We study the optimization problem associated with fitting two-layer ReLU neural networks with respect to the squared loss, where labels are generated by a target network. Use is made of the rich symmetry structure to develop a novel set of tools for studying the mechanism by which over-parameterization annihilates spurious minima. Sharp analytic estimates are obtained for the loss and the Hessian spectrum at different minima, and it is proved that adding neurons can turn symmetric spurious minima into saddles; minima of lesser symmetry require more neurons. Using Cauchy's interlacing theorem, we prove the existence of descent directions in certain subspaces arising from the symmetry structure of the loss function. This analytic approach uses techniques, new to the field, from algebraic geometry, representation theory and symmetry breaking, and confirms rigorously the effectiveness of over-parameterization in making the associated loss landscape accessible to gradient-based methods. For a fixed number of neurons and inputs, the spectral results remain true under symmetry breaking perturbation of the target.

Monitoring and patrolling large water resources is a major challenge for conservation. The problem of acquiring data of an underlying environment that usually changes within time involves a proper formulation of the information. The use of Autonomous Surface Vehicles equipped with water quality sensor modules can serve as an early-warning system agents for contamination peak-detection, algae blooms monitoring, or oil-spill scenarios. In addition to information gathering, the vehicle must plan routes that are free of obstacles on non-convex maps. This work proposes a framework to obtain a collision-free policy that addresses the patrolling task for static and dynamic scenarios. Using information gain as a measure of the uncertainty reduction over data, it is proposed a Deep Q-Learning algorithm improved by a Q-Censoring mechanism for model-based obstacle avoidance. The obtained results demonstrate the usefulness of the proposed algorithm for water resource monitoring for static and dynamic scenarios. Simulations showed the use of noise-networks are a good choice for enhanced exploration, with 3 times less redundancy in the paths. Previous coverage strategies are also outperformed both in the accuracy of the obtained contamination model by a 13% on average and by a 37% in the detection of dangerous contamination peaks. Finally, these results indicate the appropriateness of the proposed framework for monitoring scenarios with autonomous vehicles.

Contextual bandits can solve a huge range of real-world problems. However, current popular algorithms to solve them either rely on linear models, or unreliable uncertainty estimation in non-linear models, which are required to deal with the exploration-exploitation trade-off. Inspired by theories of human cognition, we introduce novel techniques that use maximum entropy exploration, relying on neural networks to find optimal policies in settings with both continuous and discrete action spaces. We present two classes of models, one with neural networks as reward estimators, and the other with energy based models, which model the probability of obtaining an optimal reward given an action. We evaluate the performance of these models in static and dynamic contextual bandit simulation environments. We show that both techniques outperform well-known standard algorithms, where energy based models have the best overall performance. This provides practitioners with new techniques that perform well in static and dynamic settings, and are particularly well suited to non-linear scenarios with continuous action spaces.

Few-shot Intent Classification (FSIC) is one of the key challenges in modular task-oriented dialog systems. While advanced FSIC methods are similar in using pretrained language models to encode texts and nearest neighbour-based inference for classification, these methods differ in details. They start from different pretrained text encoders, use different encoding architectures with varying similarity functions, and adopt different training regimes. Coupling these mostly independent design decisions and the lack of accompanying ablation studies are big obstacle to identify the factors that drive the reported FSIC performance. We study these details across three key dimensions: (1) Encoding architectures: Cross-Encoder vs Bi-Encoders; (2) Similarity function: Parameterized (i.e., trainable) functions vs non-parameterized function; (3) Training regimes: Episodic meta-learning vs the straightforward (i.e., non-episodic) training. Our experimental results on seven FSIC benchmarks reveal three important findings. First, the unexplored combination of the cross-encoder architecture (with parameterized similarity scoring function) and episodic meta-learning consistently yields the best FSIC performance. Second, Episodic training yields a more robust FSIC classifier than non-episodic one. Third, in meta-learning methods, splitting an episode to support and query sets is not a must. Our findings paves the way for conducting state-of-the-art research in FSIC and more importantly raise the community's attention to details of FSIC methods. We release our code and data publicly.

This allows one to capture potentially complex relationships between inputs and outputs. To learn the parameters of the energy function, the solution to that optimization problem is typically fed into a loss function. The key challenge for training energy networks lies in computing loss gradients, as this typically requires argmin/argmax differentiation. In this paper, building upon a generalized notion of conjugate function, which replaces the usual bilinear pairing with a general energy function, we propose generalized Fenchel-Young losses, a natural loss construction for learning energy networks. Our losses enjoy many desirable properties and their gradients can be computed efficiently without argmin/argmax differentiation. We also prove the calibration of their excess risk in the case of linear-concave energies. We demonstrate our losses on multilabel classification and imitation learning tasks.

For generative autoencoders to learn a meaningful latent representation for data generation, a careful balance must be achieved between reconstruction error and how close the distribution in the latent space is to the prior. However, this balance is challenging to achieve due to a lack of criteria that work both at the mini-batch (local) and aggregated posterior (global) level. Goodness of fit (GoF) hypothesis tests provide a measure of statistical indistinguishability between the latent distribution and a target distribution class. In this work, we develop the Goodness of Fit Autoencoder (GoFAE), which incorporates hypothesis tests at two levels. At the mini-batch level, it uses GoF test statistics as regularization objectives. At a more global level, it selects a regularization coefficient based on higher criticism, i.e., a test on the uniformity of the local GoF p-values. We justify the use of GoF tests by providing a relaxed $L_2$-Wasserstein bound on the distance between the latent distribution and target prior. We propose to use GoF tests and prove that optimization based on these tests can be done with stochastic gradient (SGD) descent on a compact Riemannian manifold. Empirically, we show that our higher criticism parameter selection procedure balances reconstruction and generation using mutual information and uniformity of p-values respectively. Finally, we show that GoFAE achieves comparable FID scores and mean squared errors with competing deep generative models while retaining statistical indistinguishability from Gaussian in the latent space based on a variety of hypothesis tests.

