In Deep Reinforcement Learning (RL), it is a challenge to learn representations that do not exhibit catastrophic forgetting or interference in non-stationary environments.

Graph neural networks (GNNs) have struggled to outperform traditional optimization methods on combinatorial problems, limiting their practical impact. We address this gap by introducing a novel chaining procedure for the graph alignment problem--a fundamental NP-hard task of finding optimal node correspondences between unlabeled graphs using only structural information. Our method trains a sequence of GNNs where each network learns to iteratively refine similarity matrices produced by previous networks. During inference, this creates a bootstrap effect: each GNN improves upon partial solutions by incorporating discrete ranking information about node alignment quality from prior iterations. We combine this with a powerful architecture that operates on node pairs rather than individual nodes, capturing global structural patterns essential for alignment that standard message-passing networks cannot represent. Extensive experiments on synthetic benchmarks demonstrate substantial improvements: our chained GNNs achieve over 3 better accuracy than existing methods on challenging instances, and uniquely solve regular graphs where all competing approaches fail. When combined with traditional optimization as post-processing, our method substantially outperforms state-of-the-art solvers on the graph alignment benchmark. "Combinatorial optimization searches for an optimum object in a finite collection of objects. Typically, the collection has a concise representation (like a graph), while the number of objects is huge."(Schrijver

In this section, we will restate our main results and give full proofs. We will show that our problem setup is a special case of that considered in Theorem 3; then, we can apply that result as a black box. Without loss of generality, assume U = [ s] . The result now follows from Theorem 3.Theorem 21 We prove Theorem 5 in two parts. We first show that although the adversary doesn't know (Theorem 6) We will proceed by contradiction.

Machine learning is vital in high-stakes domains, yet conventional validation methods rely on averaging metrics like mean squared error (MSE) or mean absolute error (MAE), which fail to quantify extreme errors. Worst-case prediction failures can have substantial consequences, but current frameworks lack statistical foundations for assessing their probability. In this work a new statistical framework, based on Extreme Value Theory (EVT), is presented that provides a rigorous approach to estimating worst-case failures. Applying EVT to synthetic and real-world datasets, this method is shown to enable robust estimation of catastrophic failure probabilities, overcoming the fundamental limitations of standard cross-validation. This work establishes EVT as a fundamental tool for assessing model reliability, ensuring safer AI deployment in new technologies where uncertainty quantification is central to decision-making or scientific analysis.

In Deep Reinforcement Learning (RL), it is a challenge to learn representations that do not exhibit catastrophic forgetting or interference in non-stationary environments. Successor Features (SFs) offer a potential solution to this challenge. However, canonical techniques for learning SFs from pixel-level observations often lead to representation collapse, wherein representations degenerate and fail to capture meaningful variations in the data. More recent methods for learning SFs can avoid representation collapse, but they often involve complex losses and multiple learning phases, reducing their efficiency. We introduce a novel, simple method for learning SFs directly from pixels. Our approach uses a combination of a Temporal-difference (TD) loss and a reward prediction loss, which together capture the basic mathematical definition of SFs. We show that our approach matches or outperforms existing SF learning techniques in both 2D (Minigrid), 3D (Miniworld) mazes and Mujoco, for both single and continual learning scenarios. As well, our technique is efficient, and can reach higher levels of performance in less time than other approaches. Our work provides a new, streamlined technique for learning SFs directly from pixel observations, with no pretraining required.

Astronomy is entering an unprecedented era of Big Data science, driven by missions like the ESA's Gaia telescope, which aims to map the Milky Way in three dimensions. Gaia's vast dataset presents a monumental challenge for traditional analysis methods. The sheer scale of this data exceeds the capabilities of manual exploration, necessitating the utilization of advanced computational techniques. In response to this challenge, we developed a novel approach leveraging deep learning to estimate the metallicity of fundamental mode (ab-type) RR Lyrae stars from their light curves in the Gaia optical G-band. Our study explores applying deep learning techniques, particularly advanced neural network architectures, in predicting photometric metallicity from time-series data. Our deep learning models demonstrated notable predictive performance, with a low mean absolute error (MAE) of 0.0565, the root mean square error (RMSE) achieved is 0.0765 and a high $R^2$ regression performance of 0.9401 measured by cross-validation. The weighted mean absolute error (wMAE) is 0.0563, while the weighted root mean square error (wRMSE) is 0.0763. These results showcase the effectiveness of our approach in accurately estimating metallicity values. Our work underscores the importance of deep learning in astronomical research, particularly with large datasets from missions like Gaia. By harnessing the power of deep learning methods, we can provide precision in analyzing vast datasets, contributing to more precise and comprehensive insights into complex astronomical phenomena.

Multimodal foundation models (MFMs) such as OFASys show the potential to unlock analysis of complex data such as images, videos, and audio data via text prompts alone. However, their performance may suffer in the face of text input that differs even slightly from their training distribution, which is surprising considering the use of modality-specific data to "ground" the text input. This study demonstrates that prompt instability is a major concern for MFMs, leading to a consistent drop in performance across all modalities, but that instability can be mitigated with additional training with augmented data. We evaluate several methods for grounded prompt perturbation, where we generate perturbations and filter based on similarity to text and/or modality data. After re-training the models on the augmented data, we find improved accuracy and more stable performance on the perturbed test data regardless of perturbation condition, suggesting that the data augmentation strategy helps the models handle domain shifts more effectively. In error analysis, we find consistent patterns of performance improvement across domains, suggesting that retraining on prompt perturbations tends to help general reasoning capabilities in MFMs.