We propose a new algorithm for efficiently solving the damped Fisher matrix in large-scale scenarios where the number of parameters significantly exceeds the number of available samples. This problem is fundamental for natural gradient descent and stochastic reconfiguration. Our algorithm is based on Cholesky decomposition and is generally applicable. Benchmark results show that the algorithm is significantly faster than existing methods.

Automatic sign language recognition is an important topic within the areas of human-computer interaction and machine learning. On the one hand, it poses a complex challenge that requires the intervention of various knowledge areas, such as video processing, image processing, intelligent systems and linguistics. On the other hand, robust recognition of sign language could assist in the translation process and the integration of hearing-impaired people. This paper offers two main contributions: first, the creation of a database of handshapes for the Argentinian Sign Language (LSA), which is a topic that has barely been discussed so far. Secondly, a technique for image processing, descriptor extraction and subsequent handshape classification using a supervised adaptation of self-organizing maps that is called ProbSom. This technique is compared to others in the state of the art, such as Support Vector Machines (SVM), Random Forests, and Neural Networks. The database that was built contains 800 images with 16 LSA handshapes, and is a first step towards building a comprehensive database of Argentinian signs. The ProbSom-based neural classifier, using the proposed descriptor, achieved an accuracy rate above 90%.

Federated learning, a decentralized approach to machine learning, faces significant challenges such as extensive communication overheads, slow convergence, and unstable improvements. These challenges primarily stem from the gradient variance due to heterogeneous client data distributions. To address this, we introduce a novel Networked Control Variates (FedNCV) framework for Federated Learning. We adopt the REINFORCE Leave-One-Out (RLOO) as a fundamental control variate unit in the FedNCV framework, implemented at both client and server levels. At the client level, the RLOO control variate is employed to optimize local gradient updates, mitigating the variance introduced by data samples. Once relayed to the server, the RLOO-based estimator further provides an unbiased and low-variance aggregated gradient, leading to robust global updates. This dual-side application is formalized as a linear combination of composite control variates. We provide a mathematical expression capturing this integration of double control variates within FedNCV and present three theoretical results with corresponding proofs. This unique dual structure equips FedNCV to address data heterogeneity and scalability issues, thus potentially paving the way for large-scale applications. Moreover, we tested FedNCV on six diverse datasets under a Dirichlet distribution with {\alpha} = 0.1, and benchmarked its performance against six SOTA methods, demonstrating its superiority.

We present a novel extension to the family of Soft Actor-Critic (SAC) algorithms. We argue that based on the Maximum Entropy Principle, discrete SAC can be further improved via additional statistical constraints derived from a surrogate critic policy. Furthermore, our findings suggests that these constraints provide an added robustness against potential domain shifts, which are essential for safe deployment of reinforcement learning agents in the real-world. We provide theoretical analysis and show empirical results on low data regimes for both in-distribution and out-of-distribution variants of Atari 2600 games.

We present a new loss function that addresses the out-of-distribution (OOD) calibration problem. While many objective functions have been proposed to effectively calibrate models in-distribution, our findings show that they do not always fare well OOD. Based on the Principle of Maximum Entropy, we incorporate helpful statistical constraints observed during training, delivering better model calibration without sacrificing accuracy. We provide theoretical analysis and show empirically that our method works well in practice, achieving state-of-the-art calibration on both synthetic and real-world benchmarks.

Out-of-distribution (OOD) detection is important for deploying reliable machine learning models on real-world applications. Recent advances in outlier exposure have shown promising results on OOD detection via fine-tuning model with informatively sampled auxiliary outliers. However, previous methods assume that the collected outliers can be sufficiently large and representative to cover the boundary between ID and OOD data, which might be impractical and challenging. In this work, we propose a novel framework, namely, Diversified Outlier Exposure (DivOE), for effective OOD detection via informative extrapolation based on the given auxiliary outliers. Specifically, DivOE introduces a new learning objective, which diversifies the auxiliary distribution by explicitly synthesizing more informative outliers for extrapolation during training. It leverages a multi-step optimization method to generate novel outliers beyond the original ones, which is compatible with many variants of outlier exposure. Extensive experiments and analyses have been conducted to characterize and demonstrate the effectiveness of the proposed DivOE.