1. The popularity of Machine learning (ML), Deep learning (DL), and Artificial intelligence (AI) has risen sharply in recent years. Despite this spike in popularity, the inner workings of ML and DL algorithms are often perceived as opaque, and their relationship to classical data analysis tools remains debated. 2. Although it is often assumed that ML and DL excel primarily at making predictions, ML and DL can also be used for analytical tasks traditionally addressed with statistical models. Moreover, most recent discussions and reviews on ML focus mainly on DL, missing out on synthesizing the wealth of ML algorithms with different advantages and general principles. 3. Here, we provide a comprehensive overview of the field of ML and DL, starting by summarizing its historical developments, existing algorithm families, differences to traditional statistical tools, and universal ML principles. We then discuss why and when ML and DL models excel at prediction tasks and where they could offer alternatives to traditional statistical methods for inference, highlighting current and emerging applications for ecological problems. Finally, we summarize emerging trends such as scientific and causal ML, explainable AI, and responsible AI that may significantly impact ecological data analysis in the future. 4. We conclude that ML and DL are powerful new tools for predictive modeling and data analysis. The superior performance of ML and DL algorithms compared to statistical models can be explained by their higher flexibility and automatic data-dependent complexity optimization. However, their use for causal inference is still disputed as the focus of ML and DL methods on predictions creates challenges for the interpretation of these models. Nevertheless, we expect ML and DL to become an indispensable tool in E&E, comparable to other traditional statistical tools.

Given a convex function $f\colon\mathbb{R}^{d}\to\mathbb{R}$, the problem of sampling from a distribution $\propto e^{-f(x)}$ is called log-concave sampling. This task has wide applications in machine learning, physics, statistics, etc. In this work, we develop quantum algorithms for sampling log-concave distributions and for estimating their normalizing constants $\int_{\mathbb{R}^d}e^{-f(x)}\mathrm{d} x$. First, we use underdamped Langevin diffusion to develop quantum algorithms that match the query complexity (in terms of the condition number $\kappa$ and dimension $d$) of analogous classical algorithms that use gradient (first-order) queries, even though the quantum algorithms use only evaluation (zeroth-order) queries. For estimating normalizing constants, these algorithms also achieve quadratic speedup in the multiplicative error $\epsilon$. Second, we develop quantum Metropolis-adjusted Langevin algorithms with query complexity $\widetilde{O}(\kappa^{1/2}d)$ and $\widetilde{O}(\kappa^{1/2}d^{3/2}/\epsilon)$ for log-concave sampling and normalizing constant estimation, respectively, achieving polynomial speedups in $\kappa,d,\epsilon$ over the best known classical algorithms by exploiting quantum analogs of the Monte Carlo method and quantum walks. We also prove a $1/\epsilon^{1-o(1)}$ quantum lower bound for estimating normalizing constants, implying near-optimality of our quantum algorithms in $\epsilon$.

In recent centralized nonconvex distributed learning and federated learning, local methods are one of the promising approaches to reduce communication time. However, existing work has mainly focused on studying first-order optimality guarantees. On the other side, second-order optimality guaranteed algorithms, i.e., algorithms escaping saddle points, have been extensively studied in the non-distributed optimization literature. In this paper, we study a new local algorithm called Bias-Variance Reduced Local Perturbed SGD (BVR-L-PSGD), that combines the existing bias-variance reduced gradient estimator with parameter perturbation to find second-order optimal points in centralized nonconvex distributed optimization. BVR-L-PSGD enjoys second-order optimality with nearly the same communication complexity as the best known one of BVR-L-SGD to find first-order optimality. Particularly, the communication complexity is better than non-local methods when the local datasets heterogeneity is smaller than the smoothness of the local loss. In an extreme case, the communication complexity approaches to $\widetilde \Theta(1)$ when the local datasets heterogeneity goes to zero. Numerical results validate our theoretical findings.

To produce important investment decisions, investors require financial records and economic information. However, most companies manipulate investors and financial institutions by inflating their financial statements. Fraudulent Financial Activities exist in any monetary or financial transaction scenario, whether physical or electronic. A challenging problem that arises in this domain is the issue that affects and troubles individuals and institutions. This problem has attracted more attention in the field in part owing to the prevalence of financial fraud and the paucity of previous research. For this purpose, in this study, the main approach to solve this problem, an anomaly detection-based approach based on a combination of feature selection based on squirrel optimization pattern and classification methods have been used. The aim is to develop this method to provide a model for detecting anomalies in financial statements using a combination of selected features with the nearest neighbor classifications, neural networks, support vector machine, and Bayesian. Anomaly samples are then analyzed and compared to recommended techniques using assessment criteria. Squirrel optimization's meta-exploratory capability, along with the approach's ability to identify abnormalities in financial data, has been shown to be effective in implementing the suggested strategy. They discovered fake financial statements because of their expertise.