arXiv subjects

Romuald Elie

Publications and source records attributed to Romuald Elie.

At least 19 recordsLinked to original sources

arXiv2026

Control Variate Score Matching for Diffusion Models

Sampling from unnormalized probability densities is a pervasive challenge across the computational and physical sciences. Diffusion models provide a powerful generative framework for this task, but their success relies on accurately estimating the score of the perturbed target distribution. Current approaches face a dichotomy between two standard estimation methods: the Denoising Score Identity (DSI) requires data samples and exhibits high variance at low noise levels, whereas the Target Score Identity (TSI) relies on the energy function and suffers from diverging variance at high noise levels. In this work, we reconcile both approaches by introducing the Control Variate Score Identity (CVSI), an unbiased estimator with an analytically optimal, state- and time-dependent control coefficient that theoretically minimizes variance over the entire diffusion process. CVSI serves as a robust plug-in estimator that significantly enhances performance and efficiency in data-free sampler learning and training-free diffusion sampling. These gains scale to complex, high-dimensional energy-based models.

cs.LG↗

arXiv2026

Kastor: An efficient fine-tuning strategy for generative emulation of PDE simulations

Machine learning offers a promising avenue to accelerate physical simulations by replacing computationally expensive traditional Partial Differential Equation (PDE) solvers with fast, differentiable surrogate models. However, standard auto-regressive ML emulators often suffer from error accumulation over long horizons and struggle to capture the stochasticity of complex physical systems. In this paper, we propose Kastor, a comprehensive methodology to adapt a deterministic physics foundation model into a highly efficient and accurate generative surrogate. First, we introduce a two-stage inference scheme that combines a large-stride causal auto-regressive model with a non-causal temporal super-resolution network, significantly reducing error accumulation while minimizing computational cost. Second, we present Mean prediction regularization (MPR), a novel training objective that constrains the generative model to predict the deterministic distribution mean under null noise conditioning. This regularization dramatically improves the performance and stability of both Functional Generative Networks (FGN) and diffusion-based emulators. Finally, we demonstrate that incorporating spatial gradient matching improves the accuracy and physical fidelity of the simulations as measured by power spectrum density. Extensive evaluations on diverse simulation datasets of the benchmark The Well show that with these components, our model outperforms competing methods in forecasting accuracy, spectral consistency, and computational efficiency. Our model achieves a 42.9% average reduction in forecasting compared to our reference based on the Walrus finetuning methodology, and outperforms Walrus for 8 out of 10 datasets on variance-normalized RMSE (VRMSE).

cs.LG↗

arXiv2026

DiffusionGemma Technical Report

We introduce DiffusionGemma, an experimental open-weight language model that uses discrete diffusion to generate text at exceptionally high speed. Rather than decoding one token at a time, DiffusionGemma iteratively refines blocks of 256 tokens in parallel, avoiding the sequential decoding bottleneck of conventional autoregressive (AR) large language models. Instead of training from scratch, we obtain DiffusionGemma by fine-tuning the mixture-of-experts Gemma 4 model with 3.8B activated and 25.2B total parameters. Our compute-efficient two-stage training pipeline uses fewer than 10% of the starting AR model's total training token budget. The first stage uses supervised fine-tuning to teach bidirectional denoising, while the second stage combines reinforcement learning with sampler distillation to jointly improve generation quality and inference efficiency. DiffusionGemma establishes a new Pareto frontier for the trade-off between generation speed and model capability. Averaged across our full evaluation suite, it generates around 20 tokens per forward pass and achieves roughly 1,500 output tokens per second on a single NVIDIA H100 GPU, which is substantially faster than AR models even with state-of-the-art speculative decoding. DiffusionGemma also retains the starting model's support for thinking mode, multimodal inputs, and long contexts. Despite diffusion fine-tuning, it remains capable of AR generation with only minor performance degradation, suggesting a path toward hybrid diffusion-AR decoding.

