Nuclear fusion plays a pivotal role in the quest for reliable and sustainable energy production. A major roadblock to achieving commercially viable fusion power is understanding plasma turbulence, which can significantly degrade plasma confinement. Modelling turbulence is crucial to design performing plasma scenarios for next-generation reactor-class devices and current experimental machines. The nonlinear gyrokinetic equation underpinning turbulence modelling evolves a 5D distribution function over time. Solving this equation numerically is extremely expensive, requiring up to weeks for a single run to converge, making it unfeasible for iterative optimisation and control studies. In this work, we propose a method for training neural surrogates for 5D gyrokinetic simulations. Our method extends a hierarchical vision transformer to five dimensions and is trained on the 5D distribution function for the adiabatic electron approximation. We demonstrate that our model can accurately infer downstream physical quantities such as heat flux time trace and electrostatic potentials for single-step predictions two orders of magnitude faster than numerical codes. Our work paves the way towards neural surrogates for plasma turbulence simulations to accelerate deployment of commercial energy production via nuclear fusion.

One of the key applications of large language models (LLMs), with temperature generative models that has garnered significant interest set to 0 and top p set to 1, across eight common is the development of specialized chatbots tasks and five identical trials per task. The study with domain-specific expertise such as legal and aimed to assess the repeatability of model outputs healthcare (Lexis; Mesko, 2023). These applications by examining whether the generated strings were illustrate how generative models can improve consistent between runs. The authors found that decision-making and improve the efficiency of professional none of the LLMs demonstrated consistent performance services in specialized fields.

We introduce the Riemannian Proximal Sampler, a method for sampling from densities defined on Riemannian manifolds. The performance of this sampler critically depends on two key oracles: the Manifold Brownian Increments (MBI) oracle and the Riemannian Heat-kernel (RHK) oracle. We establish high-accuracy sampling guarantees for the Riemannian Proximal Sampler, showing that generating samples with $\varepsilon$-accuracy requires $O(\log(1/\varepsilon))$ iterations in Kullback-Leibler divergence assuming access to exact oracles and $O(\log^2(1/\varepsilon))$ iterations in the total variation metric assuming access to sufficiently accurate inexact oracles. Furthermore, we present practical implementations of these oracles by leveraging heat-kernel truncation and Varadhan's asymptotics. In the latter case, we interpret the Riemannian Proximal Sampler as a discretization of the entropy-regularized Riemannian Proximal Point Method on the associated Wasserstein space. We provide preliminary numerical results that illustrate the effectiveness of the proposed methodology.

Real-world data is often ambiguous; for example, human annotation produces instances with multiple conflicting class labels. Partial-label learning (PLL) aims at training a classifier in this challenging setting, where each instance is associated with a set of candidate labels and one correct, but unknown, class label. A multitude of algorithms targeting this setting exists and, to enhance their prediction quality, several extensions that are applicable across a wide range of PLL methods have been introduced. While many of these extensions rely on heuristics, this article proposes a novel enhancing method that incrementally prunes candidate sets using conformal prediction. To work around the missing labeled validation set, which is typically required for conformal prediction, we propose a strategy that alternates between training a PLL classifier to label the validation set, leveraging these predicted class labels for calibration, and pruning candidate labels that are not part of the resulting conformal sets. In this sense, our method alternates between empirical risk minimization and candidate set pruning. We establish that our pruning method preserves the conformal validity with respect to the unknown ground truth. Our extensive experiments on artificial and real-world data show that the proposed approach significantly improves the test set accuracies of several state-of-the-art PLL classifiers.

Negative dependence is becoming a key driver in advancing learning capabilities beyond the limits of traditional independence. Recent developments have evidenced support towards negatively dependent systems as a learning paradigm in a broad range of fundamental machine learning challenges including optimization, sampling, dimensionality reduction and sparse signal recovery, often surpassing the performance of current methods based on statistical independence. The most popular negatively dependent model has been that of determinantal point processes (DPPs), which have their origins in quantum theory. However, other models, such as perturbed lattice models, strongly Rayleigh measures, zeros of random functions have gained salience in various learning applications. In this article, we review this burgeoning field of research, as it has developed over the past two decades or so. We also present new results on applications of DPPs to the parsimonious representation of neural networks. In the limited scope of the article, we mostly focus on aspects of this area to which the authors contributed over the recent years, including applications to Monte Carlo methods, coresets and stochastic gradient descent, stochastic networks, signal processing and connections to quantum computation. However, starting from basics of negative dependence for the uninitiated reader, extensive references are provided to a broad swath of related developments which could not be covered within our limited scope. While existing works and reviews generally focus on specific negatively dependent models (e.g. DPPs), a notable feature of this article is that it addresses negative dependence as a machine learning methodology as a whole. In this vein, it covers within its span an array of negatively dependent models and their applications well beyond DPPs, thereby putting forward a very general and rather unique perspective.

