SAGRAD (Simulated Annealing GRADient), a Fortran 77 program for computing neural networks for classification using batch learning, is discussed. Neural network training in SAGRAD is based on a combination of simulated annealing and M{\o}ller's scaled conjugate gradient algorithm, the latter a variation of the traditional conjugate gradient method, better suited for the nonquadratic nature of neural networks. Different aspects of the implementation of the training process in SAGRAD are discussed, such as the efficient computation of gradients and multiplication of vectors by Hessian matrices that are required by M{\o}ller's algorithm; the (re)initialization of weights with simulated annealing required to (re)start M{\o}ller's algorithm the first time and each time thereafter that it shows insufficient progress in reaching a possibly local minimum; and the use of simulated annealing when M{\o}ller's algorithm, after possibly making considerable progress, becomes stuck at a local minimum or flat area of weight space. Outlines of the scaled conjugate gradient algorithm, the simulated annealing procedure and the training process used in SAGRAD are presented together with results from running SAGRAD on two examples of training data.

Conformal Prediction (CP) is a principled framework for quantifying uncertainty in blackbox learning models, by constructing prediction sets with finite-sample coverage guarantees. Traditional approaches rely on scalar nonconformity scores, which fail to fully exploit the geometric structure of multivariate outputs, such as in multi-output regression or multiclass classification. Recent methods addressing this limitation impose predefined convex shapes for the prediction sets, potentially misaligning with the intrinsic data geometry. We introduce a novel CP procedure handling multivariate score functions through the lens of optimal transport. Specifically, we leverage Monge-Kantorovich vector ranks and quantiles to construct prediction region with flexible, potentially non-convex shapes, better suited to the complex uncertainty patterns encountered in multivariate learning tasks. We prove that our approach ensures finite-sample, distribution-free coverage properties, similar to typical CP methods. We then adapt our method for multi-output regression and multiclass classification, and also propose simple adjustments to generate adaptive prediction regions with asymptotic conditional coverage guarantees. Finally, we evaluate our method on practical regression and classification problems, illustrating its advantages in terms of (conditional) coverage and efficiency.

Structured large matrices are prevalent in machine learning. A particularly important class is curvature matrices like the Hessian, which are central to understanding the loss landscape of neural nets (NNs), and enable second-order optimization, uncertainty quantification, model pruning, data attribution, and more. However, curvature computations can be challenging due to the complexity of automatic differentiation, and the variety and structural assumptions of curvature proxies, like sparsity and Kronecker factorization. In this position paper, we argue that linear operators -- an interface for performing matrix-vector products -- provide a general, scalable, and user-friendly abstraction to handle curvature matrices. To support this position, we developed $\textit{curvlinops}$, a library that provides curvature matrices through a unified linear operator interface. We demonstrate with $\textit{curvlinops}$ how this interface can hide complexity, simplify applications, be extensible and interoperable with other libraries, and scale to large NNs.

Cold-start active learning (CSAL) selects valuable instances from an unlabeled dataset for manual annotation. It provides high-quality data at a low annotation cost for label-scarce text classification. However, existing CSAL methods overlook weak classes and hard representative examples, resulting in biased learning. To address these issues, this paper proposes a novel dual-diversity enhancing and uncertainty-aware (DEUCE) framework for CSAL. Specifically, DEUCE leverages a pretrained language model (PLM) to efficiently extract textual representations, class predictions, and predictive uncertainty. Then, it constructs a Dual-Neighbor Graph (DNG) to combine information on both textual diversity and class diversity, ensuring a balanced data distribution. It further propagates uncertainty information via density-based clustering to select hard representative instances. DEUCE performs well in selecting class-balanced and hard representative data by dual-diversity and informativeness. Experiments on six NLP datasets demonstrate the superiority and efficiency of DEUCE.

In this paper, we propose a novel loop closure detection algorithm that uses graph attention neural networks to encode semantic graphs to perform place recognition and then use semantic registration to estimate the 6 DoF relative pose constraint. Our place recognition algorithm has two key modules, namely, a semantic graph encoder module and a graph comparison module. The semantic graph encoder employs graph attention networks to efficiently encode spatial, semantic and geometric information from the semantic graph of the input point cloud. We then use self-attention mechanism in both node-embedding and graph-embedding steps to create distinctive graph vectors. The graph vectors of the current scan and a keyframe scan are then compared in the graph comparison module to identify a possible loop closure. Specifically, employing the difference of the two graph vectors showed a significant improvement in performance, as shown in ablation studies. Lastly, we implemented a semantic registration algorithm that takes in loop closure candidate scans and estimates the relative 6 DoF pose constraint for the LiDAR SLAM system. Extensive evaluation on public datasets shows that our model is more accurate and robust, achieving 13% improvement in maximum F1 score on the SemanticKITTI dataset, when compared to the baseline semantic graph algorithm. For the benefit of the community, we open-source the complete implementation of our proposed algorithm and custom implementation of semantic registration at https://github.com/crepuscularlight/SemanticLoopClosure