cs.CL↗

arXiv2026

Diffusion Fine-tuning with Rewarded Moment Matching Distillation

Distillation and Reinforcement Learning (RL) fine-tuning are the primary pillars of diffusion post-training. While traditionally studied in isolation, the interaction between these phases remains poorly understood, and in particular how fine-tuning impacts the generative quality of distilled models. We introduce Rewarded Moment Matching Distillation (RMMD), a novel framework that simultaneously distills diffusion models and maximizes a reward function. RMMD preserves the high-fidelity ``naturalness'' characteristic of advanced distillation (such as 8-step Moment Matching) by adapting the sampling loop for on-policy training and repurposing the distillation loss as a proxy for integral KL regularization. By evaluating the FID-Reward Pareto fronts on ImageNet, we demonstrate that RMMD achieves superior trade-offs compared to single-step baselines (DI++) and multi-step competitors (DRaFT, HyperNoise). Finally, we apply RMMD to GenCast, a state-of-the-art weather forecasting model, to distill it while optimizing the Continuous Ranked Probability Score (CRPS) metric. The resulting distilled model achieves a 7.5x speedup while outperforming the teacher model on 93% of target weather variables, and being better calibrated. This proves that RMMD scales to complex, high-dimensional scientific domains.

cs.LG↗

arXiv2026

AsyncPatch Diffusion: spatially-flexible image generation

Standard diffusion models corrupt an entire sample with a single shared noise level, forcing all spatial regions to follow the same denoising trajectory. We introduce AsyncPatch Diffusion, a joint-diffusion framework that assigns distinct noise levels to different input dimensions, such as image pixels, or latent tokens. We show how this asynchronous corruption defines a valid generative process while supporting a richer family of spatially heterogeneous denoising trajectories, and prove the first valid ELBO for this process. We show that a single pretrained model can perform spatially adaptive generation, where different regions are denoised on different schedules. A key challenge is training: naive independent noise-level sampling overemphasizes highly heterogeneous configurations and underrepresents homogeneous noise levels, that are crucial during sampling. We address this with a controlled noise-level sampler that regulates both the average corruption level and its spatial variability. AsyncPatch achieves generation quality comparable to conventional diffusion on ImageNet 256 and LSUN, while being natively suited for inpainting without task-specific fine-tuning. We further introduce input guidance, which uses clean or partially corrupted regions to guide the generation of unknown regions, improving local consistency and texture matching. Finally, we demonstrate adaptive generation strategies including uncertainty-guided acceleration and autoregressive sampling.

cs.CV↗

arXiv2026

MIND: Monge Inception Distance for Generative Models Evaluation

We propose the Monge Inception Distance (MIND), a metric for evaluating generative models that addresses key limitations of the widely adopted Fréchet Inception Distance (FID). The MIND metric leverages the sliced Wasserstein distance to compare distributions by averaging one-dimensional optimal transport distances, efficiently computed via sorting. This approach circumvents the estimation of high-dimensional means and covariance matrices, which underlie FID's poor sample complexity and vulnerability to adversarial attacks. We empirically demonstrate three primary advantages: (i) it is more sample-efficient by one order of magnitude, (ii) it is faster to compute by two orders of magnitude, (iii) it is more robust to adversarial attacks such as moment-matching. We show that MIND with 5k samples can replace the evaluation performance of FID with 50k samples, providing high correlation with this standard benchmark and superior discriminative performance. We further demonstrate that even smaller sample sizes (e.g., 1k or 2k) remain highly informative for rapid model iteration.

cs.LG↗

arXiv2026

Fair regression under localized demographic parity constraints

Demographic parity (DP) is a widely used group fairness criterion requiring predictive distributions to be invariant across sensitive groups. While natural in classification, full distributional DP is often overly restrictive in regression and can lead to substantial accuracy loss. We propose a relaxation of DP tailored to regression, enforcing parity only at a finite set of quantile levels and/or score thresholds. Concretely, we introduce a novel (${\ell}$, Z)-fair predictor, which imposes groupwise CDF constraints of the form F f |S=s (z m ) = ${\ell}$ m for prescribed pairs (${\ell}$ m , z m ). For this setting, we derive closed-form characterizations of the optimal fair discretized predictor via a Lagrangian dual formulation and quantify the discretization cost, showing that the risk gap to the continuous optimum vanishes as the grid is refined. We further develop a model-agnostic post-processing algorithm based on two samples (labeled for learning a base regressor and unlabeled for calibration), and establish finite-sample guarantees on constraint violation and excess penalized risk. In addition, we introduce two alternative frameworks where we match group and marginal CDF values at selected score thresholds. In both settings, we provide closed-form solutions for the optimal fair discretized predictor. Experiments on synthetic and real datasets illustrate an interpretable fairness-accuracy trade-off, enabling targeted corrections at decision-relevant quantiles or thresholds while preserving predictive performance.

