their proofs, we then show using a dynamical system perspective that, in the linear case, minimizing the original objective function without the use of a stop gradient or exponential moving average {\em always} leads to collapse. Conversely, we characterize explicitly the equilibria of the dynamical systems associated with these two procedures in this linear setting as algebraic varieties in their parameter space, and show that they are, in general, {\em asymptotically stable}. Our theoretical findings are illustrated by empirical experiments with real and synthetic data.

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arXiv2025

Unsupervised Imaging Inverse Problems with Diffusion Distribution Matching

This work addresses image restoration tasks through the lens of inverse problems using unpaired datasets. In contrast to traditional approaches -- which typically assume full knowledge of the forward model or access to paired degraded and ground-truth images -- the proposed method operates under minimal assumptions and relies only on small, unpaired datasets. This makes it particularly well-suited for real-world scenarios, where the forward model is often unknown or misspecified, and collecting paired data is costly or infeasible. The method leverages conditional flow matching to model the distribution of degraded observations, while simultaneously learning the forward model via a distribution-matching loss that arises naturally from the framework. Empirically, it outperforms both single-image blind and unsupervised approaches on deblurring and non-uniform point spread function (PSF) calibration tasks. It also matches state-of-the-art performance on blind super-resolution. We also showcase the effectiveness of our method with a proof of concept for lens calibration: a real-world application traditionally requiring time-consuming experiments and specialized equipment. In contrast, our approach achieves this with minimal data acquisition effort.

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arXiv2025

Learning Theory for Kernel Bilevel Optimization

Bilevel optimization has emerged as a technique for addressing a wide range of machine learning problems that involve an outer objective implicitly determined by the minimizer of an inner problem. While prior works have primarily focused on the parametric setting, a learning-theoretic foundation for bilevel optimization in the nonparametric case remains relatively unexplored. In this paper, we take a first step toward bridging this gap by studying Kernel Bilevel Optimization (KBO), where the inner objective is optimized over a reproducing kernel Hilbert space. This setting enables rich function approximation while providing a foundation for rigorous theoretical analysis. In this context, we derive novel finite-sample generalization bounds for KBO, leveraging tools from empirical process theory. These bounds further allow us to assess the statistical accuracy of gradient-based methods applied to the empirical discretization of KBO. We numerically illustrate our theoretical findings on a synthetic instrumental variable regression task.

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arXiv2025

EquiTabPFN: A Target-Permutation Equivariant Prior Fitted Networks

Recent foundational models for tabular data, such as TabPFN, excel at adapting to new tasks via in-context learning, but remain constrained to a fixed, pre-defined number of target dimensions-often necessitating costly ensembling strategies. We trace this constraint to a deeper architectural shortcoming: these models lack target equivariance, so that permuting target dimension orderings alters their predictions. This deficiency gives rise to an irreducible "equivariance gap", an error term that introduces instability in predictions. We eliminate this gap by designing a fully target-equivariant architecture-ensuring permutation invariance via equivariant encoders, decoders, and a bi-attention mechanism. Empirical evaluation on standard classification benchmarks shows that, on datasets with more classes than those seen during pre-training, our model matches or surpasses existing methods while incurring lower computational overhead.

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arXiv2024

LUDVIG: Learning-Free Uplifting of 2D Visual Features to Gaussian Splatting Scenes

We address the problem of extending the capabilities of vision foundation models such as DINO, SAM, and CLIP, to 3D tasks. Specifically, we introduce a novel method to uplift 2D image features into Gaussian Splatting representations of 3D scenes. Unlike traditional approaches that rely on minimizing a reconstruction loss, our method employs a simpler and more efficient feature aggregation technique, augmented by a graph diffusion mechanism. Graph diffusion refines 3D features, such as coarse segmentation masks, by leveraging 3D geometry and pairwise similarities induced by DINOv2. Our approach achieves performance comparable to the state of the art on multiple downstream tasks while delivering significant speed-ups. Notably, we obtain competitive segmentation results using only generic DINOv2 features, despite DINOv2 not being trained on millions of annotated segmentation masks like SAM. When applied to CLIP features, our method demonstrates strong performance in open-vocabulary object segmentation tasks, highlighting the versatility of our approach.

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arXiv2024

Functional Bilevel Optimization for Machine Learning

In this paper, we introduce a new functional point of view on bilevel optimization problems for machine learning, where the inner objective is minimized over a function space. These types of problems are most often solved by using methods developed in the parametric setting, where the inner objective is strongly convex with respect to the parameters of the prediction function. The functional point of view does not rely on this assumption and notably allows using over-parameterized neural networks as the inner prediction function. We propose scalable and efficient algorithms for the functional bilevel optimization problem and illustrate the benefits of our approach on instrumental regression and reinforcement learning tasks.

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arXiv2024

MLXP: A Framework for Conducting Replicable Experiments in Python

Replicability in machine learning (ML) research is increasingly concerning due to the utilization of complex non-deterministic algorithms and the dependence on numerous hyper-parameter choices, such as model architecture and training datasets. Ensuring reproducible and replicable results is crucial for advancing the field, yet often requires significant technical effort to conduct systematic and well-organized experiments that yield robust conclusions. Several tools have been developed to facilitate experiment management and enhance reproducibility; however, they often introduce complexity that hinders adoption within the research community, despite being well-handled in industrial settings. To address the challenge of low adoption, we propose MLXP, an open-source, simple, and lightweight experiment management tool based on Python, available at https://github.com/inria-thoth/mlxp . MLXP streamlines the experimental process with minimal practitioner overhead while ensuring a high level of reproducibility.

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arXiv2024

On Good Practices for Task-Specific Distillation of Large Pretrained Visual Models

Large pretrained visual models exhibit remarkable generalization across diverse recognition tasks. Yet, real-world applications often demand compact models tailored to specific problems. Variants of knowledge distillation have been devised for such a purpose, enabling task-specific compact models (the students) to learn from a generic large pretrained one (the teacher). In this paper, we show that the excellent robustness and versatility of recent pretrained models challenge common practices established in the literature, calling for a new set of optimal guidelines for task-specific distillation. To address the lack of samples in downstream tasks, we also show that a variant of Mixup based on stable diffusion complements standard data augmentation. This strategy eliminates the need for engineered text prompts and improves distillation of generic models into streamlined specialized networks.

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arXiv2023

SLACK: Stable Learning of Augmentations with Cold-start and KL regularization

Data augmentation is known to improve the generalization capabilities of neural networks, provided that the set of transformations is chosen with care, a selection often performed manually. Automatic data augmentation aims at automating this process. However, most recent approaches still rely on some prior information; they start from a small pool of manually-selected default transformations that are either used to pretrain the network or forced to be part of the policy learned by the automatic data augmentation algorithm. In this paper, we propose to directly learn the augmentation policy without leveraging such prior knowledge. The resulting bilevel optimization problem becomes more challenging due to the larger search space and the inherent instability of bilevel optimization algorithms. To mitigate these issues (i) we follow a successive cold-start strategy with a Kullback-Leibler regularization, and (ii) we parameterize magnitudes as continuous distributions. Our approach leads to competitive results on standard benchmarks despite a more challenging setting, and generalizes beyond natural images.

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