The notion of generalization has moved away from the classical one defined in statistical learning theory towards an emphasis on out-of-domain generalization (OODG). Recently, there is a growing focus on inductive generalization, where a progression of difficulty implicitly governs the direction of domain shifts. In inductive generalization, it is often assumed that the training data lie in the easier side, while the testing data lie in the harder side. The challenge is that training data are always finite, but a learner is expected to infer an inductive principle that could be applied in an unbounded manner. This emerging regime has appeared in the literature under different names, such as length/logical/algorithmic extrapolation, but a formal definition is lacking. This work provides such a formalization that centers on the concept of model successors. Then we outline directions to adapt well-established techniques towards the learning of model successors. This work calls for restructuring of the research discussion around inductive generalization from fragmented task-centric communities to a more unified effort, focused on universal properties of learning and computation.

The matrix recovery (completion) problem, a central problem in data science and theoretical computer science, is to recover a matrix $A$ from a relatively small sample of entries. While such a task is impossible in general, it has been shown that one can recover $A$ exactly in polynomial time, with high probability, from a random subset of entries, under three (basic and necessary) assumptions: (1) the rank of $A$ is very small compared to its dimensions (low rank), (2) $A$ has delocalized singular vectors (incoherence), and (3) the sample size is sufficiently large. There are many different algorithms for the task, including convex optimization by Candes, Tao and Recht (2009), alternating projection by Hardt and Wooters (2014) and low rank approximation with gradient descent by Keshavan, Montanari and Oh (2009, 2010). In applications, it is more realistic to assume that data is noisy. In this case, these approaches provide an approximate recovery with small root mean square error. However, it is hard to transform such approximate recovery to an exact one. Recently, results by Abbe et al. (2017) and Bhardwaj et al. (2023) concerning approximation in the infinity norm showed that we can achieve exact recovery even in the noisy case, given that the ground matrix has bounded precision. Beyond the three basic assumptions above, they required either the condition number of $A$ is small (Abbe et al.) or the gap between consecutive singular values is large (Bhardwaj et al.). In this paper, we remove these extra spectral assumptions. As a result, we obtain a simple algorithm for exact recovery in the noisy case, under only three basic assumptions. This is the first such algorithm. To analyse the algorithm, we introduce a contour integration argument which is totally different from all previous methods and may be of independent interest.

Tabular data is widely utilized in various machine learning tasks. Current tabular learning research predominantly focuses on closed environments, while in real-world applications, open environments are often encountered, where distribution and feature shifts occur, leading to significant degradation in model performance. Previous research has primarily concentrated on mitigating distribution shifts, whereas feature shifts, a distinctive and unexplored challenge of tabular data, have garnered limited attention. To this end, this paper conducts the first comprehensive study on feature shifts in tabular data and introduces the first tabular feature-shift benchmark (TabFSBench). TabFSBench evaluates impacts of four distinct feature-shift scenarios on four tabular model categories across various datasets and assesses the performance of large language models (LLMs) and tabular LLMs in the tabular benchmark for the first time. Our study demonstrates three main observations: (1) most tabular models have the limited applicability in feature-shift scenarios; (2) the shifted feature set importance has a linear relationship with model performance degradation; (3) model performance in closed environments correlates with feature-shift performance. Future research direction is also explored for each observation. TabFSBench is released for public access by using a few lines of Python codes at https://github.com/LAMDASZ-ML/TabFSBench.

Language models have recently been shown capable of performing regression tasks wherein numeric predictions are represented as decoded strings. In this work, we provide theoretical grounds for this capability and furthermore investigate the utility of causal auto-regressive sequence models when they are applied to any feature representation. We find that, despite being trained in the usual way - for next-token prediction via cross-entropy loss - decoding-based regression is as performant as traditional approaches for tabular regression tasks, while being flexible enough to capture arbitrary distributions, such as in the task of density estimation.

The training and fine-tuning of large language models (LLMs) often involve diverse textual data from multiple sources, which poses challenges due to conflicting gradient directions, hindering optimization and specialization. These challenges can undermine model generalization across tasks, resulting in reduced downstream performance. Recent research suggests that fine-tuning LLMs on carefully selected, task-specific subsets of data can match or even surpass the performance of using the entire dataset. Building on these insights, we propose the Ensembles of Low-Rank Expert Adapters (ELREA) framework to improve the model's capability to handle diverse tasks. ELREA clusters the training instructions based on their gradient directions, representing different areas of expertise and thereby reducing conflicts during optimization. Expert adapters are then trained on these clusters, utilizing the low-rank adaptation (LoRA) technique to ensure training efficiency and model scalability. During inference, ELREA combines predictions from the most relevant expert adapters based on the input data's gradient similarity to the training clusters, ensuring optimal adapter selection for each task. Experiments show that our method outperforms baseline LoRA adapters trained on the full dataset and other ensemble approaches with similar training and inference complexity across a range of domain-specific tasks.