Christophe Roux

Max Zimmer, Nico Pelleriti, Christophe Roux et al.

AI tools and agents are reshaping how researchers work, from proving theorems to training neural networks. Yet for many, it remains unclear how these tools fit into everyday research practice. This paper is a practical guide to AI-assisted research in mathematics and machine learning: We discuss how researchers can use modern AI systems productively, where these systems help most, and what kinds of guardrails are needed to use them responsibly. It is organized into three parts: (I) a five-level taxonomy of AI integration, (II) an open-source framework that, through a set of methodological rules formulated as agent prompts, turns CLI coding agents (e.g., Claude Code, Codex CLI, OpenCode) into autonomous research assistants, and (III) case studies from deep learning and mathematics. The framework runs inside a sandboxed container, works with any frontier LLM through existing CLI agents, is simple enough to install and use within minutes, and scales from personal-laptop prototyping to multi-node, multi-GPU experimentation across compute clusters. In practice, our longest autonomous session ran for over 20 hours, dispatching independent experiments across multiple nodes without human intervention. We stress that our framework is not intended to replace the researcher in the loop, but to augment them. Our code is publicly available at https://github.com/ZIB-IOL/The-Agentic-Researcher.

Christophe Roux, Max Zimmer, Sebastian Pokutta

Federated Learning (FL) algorithms using Knowledge Distillation (KD) have received increasing attention due to their favorable properties with respect to privacy, non-i.i.d. data and communication cost. These methods depart from transmitting model parameters and instead communicate information about a learning task by sharing predictions on a public dataset. In this work, we study the performance of such approaches in the byzantine setting, where a subset of the clients act in an adversarial manner aiming to disrupt the learning process. We show that KD-based FL algorithms are remarkably resilient and analyze how byzantine clients can influence the learning process. Based on these insights, we introduce two new byzantine attacks and demonstrate their ability to break existing byzantine-resilient methods. Additionally, we propose a novel defence method which enhances the byzantine resilience of KD-based FL algorithms. Finally, we provide a general framework to obfuscate attacks, making them significantly harder to detect, thereby improving their effectiveness. Our findings serve as an important building block in the analysis of byzantine FL, contributing through the development of new attacks and new defence mechanisms, further advancing the robustness of KD-based FL algorithms.

Christophe Roux, David Martínez-Rubio, Sebastian Pokutta

We introduce a Riemannian optimistic online learning algorithm for Hadamard manifolds based on inexact implicit updates. Unlike prior work, our method can handle in-manifold constraints, and matches the best known regret bounds in the Euclidean setting with no dependence on geometric constants, like the minimum curvature. Building on this, we develop algorithms for g-convex, g-concave smooth min-max problems on Hadamard manifolds. Notably, one method nearly matches the gradient oracle complexity of the lower bound for Euclidean problems, for the first time.

Max Zimmer, Christophe Roux, Moritz Wagner et al.

The resource requirements of neural networks can be significantly reduced through pruning - the removal of seemingly less important parameters. However, for LLMs, full retraining to recover pruning-induced performance degradation is often prohibitive and classical approaches such as magnitude pruning are suboptimal on Transformers. State-of-the-art methods hence solve a layer-wise mask selection problem: finding a pruning mask that minimizes per-layer pruning error on a small set of calibration data. Exactly solving this problem is computationally infeasible due to its combinatorial nature and the size of the search space, and existing approaches rely on approximations or heuristics. We demonstrate that the mask selection problem can be made drastically more tractable at LLM scale. To that end, we decouple the rows by enforcing equal sparsity levels per row. This allows us to derive optimal 1-swaps (exchanging one kept and one pruned weight) computable efficiently via the Gram matrix. We propose a simple 1-swap algorithm that warmstarts from any pruning mask, runs efficiently on GPUs at LLM scale, and is essentially hyperparameter-free. Our approach reduces per-layer pruning error by up to 60% over Wanda (Sun et al., 2024) and consistently improves perplexity and zero-shot accuracy across state-of-the-art GPT architectures.

Moritz Wagner, Christophe Roux, Max Zimmer et al.