Recent advances in large language models (LLMs) have shown remarkable performance across diverse tasks. However, these models are typically deployed with fixed weights, which limits their ability to adapt dynamically to the variability inherent in real-world data during inference. This paper introduces ChameleonLLM, a novel framework that enables inference-time adaptation of LLMs by leveraging batch-aware clustering and on-the-fly generation of low-rank updates. Unlike traditional fine-tuning approaches such as Low-Rank Adaptation (LoRA) or methods that rely on a fixed set of pre-learned uniforms (changeable masks), our method dynamically generates adaptive modifications to the decoder weights based on the aggregated statistics of clustered batches. By intelligently grouping similar inputs and computing context-aware low-rank updates via a hyper-network, ChameleonLLM achieves significant performance gains, outperforming conventional LoRA methods while eliminating the overhead of maintaining multiple expert models. Our experiments highlight the potential of our approach to serve as a versatile and highly adaptive solution for language model inference. ChameleonLLM is open-sourced to ensure the reproducibility of our experiments: https://anonymous.4open.science/r/ChamaleonLLM/

This paper is focused on statistical learning from data that come as probability measures. In this setting, popular approaches consist in embedding such data into a Hilbert space with either Linearized Optimal Transport or Kernel Mean Embedding. However, the cost of computing such embeddings prohibits their direct use in large-scale settings. We study two methods based on measure quantization for approximating input probability measures with discrete measures of small-support size. The first one is based on optimal quantization of each input measure, while the second one relies on mean-measure quantization. We study the consistency of such approximations, and its implication for scalable embeddings of probability measures into a Hilbert space at a low computational cost. We finally illustrate our findings with various numerical experiments.

The ability to identify useful features or representations of the input data based on training data that achieves low prediction error on test data across multiple prediction tasks is considered the key to multitask learning success. In practice, however, one faces the issue of the choice of prediction tasks and the availability of test data from the chosen tasks while comparing the relative performance of different features. In this work, we develop a class of pseudometrics called Uniform Kernel Prober (UKP) for comparing features or representations learned by different statistical models such as neural networks when the downstream prediction tasks involve kernel ridge regression. The proposed pseudometric, UKP, between any two representations, provides a uniform measure of prediction error on test data corresponding to a general class of kernel ridge regression tasks for a given choice of a kernel without access to test data. Additionally, desired invariances in representations can be successfully captured by UKP only through the choice of the kernel function and the pseudometric can be efficiently estimated from $n$ input data samples with $O(\frac{1}{\sqrt{n}})$ estimation error. We also experimentally demonstrate the ability of UKP to discriminate between different types of features or representations based on their generalization performance on downstream kernel ridge regression tasks.

Modern adaptive optimization methods, such as Adam and its variants, have emerged as the most widely used tools in deep learning over recent years. These algorithms offer automatic mechanisms for dynamically adjusting the update step based on estimates of gradient statistics. Compared to traditional algorithms like Stochastic Gradient Descent, these adaptive methods are typically more robust to model scale and hyperparameter tuning. However, the gradient statistics employed by these methods often do not leverage sufficient gradient covariance information, leading to suboptimal updates in certain directions of the parameter space and potentially slower convergence. In this work, we keep track of such covariance statistics in the form of a structured preconditioner matrix. Unlike other works, our approach does not apply direct approximations to estimate this matrix. We instead implement an invertible transformation that maps the preconditioner matrix into a new space where it becomes approximately diagonal. This enables a diagonal approximation of the preconditioner matrix in the transformed space, offering several computational advantages. Empirical results show that our approach can substantially enhance the convergence speed of modern adaptive optimizers. Notably, for large language models like LLaMA, we can achieve a speedup of 2x compared to the baseline Adam. Additionally, our method can be integrated with memory-efficient optimizers like Adafactor to manage computational overhead.

We investigate the problem of distributed training under partial observability, whereby cooperative multi-agent reinforcement learning agents (MARL) maximize the expected cumulative joint reward. We propose distributed value decomposition networks (DVDN) that generate a joint Q-function that factorizes into agent-wise Q-functions. Whereas the original value decomposition networks rely on centralized training, our approach is suitable for domains where centralized training is not possible and agents must learn by interacting with the physical environment in a decentralized manner while communicating with their peers. DVDN overcomes the need for centralized training by locally estimating the shared objective. We contribute with two innovative algorithms, DVDN and DVDN (GT), for the heterogeneous and homogeneous agents settings respectively. Empirically, both algorithms approximate the performance of value decomposition networks, in spite of the information loss during communication, as demonstrated in ten MARL tasks in three standard environments.