Line search (or backtracking) procedures have been widely employed into first-order methods for solving convex optimization problems, especially those with unknown problem parameters (e.g., Lipschitz constant). In this paper, we show that line search is superfluous in attaining the optimal rate of convergence for solving a convex optimization problem whose parameters are not given a priori. In particular, we present a novel accelerated gradient descent type algorithm called auto-conditioned fast gradient method (AC-FGM) that can achieve an optimal $\mathcal{O}(1/k^2)$ rate of convergence for smooth convex optimization without requiring the estimate of a global Lipschitz constant or the employment of line search procedures. We then extend AC-FGM to solve convex optimization problems with H\"{o}lder continuous gradients and show that it automatically achieves the optimal rates of convergence uniformly for all problem classes with the desired accuracy of the solution as the only input. Finally, we report some encouraging numerical results that demonstrate the advantages of AC-FGM over the previously developed parameter-free methods for convex optimization.

Cross-device Federated Learning (FL) faces significant challenges where low-end clients that could potentially make unique contributions are excluded from training large models due to their resource bottlenecks. Recent research efforts have focused on model-heterogeneous FL, by extracting reduced-size models from the global model and applying them to local clients accordingly. Despite the empirical success, general theoretical guarantees of convergence on this method remain an open question. This paper presents a unifying framework for heterogeneous FL algorithms with online model extraction and provides a general convergence analysis for the first time. In particular, we prove that under certain sufficient conditions and for both IID and non-IID data, these algorithms converge to a stationary point of standard FL for general smooth cost functions. Moreover, we introduce the concept of minimum coverage index, together with model reduction noise, which will determine the convergence of heterogeneous federated learning, and therefore we advocate for a holistic approach that considers both factors to enhance the efficiency of heterogeneous federated learning.

A recent empirical observation (Li et al., 2022b) of activation sparsity in MLP blocks offers an opportunity to drastically reduce computation costs for free. Although having attributed it to training dynamics, existing theoretical explanations of activation sparsity are restricted to shallow networks, small training steps and special training, despite its emergence in deep models standardly trained for a large number of steps. To fill these gaps, we propose the notion of gradient sparsity as one source of activation sparsity and a theoretical explanation based on it that sees sparsity a necessary step to adversarial robustness w.r.t. hidden features and parameters, which is approximately the flatness of minima for well-learned models. The theory applies to standardly trained LayerNorm-ed MLPs, and further to Transformers or other architectures trained with weight noises. Eliminating other sources of flatness except for sparsity, we discover the phenomenon that the ratio between the largest and smallest non-zero singular values of weight matrices is small. When discussing the emergence of this spectral concentration, we use random matrix theory (RMT) as a powerful tool to analyze stochastic gradient noises. Validational experiments are conducted to verify our gradient-sparsity-based explanation. We propose two plug-and-play modules for both training and finetuning for sparsity. Experiments on ImageNet-1k and C4 demonstrate their 50% sparsity improvements, indicating further potential cost reduction in both training and inference.

Inspired by Gauss-Newton-like methods, we study the benefit of leveraging the structure of deep learning objectives, namely, the composition of a convex loss function and of a nonlinear network, in order to derive better direction oracles than stochastic gradients, based on the idea of partial linearization. In a departure from previous works, we propose to compute such direction oracles via their dual formulation, leading to both computational benefits and new insights. We demonstrate that the resulting oracles define descent directions that can be used as a drop-in replacement for stochastic gradients, in existing optimization algorithms. We empirically study the advantage of using the dual formulation as well as the computational trade-offs involved in the computation of such oracles.