It is shown that, under mild technical assumptions and the introduction of the \textit{suboptimality gap}, the independent NPG method with an oracle providing exact policy evaluation asymptotically reaches an $\epsilon$-Nash Equilibrium (NE) within $\mathcal{O}(1/\epsilon)$ iterations. This improves upon the previous best result of $\mathcal{O}(1/\epsilon^2)$ iterations and is of the same order, $\mathcal{O}(1/\epsilon)$, that is achievable for the single-agent case. Empirical results for a synthetic potential game and a congestion game are presented to verify the theoretical bounds.

Confocal fluorescence microscopy is one of the most accessible and widely used imaging techniques for the study of biological processes at the cellular and subcellular levels. Scanning confocal microscopy allows the capture of high-quality images from thick three-dimensional (3D) samples, yet suffers from well-known limitations such as photobleaching and phototoxicity of specimens caused by intense light exposure, which limits its use in some applications, especially for living cells. Cellular damage can be alleviated by changing imaging parameters to reduce light exposure, often at the expense of image quality.Machine/deep learning methods for single-image super-resolution (SISR) can be applied to restore image quality by upscaling lower-resolution (LR) images to produce high-resolution images (HR). These SISR methods have been successfully applied to photo-realistic images due partly to the abundance of publicly available datasets. In contrast, the lack of publicly available data partly limits their application and success in scanning confocal microscopy.In this paper, we introduce a large scanning confocal microscopy dataset named SR-CACO-2 that is comprised of low-and high-resolution image pairs marked for three different fluorescent markers. It allows to evaluate the performance of SISR methods on three different upscaling levels (X2, X4, X8).

We propose weakly coupled deep Q-networks (WCDQN), a novel deep reinforcement learning algorithm that enhances performance in a class of structured problems called weakly coupled Markov decision processes (WCMDP). WCMDPs consist of multiple independent subproblems connected by an action space constraint, which is a structural property that frequently emerges in practice. Despite this appealing structure, WCMDPs quickly become intractable as the number of subproblems grows. WCDQN employs a single network to train multiple DQN ``subagents,'' one for each subproblem, and then combine their solutions to establish an upper bound on the optimal action value.

Current PEFT methods for LLMs can achieve high quality, efficient training, or scalable serving, but not all three simultaneously. To address this limitation, we investigate sparse fine-tuning and observe a remarkable improvement in generalization ability. Utilizing this key insight, we propose a family of Structured Sparse Fine-Tuning (S${^2}$FT) methods for LLMs, which concurrently achieve state-of-the-art fine-tuning performance, training efficiency, and inference scalability. S${^2}$FT accomplishes this by selecting sparsely and computing densely. Based on the coupled structures in LLMs, \model selects a few attention heads and channels in the MHA and FFN modules for each Transformer block, respectively. Next, it co-permutes the weight matrices on both sides of all coupled structures to connect the selected subsets in each layer into a dense submatrix. Finally, S${^2}$FT performs in-place gradient updates on all selected submatrices.Through theoretical analyses and empirical results, our method prevents forgetting while simplifying optimization, delivers SOTA performance on both commonsense and arithmetic reasoning with 4.6% and 1.3% average improvements compared to LoRA, and surpasses full FT by 11.5% when generalizing to various domains after instruction tuning. Using our partial back-propagation algorithm, S${^2}$FT saves training memory up to 3$\times$ and improves latency by 1.5-2.7$\times$

Predicting upcoming events is critical to our ability to effectively interact with ourenvironment and conspecifics. In natural language processing, transformer models,which are trained on next-word prediction, appear to construct a general-purposerepresentation of language that can support diverse downstream tasks. However, westill lack an understanding of how a predictive objective shapes such representations.Inspired by recent work in vision neuroscience Hénaff et al. (2019), here we test ahypothesis about predictive representations of autoregressive transformer models.In particular, we test whether the neural trajectory of a sequence of words in asentence becomes progressively more straight as it passes through the layers of thenetwork. The key insight behind this hypothesis is that straighter trajectories shouldfacilitate prediction via linear extrapolation. We quantify straightness using a 1-dimensional curvature metric, and present four findings in support of the trajectorystraightening hypothesis: i) In trained models, the curvature progressively decreasesfrom the first to the middle layers of the network.