While Neural Network pruning typically requires retraining the model to recover pruning-induced performance degradation, state-of-the-art Large Language Models (LLMs) pruning methods instead solve a layer-wise mask selection and reconstruction problem on a small set of calibration data to avoid full retraining, as it is considered computationally infeasible for LLMs. Reconstructing single matrices in isolation has favorable properties, such as convexity of the objective and significantly reduced memory requirements compared to full retraining. In practice, however, reconstruction is often implemented at coarser granularities, e.g., reconstructing a whole transformer block against its dense activations instead of a single matrix. In this work, we study the key design choices when reconstructing or retraining the remaining weights after pruning. We conduct an extensive computational study on state-of-the-art GPT architectures, and report several surprising findings that challenge common intuitions about retraining after pruning. In particular, we observe a free lunch scenario: reconstructing attention and MLP components separately within each transformer block is nearly the most resource-efficient yet achieves the best perplexity. Most importantly, this Pareto-optimal setup achieves better performance than full retraining, despite requiring only a fraction of the memory. Furthermore, we demonstrate that simple and efficient pruning criteria such as Wanda can outperform much more complex approaches when the reconstruction step is properly executed, highlighting its importance. Our findings challenge the narrative that retraining should be avoided at all costs and provide important insights into post-pruning performance recovery for LLMs.

Christophe Roux, Max Zimmer, Alexandre d'Aspremont et al.

Pruning is a common technique to reduce the compute and storage requirements of Neural Networks. While conventional approaches typically retrain the model to recover pruning-induced performance degradation, state-of-the-art Large Language Model (LLM) pruning methods operate layer-wise, minimizing the per-layer pruning error on a small calibration dataset to avoid full retraining, which is considered computationally prohibitive for LLMs. However, finding the optimal pruning mask is a hard combinatorial problem and solving it to optimality is intractable. Existing methods hence rely on greedy heuristics that ignore the weight interactions in the pruning objective. In this work, we instead consider the convex relaxation of these combinatorial constraints and solve the resulting problem using the Frank-Wolfe (FW) algorithm. Our method drastically reduces the per-layer pruning error, outperforms strong baselines on state-of-the-art GPT architectures, and remains memory-efficient. We provide theoretical justification by showing that, combined with the convergence guarantees of the FW algorithm, we obtain an approximate solution to the original combinatorial problem upon rounding the relaxed solution to integrality.

David Martínez-Rubio, Christophe Roux, Christopher Criscitiello et al.

In this work, we study optimization problems of the form $\min_x \max_y f(x, y)$, where $f(x, y)$ is defined on a product Riemannian manifold $\mathcal{M} \times \mathcal{N}$ and is $μ_x$-strongly geodesically convex (g-convex) in $x$ and $μ_y$-strongly g-concave in $y$, for $μ_x, μ_y \geq 0$. We design accelerated methods when $f$ is $(L_x, L_y, L_{xy})$-smooth and $\mathcal{M}$, $\mathcal{N}$ are Hadamard. To that aim we introduce new g-convex optimization results, of independent interest: we show global linear convergence for metric-projected Riemannian gradient descent and improve existing accelerated methods by reducing geometric constants. Additionally, we complete the analysis of two previous works applying to the Riemannian min-max case by removing an assumption about iterates staying in a pre-specified compact set.

Christophe Roux, Elias Wirth, Sebastian Pokutta et al.

Several learning problems involve solving min-max problems, e.g., empirical distributional robust learning or learning with non-standard aggregated losses. More specifically, these problems are convex-linear problems where the minimization is carried out over the model parameters $w\in\mathcal{W}$ and the maximization over the empirical distribution $p\in\mathcal{K}$ of the training set indexes, where $\mathcal{K}$ is the simplex or a subset of it. To design efficient methods, we let an online learning algorithm play against a (combinatorial) bandit algorithm. We argue that the efficiency of such approaches critically depends on the structure of $\mathcal{K}$ and propose two properties of $\mathcal{K}$ that facilitate designing efficient algorithms. We focus on a specific family of sets $\mathcal{S}_{n,k}$ encompassing various learning applications and provide high-probability convergence guarantees to the minimax values.

Thomas Kerdreux, Christophe Roux, Alexandre d'Aspremont et al.

Linear bandit algorithms yield $\tilde{\mathcal{O}}(n\sqrt{T})$ pseudo-regret bounds on compact convex action sets $\mathcal{K}\subset\mathbb{R}^n$ and two types of structural assumptions lead to better pseudo-regret bounds. When $\mathcal{K}$ is the simplex or an $\ell_p$ ball with $p\in]1,2]$, there exist bandits algorithms with $\tilde{\mathcal{O}}(\sqrt{nT})$ pseudo-regret bounds. Here, we derive bandit algorithms for some strongly convex sets beyond $\ell_p$ balls that enjoy pseudo-regret bounds of $\tilde{\mathcal{O}}(\sqrt{nT})$, which answers an open question from [BCB12, §5.5.]. Interestingly, when the action set is uniformly convex but not necessarily strongly convex, we obtain pseudo-regret bounds with a dimension dependency smaller than $\mathcal{O}(\sqrt{n})$. However, this comes at the expense of asymptotic rates in $T$ varying between $\tilde{\mathcal{O}}(\sqrt{T})$ and $\tilde{\mathcal{O}}(T)$.