A.1 Quantum chemistry At the center of quantum chemistry methods lies the electronic Schrödinger equation Ĥ

Machine learning has enabled the prediction of quantum chemical properties with high accuracy and efficiency, allowing to bypass computationally costly ab initio calculations. Instead of training on a fixed set of properties, more recent approaches attempt to learn the electronic wavefunction (or density) as a central quantity of atomistic systems, from which all other observables can be derived. This is complicated by the fact that wavefunctions transform non-trivially under molecular rotations, which makes them a challenging prediction target. To solve this issue, we introduce general SE(3)-equivariant operations and building blocks for constructing deep learning architectures for geometric point cloud data and apply them to reconstruct wavefunctions of atomistic systems with unprecedented accuracy. Our model achieves speedups of over three orders of magnitude compared to ab initio methods and reduces prediction errors by up to two orders of magnitude compared to the previous state-of-the-art. This accuracy makes it possible to derive properties such as energies and forces directly from the wavefunction in an end-to-end manner. We demonstrate the potential of our approach in a transfer learning application, where a model trained on low accuracy reference wavefunctions implicitly learns to correct for electronic many-body interactions from observables computed at a higher level of theory.

The two columns visualize the inputs, features, and atoms of the source domain and the target domain, respectively. Only the output feature in the first channel of each convolutional layer is visualized for comparison. Domain invariant features, the last row, are obtained by manually adapting source domain atoms to generated target domain atoms. B.1 Unsupervised DA for Image Segmentation For the image segmentation experiments in Section 5.2, we provide more qualitative results in Figure A.2. In Table A.1, we provide comparisons on additional parameters and computation introduced by one extra domain with and without the proposed domain-adaptive filter decomposition.

We propose the first general PAC-Bayesian generalization bounds for adversarial robustness, that estimate, at test time, how much a model will be invariant to imperceptible perturbations in the input. Instead of deriving a worst-case analysis of the risk of a hypothesis over all the possible perturbations, we leverage the PAC-Bayesian framework to bound the averaged risk on the perturbations for majority votes (over the whole class of hypotheses). Our theoretically founded analysis has the advantage to provide general bounds (i) that are valid for any kind of attacks (i.e., the adversarial attacks), (ii) that are tight thanks to the PAC-Bayesian framework, (iii) that can be directly minimized during the learning phase to obtain a robust model on different attacks at test time.

In the context of modern machine learning, models deployed in real-world scenarios often encounter diverse data shifts like covariate and semantic shifts, leading to challenges in both out-of-distribution (OOD) generalization and detection. Despite considerable attention to these issues separately, a unified framework for theoretical understanding and practical usage is lacking. To bridge the gap, we introduce a graph-theoretic framework to jointly tackle both OOD generalization and detection problems. By leveraging the graph formulation, data representations are obtained through the factorization of the graph's adjacency matrix, enabling us to derive provable error quantifying OOD generalization and detection performance.

Although reinforcement learning has found widespread use in dense reward settings, training autonomous agents with sparse rewards remains challenging. To address this difficulty, prior work has shown promising results when using not only task-specific demonstrations but also task-agnostic albeit somewhat related demonstrations. In most cases, the available demonstrations are distilled into an implicit prior, commonly represented via a single deep net. Explicit priors in the form of a database that can be queried have also been shown to lead to encouraging results. To better benefit from available demonstrations, we develop a method to Combine Explicit and Implicit Priors (CEIP). CEIP exploits multiple implicit priors in the form of normalizing flows in parallel to form a single complex prior. Moreover, CEIP uses an effective explicit retrieval and push-forward mechanism to condition the implicit priors. In three challenging environments, we find the proposed CEIP method to improve upon sophisticated state-of-the-art techniques.

Parameter-efficient finetuning (PEFT) methods effectively adapt large language models (LLMs) to diverse downstream tasks, reducing storage and GPU memory demands. Despite these advantages, several applications pose new challenges to PEFT beyond mere parameter efficiency. One notable challenge involves the efficient deployment of LLMs equipped with multiple task-or user-specific adapters, particularly when different adapters are needed for distinct requests within the same batch. Another challenge is the interpretability of LLMs, which is crucial for understanding how LLMs function. Previous studies introduced various approaches to address different challenges. In this paper, we introduce a novel method, RoAd, which employs a straightforward 2D rotation to adapt LLMs and addresses all the above challenges: (1) RoAd is remarkably parameter-efficient, delivering optimal performance on GLUE, eight commonsense reasoning tasks and four arithmetic reasoning tasks with < 0.1% trainable parameters; (2) RoAd facilitates the efficient serving of requests requiring different adapters within a batch, with an overhead comparable to element-wise multiplication instead of batch matrix multiplication; (3) RoAd enhances LLM's interpretability through integration within a framework of distributed interchange intervention, demonstrated via composition experiments.