We consider off-dynamics reinforcement learning (RL) where one needs to transfer policies across different domains with dynamics mismatch. Despite the focus on developing dynamics-aware algorithms, this field is hindered due to the lack of a standard benchmark. To bridge this gap, we introduce ODRL, the first benchmark tailored for evaluating off-dynamics RL methods. ODRL contains four experimental settings where the source and target domains can be either online or offline, and provides diverse tasks and a broad spectrum of dynamics shifts, making it a reliable platform to comprehensively evaluate the agent's adaptation ability to the target domain. Furthermore, ODRL includes recent off-dynamics RL algorithms in a unified framework and introduces some extra baselines for different settings, all implemented in a single-file manner. To unpack the true adaptation capability of existing methods, we conduct extensive benchmarking experiments, which show that no method has universal advantages across varied dynamics shifts. We hope this benchmark can serve as a cornerstone for future research endeavors.

Many areas of machine learning and science involve large linear algebra problems, such as eigendecompositions, solving linear systems, computing matrix exponentials, and trace estimation. The matrices involved often have Kronecker, convolutional, block diagonal, sum, or product structure. In this paper, we propose a simple but general framework for large-scale linear algebra problems in machine learning, named CoLA (Compositional Linear Algebra).

Presenting users with diverse responses from foundation models is crucial for enhancing user experience and accommodating varying preferences. However, generating multiple high-quality and diverse responses without sacrificing accuracy remains a challenge, especially when using greedy sampling. In this work, we propose a novel framework, Synthesize-Partition-Adapt (SPA), that leverages the abundant synthetic data available in many domains to elicit diverse responses from foundation models.By leveraging signal provided by data attribution methods such as influence functions, SPA partitions data into subsets, each targeting unique aspects of the data, and trains multiple model adaptations optimized for these subsets.Experimental results demonstrate the effectiveness of our approach in diversifying foundation model responses while maintaining high quality, showcased through the HumanEval and MBPP tasks in the code generation domain and several tasks in the natural language understanding domain, highlighting its potential to enrich user experience across various applications.

Each cloud of data points is obtained via a double-stochastic process, where the sample is obtained from a Gaussian distribution whose variance is itself a random parameter sampled from a scalar distribution $\varrho$. As a result, our analysis covers a large family of data distributions, including the case of power-law-tailed distributions with no covariance, and allows us to test recent ''Gaussian universality'' claims. We study the generalisation performance of the obtained estimator, we analyse the role of regularisation, and we analytically characterise the separability transition.

The essence of multi-modal fusion lies in exploiting the complementary information inherent in diverse modalities.However, most prevalent fusion methods rely on traditional neural architectures and are inadequately equipped to capture the dynamics of interactions across modalities, particularly in presence of complex intra-and inter-modality correlations.Recent advancements in State Space Models (SSMs), notably exemplified by the Mamba model, have emerged as promising contenders. Particularly, its state evolving process implies stronger modality fusion paradigm, making multi-modal fusion on SSMs an appealing direction. However, fusing multiple modalities is challenging for SSMs due to its hardware-aware parallelism designs. To this end, this paper proposes the Coupled SSM model, for coupling state chains of multiple modalities while maintaining independence of intra-modality state processes. Specifically, in our coupled scheme, we devise an inter-modal hidden states transition scheme, in which the current state is dependent on the states of its own chain and that of the neighbouring chains at the previous time-step. To fully comply with the hardware-aware parallelism, we obtain the global convolution kernel by deriving the state equation while introducing the historical state.Extensive experiments on CMU-MOSEI, CH-SIMS, CH-SIMSV2 through multi-domain input verify the effectiveness of our model compared to current state-of-the-art methods, improved F1-Score by 0.4%, 0.9%, and 2.3% on the three datasets respectively, 49% faster inference and 83.7% GPU memory save. The results demonstrate that Coupled Mamba model is capable of enhanced multi-modal fusion.