stat.ML↗

arXiv2026

Optimal Stopping in Latent Diffusion Models

We identify and analyze a surprising phenomenon of Latent Diffusion Models (LDMs) where the final steps of the diffusion can degrade sample quality. In contrast to conventional arguments that justify early stopping for numerical stability, this phenomenon is intrinsic to the dimensionality reduction in LDMs. We provide a principled explanation by analyzing the interaction between latent dimension and stopping time. Under a Gaussian framework with linear autoencoders, we characterize the conditions under which early stopping is needed to minimize the distance between generated and target distributions. More precisely, we show that lower-dimensional representations benefit from earlier termination, whereas higher-dimensional latent spaces require later stopping time. We further establish that the latent dimension interplays with other hyperparameters of the problem such as constraints in the parameters of score matching. Experiments on synthetic and real datasets illustrate these properties, underlining that early stopping can improve generative quality. Together, our results offer a theoretical foundation for understanding how the latent dimension influences the sample quality, and highlight stopping time as a key hyperparameter in LDMs.

stat.ML↗

arXiv2026

Clustering in Deep Stochastic Transformers

Transformers have revolutionized deep learning across various domains but understanding the precise token dynamics remains a theoretical challenge. Existing theories of deep Transformers with layer normalization typically predict that tokens cluster to a single point; however, these results rely on deterministic weight assumptions, which fail to capture the standard initialization scheme in Transformers. In this work, we show that accounting for the intrinsic stochasticity of random initialization alters this picture. More precisely, we analyze deep Transformers where noise arises from the random initialization of value matrices. Under diffusion scaling and token-wise RMS normalization, we prove that, as the number of Transformer layers goes to infinity, the discrete token dynamics converge to an interacting-particle system on the sphere where tokens are driven by a \emph{common} matrix-valued Brownian noise. In this limit, we show that initialization noise prevents the collapse to a single cluster predicted by deterministic models. For two tokens, we prove a phase transition governed by the interaction strength and the token dimension: unlike deterministic attention flows, antipodal configurations become attracting with positive probability. Numerical experiments confirm the predicted transition, reveal that antipodal formations persist for more than two tokens, and demonstrate that suppressing the intrinsic noise degrades accuracy.

stat.ML↗

arXiv2025

Dimension-free error estimate for diffusion model and optimal scheduling

Diffusion generative models have emerged as powerful tools for producing synthetic data from an empirically observed distribution. A common approach involves simulating the time-reversal of an Ornstein-Uhlenbeck (OU) process initialized at the true data distribution. Since the score function associated with the OU process is typically unknown, it is approximated using a trained neural network. This approximation, along with finite time simulation, time discretization and statistical approximation, introduce several sources of error whose impact on the generated samples must be carefully understood. Previous analyses have quantified the error between the generated and the true data distributions in terms of Wasserstein distance or Kullback-Leibler (KL) divergence. However, both metrics present limitations: KL divergence requires absolute continuity between distributions, while Wasserstein distance, though more general, leads to error bounds that scale poorly with dimension, rendering them impractical in high-dimensional settings. In this work, we derive an explicit, dimension-free bound on the discrepancy between the generated and the true data distributions. The bound is expressed in terms of a smooth test functional with bounded first and second derivatives. The key novelty lies in the use of this weaker, functional metric to obtain dimension-independent guarantees, at the cost of higher regularity on the test functions. As an application, we formulate and solve a variational problem to minimize the time-discretization error, leading to the derivation of an optimal time-scheduling strategy for the reverse-time diffusion. Interestingly, this scheduler has appeared previously in the literature in a different context; our analysis provides a new justification for its optimality, now grounded in minimizing the discretization bias in generative sampling.

