In density functional theory, the charge density is the core attribute of atomic systems from which all chemical properties can be derived. Machine learning methods are promising as a means of significantly accelerating charge density predictions, yet existing approaches either lack accuracy or scalability. We propose a recipe that can achieve both. In particular, we identify three key ingredients: (1) representing the charge density with atomic and virtual orbitals (spherical fields centered at atom/virtual coordinates); (2) using expressive and learnable orbital basis sets (basis functions for the spherical fields); and (3) using a highcapacity equivariant neural network architecture. Our method achieves state-ofthe-art accuracy while being more than an order of magnitude faster than existing methods. Furthermore, our method enables flexible efficiency-accuracy trade-offs by adjusting the model and/or basis set sizes.

When training node embedding models to represent large directed graphs (digraphs), it is impossible to observe all entries of the adjacency matrix during training. As a consequence most methods employ sampling. For very large digraphs, however, this means many (most) entries may be unobserved during training. In general, observing every entry would be necessary to uniquely identify a graph, however if we know the graph has a certain property some entries can be omitted - for example, only half the entries would be required for a symmetric graph. In this work, we develop a novel framework to identify a subset of entries required to uniquely distinguish a graph among all transitively-closed DAGs. We give an explicit algorithm to compute the provably minimal set of entries, and demonstrate empirically that one can train node embedding models with greater efficiency and performance, provided the energy function has an appropriate inductive bias. We achieve robust performance on synthetic hierarchies and a larger real-world taxonomy, observing improved convergence rates in a resource-constrained setting while reducing the set of training examples by as much as 99%.

Large Language Models (LLMs) have shown state-of-the-art performance in a variety of tasks, including arithmetic and reasoning; however, to gauge the intellectual capabilities of LLMs, causal reasoning has become a reliable proxy for validating a general understanding of the mechanics and intricacies of the world similar to humans. Previous works in natural language processing (NLP) have either focused on open-ended causal reasoning via causal commonsense reasoning (CCR) or framed a symbolic representation-based question answering for theoretically backed-up analysis via a causal inference engine. The former adds an advantage of real-world grounding but lacks theoretically backed-up analysis/validation, whereas the latter is far from real-world grounding. In this work, we bridge this gap by proposing the COLD (Causal reasOning in cLosed Daily activities) framework, which is built upon human understanding of daily real-world activities to reason about the causal nature of events. We show that the proposed framework facilitates the creation of enormous causal queries ( 9 million) and comes close to the mini-turing test, simulating causal reasoning to evaluate the understanding of a daily real-world task. We evaluate multiple LLMs on the created causal queries and find that causal reasoning is challenging even for activities trivial to humans. We further explore (the causal reasoning abilities of LLMs) using the backdoor criterion to determine the causal strength between events.

Visual representations become progressively more abstract along the cortical hierarchy. These abstract representations define notions like objects and shapes, but at the cost of spatial specificity. By contrast, low-level regions represent spatially local but simple input features. How do spatially non-specific representations of abstract concepts in high-level areas flexibly modulate the low-level sensory representations in appropriate ways to guide context-driven and goal-directed behaviors across a range of tasks? We build a biologically motivated and trainable neural network model of dynamics in the visual pathway, incorporating local, lateral, and feedforward synaptic connections, excitatory and inhibitory neurons, and longrange top-down inputs conceptualized as low-rank modulations of the input-driven sensory responses by high-level areas. We study this Dynamical Cortical network (DCnet) in a visual cue-delay-search task and show that the model uses its own cue representations to adaptively modulate its perceptual responses to solve the task, outperforming state-of-the-art DNN vision and LLM models. The model's population states over time shed light on the nature of contextual modulatory dynamics, generating predictions for experiments. We fine-tune the same model on classic psychophysics attention tasks, and find that the model closely replicates known reaction time results. This work represents a promising new foundation for understanding and making predictions about perturbations to visual processing in the brain.

DrivAerNet++ comprises 8,000 diverse car designs modeled with high-fidelity computational fluid dynamics (CFD) simulations. The dataset includes diverse car configurations such as fastback, notchback, and estateback, with different underbody and wheel designs to represent both internal combustion engines and electric vehicles.

Data distillation and coresets have emerged as popular approaches to generate a smaller representative set of samples for downstream learning tasks to handle large-scale datasets. At the same time, machine learning is being increasingly applied to decision-making processes at a societal level, making it imperative for modelers to address inherent biases towards subgroups present in the data. While current approaches focus on creating fair synthetic representative samples by optimizing local properties relative to the original samples, their impact on downstream learning processes has yet to be explored. In this work, we present fair Wasserstein coresets (FWC), a novel coreset approach which generates fair synthetic representative samples along with sample-level weights to be used in downstream learning tasks. FWC uses an efficient majority minimization algorithm to minimize the Wasserstein distance between the original dataset and the weighted synthetic samples while enforcing demographic parity. We show that an unconstrained version of FWC is equivalent to Lloyd's algorithm for k-medians and k-means clustering. Experiments conducted on both synthetic and real datasets show that FWC: (i) achieves a competitive fairness-utility tradeoff in downstream models compared to existing approaches, (ii) improves downstream fairness when added to the existing training data and (iii) can be used to reduce biases in predictions from large language models (GPT-3.5 and GPT-4).

Neural Information Processing Systems http://nips.cc/

We introduce an online active exploration algorithm for data-efficiently learning an abstract symbolic model of an environment. Our algorithm is divided into two parts: the first part quickly generates an intermediate Bayesian symbolic model from the data that the agent has collected so far, which the agent can then use along with the second part to guide its future exploration towards regions of the state space that the model is uncertain about. We show that our algorithm outperforms random and greedy exploration policies on two different computer game domains. The first domain is an Asteroids-inspired game with complex dynamics but basic logical structure. The second is the Treasure Game, with simpler dynamics but more complex logical structure.

Neural Information Processing Systems http://nips.cc/

We revisit isotonic regression on linear orders, the problem of fitting monotonic functions to best explain the data, in an online setting. It was previously shown that online isotonic regression is unlearnable in a fully adversarial model, which lead to its study in the fixed design model. Here, we instead develop the more practical random permutation model. We show that the regret is bounded above by the excess leave-one-out loss for which we develop efficient algorithms and matching lower bounds. We also analyze the class of simple and popular forward algorithms and recommend where to look for algorithms for online isotonic regression on partial orders.