A common approach to modeling networks assigns each node to a position on a low-dimensional manifold where distance is inversely proportional to connection likelihood. More positive manifold curvature encourages more and tighter communities; negative curvature induces repulsion. We consistently estimate manifold type, dimension, and curvature from simply connected, complete Riemannian manifolds of constant curvature. We represent the graph as a noisy distance matrix based on the ties between cliques, then develop hypothesis tests to determine whether the observed distances could plausibly be embedded isometrically in each of the candidate geometries. We apply our approach to data-sets from economics and neuroscience.

Large language models (LLMs) have been shown to be able to perform new tasks based on a few demonstrations or natural language instructions. While these capabilities have led to widespread adoption, most LLMs are developed by resource-rich organizations and are frequently kept from the public. As a step towards democratizing this powerful technology, we present BLOOM, a 176B-parameter open-access language model designed and built thanks to a collaboration of hundreds of researchers. BLOOM is a decoder-only Transformer language model that was trained on the ROOTS corpus, a dataset comprising hundreds of sources in 46 natural and 13 programming languages (59 in total). We find that BLOOM achieves competitive performance on a wide variety of benchmarks, with stronger results after undergoing multitask prompted finetuning. To facilitate future research and applications using LLMs, we publicly release our models and code under the Responsible AI License.

While the capabilities of autonomous systems have been steadily improving in recent years, these systems still struggle to rapidly explore previously unknown environments without the aid of GPS-assisted navigation. The DARPA Subterranean (SubT) Challenge aimed to fast track the development of autonomous exploration systems by evaluating their performance in real-world underground search-and-rescue scenarios. Subterranean environments present a plethora of challenges for robotic systems, such as limited communications, complex topology, visually-degraded sensing, and harsh terrain. The presented solution enables long-term autonomy with minimal human supervision by combining a powerful and independent single-agent autonomy stack, with higher level mission management operating over a flexible mesh network. The autonomy suite deployed on quadruped and wheeled robots was fully independent, freeing the human supervision to loosely supervise the mission and make high-impact strategic decisions. We also discuss lessons learned from fielding our system at the SubT Final Event, relating to vehicle versatility, system adaptability, and re-configurable communications.

We introduce a new tool for stochastic convex optimization (SCO): a Reweighted Stochastic Query (ReSQue) estimator for the gradient of a function convolved with a (Gaussian) probability density. Combining ReSQue with recent advances in ball oracle acceleration [CJJJLST20, ACJJS21], we develop algorithms achieving state-of-the-art complexities for SCO in parallel and private settings. For a SCO objective constrained to the unit ball in $\mathbb{R}^d$, we obtain the following results (up to polylogarithmic factors). We give a parallel algorithm obtaining optimization error $\epsilon_{\text{opt}}$ with $d^{1/3}\epsilon_{\text{opt}}^{-2/3}$ gradient oracle query depth and $d^{1/3}\epsilon_{\text{opt}}^{-2/3} + \epsilon_{\text{opt}}^{-2}$ gradient queries in total, assuming access to a bounded-variance stochastic gradient estimator. For $\epsilon_{\text{opt}} \in [d^{-1}, d^{-1/4}]$, our algorithm matches the state-of-the-art oracle depth of [BJLLS19] while maintaining the optimal total work of stochastic gradient descent. We give an $(\epsilon_{\text{dp}}, \delta)$-differentially private algorithm which, given $n$ samples of Lipschitz loss functions, obtains near-optimal optimization error and makes $\min(n, n^2\epsilon_{\text{dp}}^2 d^{-1}) + \min(n^{4/3}\epsilon_{\text{dp}}^{1/3}, (nd)^{2/3}\epsilon_{\text{dp}}^{-1})$ queries to the gradients of these functions. In the regime $d \le n \epsilon_{\text{dp}}^{2}$, where privacy comes at no cost in terms of the optimal loss up to constants, our algorithm uses $n + (nd)^{2/3}\epsilon_{\text{dp}}^{-1}$ queries and improves recent advancements of [KLL21, AFKT21]. In the moderately low-dimensional setting $d \le \sqrt n \epsilon_{\text{dp}}^{3/2}$, our query complexity is near-linear.