stat.ML↗

arXiv2025

Language Agents as Digital Representatives in Collective Decision-Making

Consider the process of collective decision-making, in which a group of individuals interactively select a preferred outcome from among a universe of alternatives. In this context, "representation" is the activity of making an individual's preferences present in the process via participation by a proxy agent -- i.e. their "representative". To this end, learned models of human behavior have the potential to fill this role, with practical implications for multi-agent scenario studies and mechanism design. In this work, we investigate the possibility of training \textit{language agents} to behave in the capacity of representatives of human agents, appropriately expressing the preferences of those individuals whom they stand for. First, we formalize the setting of \textit{collective decision-making} -- as the episodic process of interaction between a group of agents and a decision mechanism. On this basis, we then formalize the problem of \textit{digital representation} -- as the simulation of an agent's behavior to yield equivalent outcomes from the mechanism. Finally, we conduct an empirical case study in the setting of \textit{consensus-finding} among diverse humans, and demonstrate the feasibility of fine-tuning large language models to act as digital representatives.

cs.LG↗

arXiv2024

Diversity-Rewarded CFG Distillation

Generative models are transforming creative domains such as music generation, with inference-time strategies like Classifier-Free Guidance (CFG) playing a crucial role. However, CFG doubles inference cost while limiting originality and diversity across generated contents. In this paper, we introduce diversity-rewarded CFG distillation, a novel finetuning procedure that distills the strengths of CFG while addressing its limitations. Our approach optimises two training objectives: (1) a distillation objective, encouraging the model alone (without CFG) to imitate the CFG-augmented predictions, and (2) an RL objective with a diversity reward, promoting the generation of diverse outputs for a given prompt. By finetuning, we learn model weights with the ability to generate high-quality and diverse outputs, without any inference overhead. This also unlocks the potential of weight-based model merging strategies: by interpolating between the weights of two models (the first focusing on quality, the second on diversity), we can control the quality-diversity trade-off at deployment time, and even further boost performance. We conduct extensive experiments on the MusicLM (Agostinelli et al., 2023) text-to-music generative model, where our approach surpasses CFG in terms of quality-diversity Pareto optimality. According to human evaluators, our finetuned-then-merged model generates samples with higher quality-diversity than the base model augmented with CFG. Explore our generations at https://google-research.github.io/seanet/musiclm/diverse_music/.

cs.LG↗

arXiv2024

Fair Active Learning: Solving the Labeling Problem in Insurance

This paper addresses significant obstacles that arise from the widespread use of machine learning models in the insurance industry, with a specific focus on promoting fairness. The initial challenge lies in effectively leveraging unlabeled data in insurance while reducing the labeling effort and emphasizing data relevance through active learning techniques. The paper explores various active learning sampling methodologies and evaluates their impact on both synthetic and real insurance datasets. This analysis highlights the difficulty of achieving fair model inferences, as machine learning models may replicate biases and discrimination found in the underlying data. To tackle these interconnected challenges, the paper introduces an innovative fair active learning method. The proposed approach samples informative and fair instances, achieving a good balance between model predictive performance and fairness, as confirmed by numerical experiments on insurance datasets.

stat.ML↗

arXiv2024

Using deep reinforcement learning to promote sustainable human behaviour on a common pool resource problem

A canonical social dilemma arises when finite resources are allocated to a group of people, who can choose to either reciprocate with interest, or keep the proceeds for themselves. What resource allocation mechanisms will encourage levels of reciprocation that sustain the commons? Here, in an iterated multiplayer trust game, we use deep reinforcement learning (RL) to design an allocation mechanism that endogenously promotes sustainable contributions from human participants to a common pool resource. We first trained neural networks to behave like human players, creating a stimulated economy that allowed us to study how different mechanisms influenced the dynamics of receipt and reciprocation. We then used RL to train a social planner to maximise aggregate return to players. The social planner discovered a redistributive policy that led to a large surplus and an inclusive economy, in which players made roughly equal gains. The RL agent increased human surplus over baseline mechanisms based on unrestricted welfare or conditional cooperation, by conditioning its generosity on available resources and temporarily sanctioning defectors by allocating fewer resources to them. Examining the AI policy allowed us to develop an explainable mechanism that performed similarly and was more popular among players. Deep reinforcement learning can be used to discover mechanisms that promote sustainable human behaviour.

