We consider minimizing the average of a very large number of smooth and possibly non-convex functions. This optimization problem has deserved much attention in the past years due to the many applications in different fields, the most challenging being training Machine Learning models. Widely used approaches for solving this problem are mini-batch gradient methods which, at each iteration, update the decision vector moving along the gradient of a mini-batch of the component functions. We consider the Incremental Gradient (IG) and the Random reshuffling (RR) methods which proceed in cycles, picking batches in a fixed order or by reshuffling the order after each epoch. Convergence properties of these schemes have been proved under different assumptions, usually quite strong. We aim to define ease-controlled modifications of the IG/RR schemes, which require a light additional computational effort and can be proved to converge under very weak and standard assumptions. In particular, we define two algorithmic schemes, monotone or non-monotone, in which the IG/RR iteration is controlled by using a watchdog rule and a derivative-free line search that activates only sporadically to guarantee convergence. The two schemes also allow controlling the updating of the stepsize used in the main IG/RR iteration, avoiding the use of preset rules. We prove convergence under the lonely assumption of Lipschitz continuity of the gradients of the component functions and perform extensive computational analysis using Deep Neural Architectures and a benchmark of datasets. We compare our implementation with both full batch gradient methods and online standard implementation of IG/RR methods, proving that the computational effort is comparable with the corresponding online methods and that the control on the learning rate may allow faster decrease.

In recent years there has been growing attention to interpretable machine learning models which can give explanatory insights on their behavior. Thanks to their interpretability, decision trees have been intensively studied for classification tasks, and due to the remarkable advances in mixed-integer programming (MIP), various approaches have been proposed to formulate the problem of training an Optimal Classification Tree (OCT) as a MIP model. We present a novel mixed-integer quadratic formulation for the OCT problem, which exploits the generalization capabilities of Support Vector Machines for binary classification. Our model, denoted as Margin Optimal Classification Tree (MARGOT), encompasses the use of maximum margin multivariate hyperplanes nested in a binary tree structure. To enhance the interpretability of our approach, we analyse two alternative versions of MARGOT, which include feature selection constraints inducing local sparsity of the hyperplanes. First, MARGOT has been tested on non-linearly separable synthetic datasets in 2-dimensional feature space to provide a graphical representation of the maximum margin approach. Finally, the proposed models have been tested on benchmark datasets from the UCI repository. The MARGOT formulation turns out to be easier to solve than other OCT approaches, and the generated tree better generalizes on new observations. The two interpretable versions are effective in selecting the most relevant features and maintaining good prediction quality.

最近，增强学习方法（RL）在NP-HARD组合优化问题上的应用已成为一个流行的话题。这本质上是由于传统组合算法的性质，通常是基于试验过程。 RL旨在自动化此过程。在这方面，本文着重于RL在车辆路由问题（VRP）中的应用，这是属于NP-HARD问题的著名组合问题。首先，在这项工作中，该问题被建模为马尔可夫决策过程（MDP），然后应用PPO方法（属于Actor-Critic-Critic cornforcion学习方法类别）。在第二阶段，已经建立了演员和评论家背后的神经建筑，选择采用基于卷积神经网络的神经建筑，包括演员和评论家。这种选择有效地解决了不同大小的问题。在各种实例上进行的实验表明该算法具有良好的概括能力，并且可以在短时间内达到良好的解决方案。提出的算法与最先进的求解器或最先进的求解器之间的比较表明，后者仍然优于强化学习算法。但是，有一些未来的研究观点，旨在升级提出的算法的当前性能。

Associazione Medici Diabetologi（AMD）收集并管理着全球最大的糖尿病患者记录集合之一，也称为AMD数据库。本文介绍了一个正在进行的项目的初步结果，该项目的重点是人工智能和机器学习技术的应用，以概念化，清洁和分析如此重要且有价值的数据集，目的是提供预测性见解，以更好地支持糖尿病学家的诊断糖尿病学家和治疗选择。

Models of sensory processing and learning in the cortex need to efficiently assign credit to synapses in all areas. In deep learning, a known solution is error backpropagation, which however requires biologically implausible weight transport from feed-forward to feedback paths. We introduce Phaseless Alignment Learning (PAL), a bio-plausible method to learn efficient feedback weights in layered cortical hierarchies. This is achieved by exploiting the noise naturally found in biophysical systems as an additional carrier of information. In our dynamical system, all weights are learned simultaneously with always-on plasticity and using only information locally available to the synapses. Our method is completely phase-free (no forward and backward passes or phased learning) and allows for efficient error propagation across multi-layer cortical hierarchies, while maintaining biologically plausible signal transport and learning. Our method is applicable to a wide class of models and improves on previously known biologically plausible ways of credit assignment: compared to random synaptic feedback, it can solve complex tasks with less neurons and learn more useful latent representations. We demonstrate this on various classification tasks using a cortical microcircuit model with prospective coding.