Attention mechanisms form a core component of several successful deep learning architectures, and are based on one key idea: ''The output depends only on a small (but unknown) segment of the input.'' In several practical applications like image captioning and language translation, this is mostly true. In trained models with an attention mechanism, the outputs of an intermediate module that encodes the segment of input responsible for the output is often used as a way to peek into the `reasoning` of the network. We make such a notion more precise for a variant of the classification problem that we term selective dependence classification (SDC) when used with attention model architectures. Under such a setting, we demonstrate various error modes where an attention model can be accurate but fail to be interpretable, and show that such models do occur as a result of training. We illustrate various situations that can accentuate and mitigate this behaviour. Finally, we use our objective definition of interpretability for SDC tasks to evaluate a few attention model learning algorithms designed to encourage sparsity and demonstrate that these algorithms help improve interpretability.

Recent advances in deep learning have enabled us to address the curse of dimensionality (COD) by solving problems in higher dimensions. A subset of such approaches of addressing the COD has led us to solving high-dimensional PDEs. This has resulted in opening doors to solving a variety of real-world problems ranging from mathematical finance to stochastic control for industrial applications. Although feasible, these deep learning methods are still constrained by training time and memory. Tackling these shortcomings, Tensor Neural Networks (TNN) demonstrate that they can provide significant parameter savings while attaining the same accuracy as compared to the classical Dense Neural Network (DNN). In addition, we also show how TNN can be trained faster than DNN for the same accuracy. Besides TNN, we also introduce Tensor Network Initializer (TNN Init), a weight initialization scheme that leads to faster convergence with smaller variance for an equivalent parameter count as compared to a DNN. We benchmark TNN and TNN Init by applying them to solve the parabolic PDE associated with the Heston model, which is widely used in financial pricing theory.

Artificial neural networks can learn complex, salient data features to achieve a given task. On the opposite end of the spectrum, mathematically grounded methods such as topological data analysis allow users to design analysis pipelines fully aware of data constraints and symmetries. We introduce a class of persistence-based neural network layers. Persistence-based layers allow the users to easily inject knowledge about symmetries (equivariance) respected by the data, are equipped with learnable weights, and can be composed with state-of-the-art neural architectures.

KL-regularized reinforcement learning from expert demonstrations has proved successful in improving the sample efficiency of deep reinforcement learning algorithms, allowing them to be applied to challenging physical real-world tasks. However, we show that KL-regularized reinforcement learning with behavioral reference policies derived from expert demonstrations can suffer from pathological training dynamics that can lead to slow, unstable, and suboptimal online learning. We show empirically that the pathology occurs for commonly chosen behavioral policy classes and demonstrate its impact on sample efficiency and online policy performance. Finally, we show that the pathology can be remedied by non-parametric behavioral reference policies and that this allows KL-regularized reinforcement learning to significantly outperform state-of-the-art approaches on a variety of challenging locomotion and dexterous hand manipulation tasks.

Periocular refers to the region of the face that surrounds the eye socket. This is a feature-rich area that can be used by itself to determine the identity of an individual. It is especially useful when the iris or the face cannot be reliably acquired. This can be the case of unconstrained or uncooperative scenarios, where the face may appear partially occluded, or the subject-to-camera distance may be high. However, it has received revived attention during the pandemic due to masked faces, leaving the ocular region as the only visible facial area, even in controlled scenarios. This paper discusses the state-of-the-art of periocular biometrics, giving an overall framework of its most significant research aspects.

Three main points: 1. Data Science (DS) will be increasingly important to heliophysics; 2. Methods of heliophysics science discovery will continually evolve, requiring the use of learning technologies [e.g., machine learning (ML)] that are applied rigorously and that are capable of supporting discovery; and 3. To grow with the pace of data, technology, and workforce changes, heliophysics requires a new approach to the representation of knowledge.