cs.AI↗

arXiv2024

Approximating the Core via Iterative Coalition Sampling

The core is a central solution concept in cooperative game theory, defined as the set of feasible allocations or payments such that no subset of agents has incentive to break away and form their own subgroup or coalition. However, it has long been known that the core (and approximations, such as the least-core) are hard to compute. This limits our ability to analyze cooperative games in general, and to fully embrace cooperative game theory contributions in domains such as explainable AI (XAI), where the core can complement the Shapley values to identify influential features or instances supporting predictions by black-box models. We propose novel iterative algorithms for computing variants of the core, which avoid the computational bottleneck of many other approaches; namely solving large linear programs. As such, they scale better to very large problems as we demonstrate across different classes of cooperative games, including weighted voting games, induced subgraph games, and marginal contribution networks. We also explore our algorithms in the context of XAI, providing further evidence of the power of the core for such applications.

cs.GT↗

arXiv2023

TacticAI: an AI assistant for football tactics

Identifying key patterns of tactics implemented by rival teams, and developing effective responses, lies at the heart of modern football. However, doing so algorithmically remains an open research challenge. To address this unmet need, we propose TacticAI, an AI football tactics assistant developed and evaluated in close collaboration with domain experts from Liverpool FC. We focus on analysing corner kicks, as they offer coaches the most direct opportunities for interventions and improvements. TacticAI incorporates both a predictive and a generative component, allowing the coaches to effectively sample and explore alternative player setups for each corner kick routine and to select those with the highest predicted likelihood of success. We validate TacticAI on a number of relevant benchmark tasks: predicting receivers and shot attempts and recommending player position adjustments. The utility of TacticAI is validated by a qualitative study conducted with football domain experts at Liverpool FC. We show that TacticAI's model suggestions are not only indistinguishable from real tactics, but also favoured over existing tactics 90% of the time, and that TacticAI offers an effective corner kick retrieval system. TacticAI achieves these results despite the limited availability of gold-standard data, achieving data efficiency through geometric deep learning.

cs.LG↗

arXiv2023

A new Mertens decomposition of $\mathscr{Y}^{g,ξ}$-submartingale systems. Application to BSDEs with weak constraints at stopping times

We first introduce the concept of $\mathscr{Y}^{g,ξ}$-submartingale systems, where the nonlinear operator $\mathscr{Y}^{g,ξ}$ corresponds to the first component of the solution of a reflected BSDE with generator $g$ and lower obstacle $ξ$. We first show that, in the case of a left-limited right-continuous obstacle, any $\mathscr{Y}^{g,ξ}$-submartingale system can be aggregated by a process which is right-lower semicontinuous. We then prove a \textit{Mertens decomposition}, by using an original approach which does not make use of the standard penalization technique. These results are in particular useful for the treatment of control/stopping game problems and, to the best of our knowledge, they are completely new in the literature. As an application, we introduce a new class of \textit{Backward Stochastic Differential Equations (in short BSDEs) with weak constraints at stopping times}, which are related to the partial hedging of American options. We study the wellposedness of such equations and, using the $\mathscr{Y}^{g,ξ}$-Mertens decomposition, we show that the family of minimal time-$t$-values $Y_t$, with $(Y,Z)$ a supersolution of the BSDE with weak constraints, admits a representation in terms of a reflected backward stochastic differential equation.

math.OC↗

arXiv2023

Fairness guarantee in multi-class classification

Algorithmic Fairness is an established area of machine learning, willing to reduce the influence of hidden bias in the data. Yet, despite its wide range of applications, very few works consider the multi-class classification setting from the fairness perspective. We focus on this question and extend the definition of approximate fairness in the case of Demographic Parity to multi-class classification. We specify the corresponding expressions of the optimal fair classifiers. This suggests a plug-in data-driven procedure, for which we establish theoretical guarantees. The enhanced estimator is proved to mimic the behavior of the optimal rule both in terms of fairness and risk. Notably, fairness guarantees are distribution-free. The approach is evaluated on both synthetic and real datasets and reveals very effective in decision making with a preset level of unfairness. In addition, our method is competitive (if not better) with the state-of-the-art in binary and multi-class tasks.

math.ST↗