Michael Wunder

Hanna Mazzawi, Xavi Gonzalvo, Michael Wunder et al.

In recent years, deep learning has made remarkable progress in a wide range of domains, with a particularly notable impact on natural language processing tasks. One of the challenges associated with training deep neural networks in the context of LLMs is the need for large amounts of computational resources and time. To mitigate this, network growing algorithms offer potential cost savings, but their underlying mechanisms are poorly understood. We present two notable contributions in this paper. First, we present Deep Fusion, an efficient approach to network training that leverages pre-trained initializations of smaller networks. Second, we propose a theoretical framework using backward error analysis to illustrate the dynamics of mid-training network growth. Our experiments show how Deep Fusion is a practical and effective approach that not only accelerates the training process but also reduces computational requirements, maintaining or surpassing traditional training methods' performance in various NLP tasks and T5 model sizes. Finally, we validate our theoretical framework, which guides the optimal use of Deep Fusion, showing that with carefully optimized training dynamics, it significantly reduces both training time and resource consumption.

Gheorghe Comanici, Eric Bieber, Mike Schaekermann et al. · amazon-science, baidu

In this report, we introduce the Gemini 2.X model family: Gemini 2.5 Pro and Gemini 2.5 Flash, as well as our earlier Gemini 2.0 Flash and Flash-Lite models. Gemini 2.5 Pro is our most capable model yet, achieving SoTA performance on frontier coding and reasoning benchmarks. In addition to its incredible coding and reasoning skills, Gemini 2.5 Pro is a thinking model that excels at multimodal understanding and it is now able to process up to 3 hours of video content. Its unique combination of long context, multimodal and reasoning capabilities can be combined to unlock new agentic workflows. Gemini 2.5 Flash provides excellent reasoning abilities at a fraction of the compute and latency requirements and Gemini 2.0 Flash and Flash-Lite provide high performance at low latency and cost. Taken together, the Gemini 2.X model generation spans the full Pareto frontier of model capability vs cost, allowing users to explore the boundaries of what is possible with complex agentic problem solving.

Kyriakos Axiotis, Vincent Cohen-Addad, Monika Henzinger et al.

We study the data selection problem, whose aim is to select a small representative subset of data that can be used to efficiently train a machine learning model. We present a new data selection approach based on $k$-means clustering and sensitivity sampling. Assuming access to an embedding representation of the data with respect to which the model loss is Hölder continuous, our approach provably allows selecting a set of ``typical'' $k + 1/\varepsilon^2$ elements whose average loss corresponds to the average loss of the whole dataset, up to a multiplicative $(1\pm\varepsilon)$ factor and an additive $\varepsilon λΦ_k$, where $Φ_k$ represents the $k$-means cost for the input embeddings and $λ$ is the Hölder constant. We furthermore demonstrate the performance and scalability of our approach on fine-tuning foundation models and show that it outperforms state-of-the-art methods. We also show how it can be applied on linear regression, leading to a new sampling strategy that surprisingly matches the performances of leverage score sampling, while being conceptually simpler and more scalable.

Benoit Dherin, Michael Munn, Hanna Mazzawi et al.

One of the most striking features of Large Language Models (LLM) is their ability to learn in context. Namely at inference time an LLM is able to learn new patterns without any additional weight update when these patterns are presented in the form of examples in the prompt, even if these patterns were not seen during training. The mechanisms through which this can happen are still largely unknown. In this work, we show that the stacking of a self-attention layer with an MLP, allows the transformer block to implicitly modify the weights of the MLP layer according to the context. We argue through theory and experimentation that this simple mechanism may be the reason why LLMs can learn in context and not only during training. Specifically, we show under mild simplifying assumptions how a transformer block implicitly transforms a context into a low-rank weight-update of the MLP layer.

Hanna Mazzawi, Benoit Dherin, Michael Munn et al.

A growing body of research has demonstrated that the behavior of large language models can be effectively controlled at inference time by directly modifying their internal states, either through vector additions to their activations or through updates to their weight matrices. These techniques, while powerful, are often guided by empirical heuristics, such as deriving steering vectors from the average activations of contrastive prompts. This work provides a theoretical foundation for these interventions, explaining how they emerge from the fundamental computations of the transformer architecture. Building on the recent finding that a prompt's influence can be mathematically mapped to implicit weight updates (Dherin et al., 2025), we generalize this theory to deep, multi-block transformers. We show how the information contained in any chunk of a user prompt is represented and composed internally through weight vectors and weight matrices. We then derive a principled method for condensing this information into token-independent thought vectors and thought matrices. These constructs provide a theoretical explanation for existing vector- and matrix-based model editing techniques and offer a direct, computationally-grounded method for transmuting textual input into reusable weight updates.

Benoit Dherin, Michael Munn, Hanna Mazzawi et al.

Modern deep learning algorithms use variations of gradient descent as their main learning methods. Gradient descent can be understood as the simplest Ordinary Differential Equation (ODE) solver; namely, the Euler method applied to the gradient flow differential equation. Since Euler, many ODE solvers have been devised that follow the gradient flow equation more precisely and more stably. Runge-Kutta (RK) methods provide a family of very powerful explicit and implicit high-order ODE solvers. However, these higher-order solvers have not found wide application in deep learning so far. In this work, we evaluate the performance of higher-order RK solvers when applied in deep learning, study their limitations, and propose ways to overcome these drawbacks. In particular, we explore how to improve their performance by naturally incorporating key ingredients of modern neural network optimizers such as preconditioning, adaptive learning rates, and momentum.