Approximate Natural Gradient Descent (NGD) methods are an important family of optimisers for deep learning models, which use approximate Fisher information matrices to pre-condition gradients during training. The empirical Fisher (EF) method approximates the Fisher information matrix empirically by reusing the per-sample gradients collected during back-propagation. Despite its ease of implementation, the EF approximation has its theoretical and practical limitations. This paper investigates the inversely-scaled projection issue of EF, which is shown to be a major cause of its poor empirical approximation quality. An improved empirical Fisher (iEF) method is proposed to address this issue, which is motivated as a generalised NGD method from a loss reduction perspective, meanwhile retaining the practical convenience of EF.

Federated learning (FL) has rapidly evolved as a promising paradigm that enables collaborative model training across distributed participants without exchanging their local data. Despite its broad applications in fields such as computer vision, graph learning, and natural language processing, the development of a data projection model that can be effectively used to visualize data in the context of FL is crucial yet remains heavily under-explored. Neighbor embedding (NE) is an essential technique for visualizing complex high-dimensional data, but collaboratively learning a joint NE model is difficult. The key challenge lies in the objective function, as effective visualization algorithms like NE require computing loss functions among pairs of data.

Out-of-distribution (OOD) detection is critical when deploying machine learning models in the real world. Outlier exposure methods, which incorporate auxiliary outlier data in the training process, can drastically improve OOD detection performance compared to approaches without advanced training strategies. We introduce Hopfield Boosting, a boosting approach, which leverages modern Hopfield energy to sharpen the decision boundary between the in-distribution and OOD data. Hopfield Boosting encourages the model to focus on hard-to-distinguish auxiliary outlier examples that lie close to the decision boundary between in-distribution and auxiliary outlier data. Our method achieves a new state-of-the-art in OOD detection with outlier exposure, improving the FPR95 from 2.28 to 0.92 on CIFAR-10, from 11.76 to 7.94 on CIFAR-100, and from 50.74 to 36.60 on ImageNet-1K.

We propose a framework for Semi-Supervised Active Clustering framework (SSAC), where the learner is allowed to interact with a domain expert, asking whether two given instances belong to the same cluster or not. We study the query and computational complexity of clustering in this framework. We consider a setting where the expert conforms to a center-based clustering with a notion of margin. We show that there is a trade off between computational complexity and query complexity; We prove that for the case of k-means clustering (i.e., when the expert conforms to a solution of k-means), having access to relatively few such queries allows efficient solutions to otherwise NP hard problems.

During natural evolution, the primary visual cortex (V1) of lower mammals typically forms salt-and-pepper organizations, while higher mammals and primates develop pinwheel structures with distinct topological properties. Despite the general belief that V1 neurons primarily serve as edge detectors, the functional advantages of pinwheel structures over salt-and-peppers are not well recognized. To this end, we propose a two-dimensional self-evolving spiking neural network that integrates Hebbian-like plasticity and empirical morphological data.

Convolutional neural networks (CNNs) contain local pooling to effectively downsize feature maps for increasing computation efficiency as well as robustness to input variations. The local pooling methods are generally formulated in a form of convex combination of local neuron activations for retaining the characteristics of an input feature map in a manner similar to image downscaling. In this paper, to improve performance of CNNs, we propose a novel local pooling method based on the Gaussian-based probabilistic model over local neuron activations for flexibly pooling (extracting) features, in contrast to the previous model restricting the output within the convex hull of local neurons. In the proposed method, the local neuron activations are aggregated into the statistics of mean and standard deviation in a Gaussian distribution, and then on the basis of those statistics, we construct the probabilistic model suitable for the pooling in accordance with the knowledge about local pooling in CNNs. Through the probabilistic model equipped with trainable parameters, the proposed method naturally integrates two schemes of adaptively training the pooling form based on input feature maps and stochastically performing the pooling throughout the end-to-end learning. The experimental results on image classification demonstrate that the proposed method favorably improves performance of various CNNs in comparison with the other pooling methods.

In the 1990s, the constant error carousel and gating were introduced as the central ideas of the Long Short-Term Memory (LSTM). Since then, LSTMs have stood the test of time and contributed to numerous deep learning success stories, in particular they constituted the first Large Language Models (LLMs). However, the advent of the Transformer technology with parallelizable self-attention at its core marked the dawn of a new era, outpacing LSTMs at scale. We now raise a simple question: How far do we get in language modeling when scaling LSTMs to billions of parameters, leveraging the latest techniques from modern LLMs, but mitigating known limitations of LSTMs? Firstly, we introduce exponential gating with appropriate normalization and stabilization techniques. Secondly, we modify the LSTM memory structure, obtaining: (i) sLSTM with a scalar memory, a scalar update, and new memory mixing, (ii) mLSTM that is fully parallelizable with a matrix memory and a covariance update rule. Integrating these LSTM extensions into residual block backbones yields xLSTM blocks that are then residually stacked into xLSTM architectures. Exponential gating and modified memory structures boost xLSTM capabilities to perform favorably when compared to state-of-the-art Transformers and State Space Models, both in performance and scaling.

Variance reduction has emerged in recent years as a strong competitor to stochastic gradient descent in non-convex problems, providing the first algorithms to improve upon the converge rate of stochastic gradient descent for finding first-order critical points. However, variance reduction techniques typically require carefully tuned learning rates and willingness to use excessively large "mega-batches" in order to achieve their improved results.

Given a collection of feature maps indexed by a set T, we study the performance of empirical risk minimization (ERM) on regression problems with square loss over the union of the linear classes induced by these feature maps. This setup aims at capturing the simplest instance of feature learning, where the model is expected to jointly learn from the data an appropriate feature map and a linear predictor. We start by studying the asymptotic quantiles of the excess risk of sequences of empirical risk minimizers. Remarkably, we show that when the set T is not too large and when there is a unique optimal feature map, these quantiles coincide, up to a factor of two, with those of the excess risk of the oracle procedure, which knows a priori this optimal feature map and deterministically outputs an empirical risk minimizer from the associated optimal linear class. We complement this asymptotic result with a non-asymptotic analysis that quantifies the decaying effect of the global complexity of the set T on the excess risk of ERM, and relates it to the size of the sublevel sets of the suboptimality of the feature maps. As an application of our results, we obtain new guarantees on the performance of the best subset selection procedure in sparse linear regression under general assumptions.

Efficiently aggregating trained neural networks from local clients into a global model on a server is a widely researched topic in federated learning. Recently, motivated by diminishing privacy concerns, mitigating potential attacks, and reducing communication overhead, one-shot federated learning (i.e., limiting client-server communication into a single round) has gained popularity among researchers. However, the one-shot aggregation performances are sensitively affected by the non-identical training data distribution, which exhibits high statistical heterogeneity in some real-world scenarios. To address this issue, we propose a novel one-shot aggregation method with layer-wise posterior aggregation, named FedLPA. FedLPA aggregates local models to obtain a more accurate global model without requiring extra auxiliary datasets or exposing any private label information, e.g., label distributions. To effectively capture the statistics maintained in the biased local datasets in the practical non-IID scenario, we efficiently infer the posteriors of each layer in each local model using layer-wise Laplace approximation and aggregate them to train the global parameters. Extensive experimental results demonstrate that FedLPA significantly improves learning performance over state-of-the-art methods across several metrics.