Language models (LMs) have demonstrated remarkable performance on downstream tasks, using in-context exemplars or human instructions. Recent works have shown that chain-of-thought (CoT) prompting can elicit models to solve complex reasoning tasks, step-by-step. However, the efficacy of prompt-based CoT methods is restricted to very large LMs such as GPT-3 (175B), thus limiting deployability. In this paper, we revisit the fine-tuning approach to enable complex reasoning in smaller LMs, optimized to efficiently perform a specific task. We propose Fine-tune-CoT, a method that leverages the capabilities of very large LMs to generate reasoning samples and teach smaller models via fine-tuning. We evaluate our method on publicly available LMs across a wide range of complex tasks and model sizes. We find that Fine-tune-CoT enables substantial reasoning capability in small models, whereas previous prompt-based baselines exhibit near-random performance. Student models can even outperform the teacher in some tasks while reducing model size requirements by several orders of magnitude. We conduct extensive ablations and sample studies to understand the reasoning capabilities of student models. We also identify several important nuances that have been overlooked in concurrent fine-tuning works on CoT and address them in our analysis.

After just a few hundred training updates, a standard probabilistic model for language generation has likely not yet learnt many semantic or syntactic rules of natural language, which inherently makes it difficult to estimate the right probability distribution over next tokens. Yet around this point, these models have identified a simple, loss-minimising behaviour: to output the unigram distribution of the target training corpus. The use of such a crude heuristic raises the question: Rather than wasting precious compute resources and model capacity for learning this strategy at early training stages, can we initialise our models with this behaviour? Here, we show that we can effectively endow our model with a separate module that reflects unigram frequency statistics as prior knowledge. Standard neural language generation architectures offer a natural opportunity for implementing this idea: by initialising the bias term in a model's final linear layer with the log-unigram distribution. Experiments in neural machine translation demonstrate that this simple technique: (i) improves learning efficiency; (ii) achieves better overall performance; and (iii) appears to disentangle strong frequency effects, encouraging the model to specialise in non-frequency-related aspects of language.

Heteroscedastic regression models a Gaussian variable's mean and variance as a function of covariates. Parametric methods that employ neural networks for these parameter maps can capture complex relationships in the data. Yet, optimizing network parameters via log likelihood gradients can yield suboptimal mean and uncalibrated variance estimates. Current solutions side-step this optimization problem with surrogate objectives or Bayesian treatments. Instead, we make two simple modifications to optimization. Notably, their combination produces a heteroscedastic model with mean estimates that are provably as accurate as those from its homoscedastic counterpart (i.e.~fitting the mean under squared error loss). For a wide variety of network and task complexities, we find that mean estimates from existing heteroscedastic solutions can be significantly less accurate than those from an equivalently expressive mean-only model. Our approach provably retains the accuracy of an equally flexible mean-only model while also offering best-in-class variance calibration. Lastly, we show how to leverage our method to recover the underlying heteroscedastic noise variance.

Active target sensing is the task of discovering and classifying an unknown number of targets in an environment and is critical in search-and-rescue missions. This paper develops a deep reinforcement learning approach to plan informative trajectories that increase the likelihood for an uncrewed aerial vehicle (UAV) to discover missing targets. Our approach efficiently (1) explores the environment to discover new targets, (2) exploits its current belief of the target states and incorporates inaccurate sensor models for high-fidelity classification, and (3) generates dynamically feasible trajectories for an agile UAV by employing a motion primitive library. Extensive simulations on randomly generated environments show that our approach is more efficient in discovering and classifying targets than several other baselines. A unique characteristic of our approach, in contrast to heuristic informative path planning approaches, is that it is robust to varying amounts of deviations of the prior belief from the true target distribution, thereby alleviating the challenge of designing heuristics specific to the application conditions.

Nucleolar organizer regions (NORs) are parts of the DNA that are involved in RNA transcription. Due to the silver affinity of associated proteins, argyrophilic NORs (AgNORs) can be visualized using silver-based staining. The average number of AgNORs per nucleus has been shown to be a prognostic factor for predicting the outcome of many tumors. Since manual detection of AgNORs is laborious, automation is of high interest. We present a deep learning-based pipeline for automatically determining the AgNOR-score from histopathological sections. An additional annotation experiment was conducted with six pathologists to provide an independent performance evaluation of our approach. Across all raters and images, we found a mean squared error of 0.054 between the AgNOR- scores of the experts and those of the model, indicating that our approach offers performance comparable to humans.