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This paper considers the learning of logical (Boolean) functions with focus on the generalization on the unseen (GOTU) setting, a strong case of out-of-distribution generalization. This is motivated by the fact that the rich combinatorial nature of data in certain reasoning tasks (e.g., arithmetic/logic) makes representative data sampling challenging, and learning successfully under GOTU gives a first vignette of an 'extrapolating' or 'reasoning' learner. We then study how different network architectures trained by (S)GD perform under GOTU and provide both theoretical and experimental evidence that for a class of network models including instances of Transformers, random features models, and diagonal linear networks, a min-degree-interpolator (MDI) is learned on the unseen. We also provide evidence that other instances with larger learning rates or mean-field networks reach leaky MDIs. These findings lead to two implications: (1) we provide an explanation to the length generalization problem (e.g., Anil et al. 2022); (2) we introduce a curriculum learning algorithm called Degree-Curriculum that learns monomials more efficiently by incrementing supports.

Precision radial velocity (RV) measurements continue to be a key tool to detect and characterise extrasolar planets. While instrumental precision keeps improving, stellar activity remains a barrier to obtain reliable measurements below 1-2 m/s accuracy. Using simulations and real data, we investigate the capabilities of a Deep Neural Network approach to produce activity free Doppler measurements of stars. As case studies we use observations of two known stars (Eps Eridani and AUMicroscopii), both with clear signals of activity induced RV variability. Synthetic data using the starsim code are generated for the observables (inputs) and the resulting RV signal (labels), and used to train a Deep Neural Network algorithm. We identify an architecture consisting of convolutional and fully connected layers that is adequate to the task. The indices investigated are mean line-profile parameters (width, bisector, contrast) and multi-band photometry. We demonstrate that the RV-independent approach can drastically reduce spurious Doppler variability from known physical effects such as spots, rotation and convective blueshift. We identify the combinations of activity indices with most predictive power. When applied to real observations, we observe a good match of the correction with the observed variability, but we also find that the noise reduction is not as good as in the simulations, probably due to the lack of detail in the simulated physics. We demonstrate that a model-driven machine learning approach is sufficient to clean Doppler signals from activity induced variability for well known physical effects. There are dozens of known activity related observables whose inversion power remains unexplored indicating that the use of additional indicators, more complete models, and more observations with optimised sampling strategies can lead to significant improvements in our detrending capabilities.

Spatiotemporal learning, which aims at extracting spatiotemporal correlations from the collected spatiotemporal data, is a research hotspot in recent years. And considering the inherent graph structure of spatiotemporal data, recent works focus on capturing spatial dependencies by utilizing Graph Convolutional Networks (GCNs) to aggregate vertex features with the guidance of adjacency matrices. In this paper, with extensive and deep-going experiments, we comprehensively analyze existing spatiotemporal graph learning models and reveal that extracting adjacency matrices with carefully design strategies, which are viewed as the key of enhancing performance on graph learning, are largely ineffective. Meanwhile, based on these experiments, we also discover that the aggregation itself is more important than the way that how vertices are aggregated. With these preliminary, a novel efficient Graph-Free Spatial (GFS) learning module based on layer normalization for capturing spatial correlations in spatiotemporal graph learning. The proposed GFS module can be easily plugged into existing models for replacing all graph convolution components. Rigorous theoretical proof demonstrates that the time complexity of GFS is significantly better than that of graph convolution operation. Extensive experiments verify the superiority of GFS in both the perspectives of efficiency and learning effect in processing graph-structured data especially extreme large scale graph data.

We propose a generalization of the standard matched pairs design in which experimental units (often geographic regions or geos) may be combined into larger units/regions called "supergeos" in order to improve the average matching quality. Unlike optimal matched pairs design which can be found in polynomial time (Lu et al. 2011), this generalized matching problem is NP-hard. We formulate it as a mixed-integer program (MIP) and show that experimental design obtained by solving this MIP can often provide a significant improvement over the standard design regardless of whether the treatment effects are homogeneous or heterogeneous. Furthermore, we present the conditions under which trimming techniques that often improve performance in the case of homogeneous effects (Chen and Au, 2022), may lead to biased estimates and show that the proposed design does not introduce such bias. We use empirical studies based on real-world advertising data to illustrate these findings.

Bird's eye view (BEV) is widely adopted by most of the current point cloud detectors due to the applicability of well-explored 2D detection techniques. However, existing methods obtain BEV features by simply collapsing voxel or point features along the height dimension, which causes the heavy loss of 3D spatial information. To alleviate the information loss, we propose a novel point cloud detection network based on a Multi-level feature dimensionality reduction strategy, called MDRNet. In MDRNet, the Spatial-aware Dimensionality Reduction (SDR) is designed to dynamically focus on the valuable parts of the object during voxel-to-BEV feature transformation. Furthermore, the Multi-level Spatial Residuals (MSR) is proposed to fuse the multi-level spatial information in the BEV feature maps. Extensive experiments on nuScenes show that the proposed method outperforms the state-of-the-art methods. The code will be available upon publication.

Dedicated tensor accelerators demonstrate the importance of linear algebra in modern applications. Such accelerators have the potential for impressive performance gains, but require programmers to rewrite code using vendor APIs - a barrier to wider scale adoption. Recent work overcomes this by matching and replacing patterns within code, but such approaches are fragile and fail to cope with the diversity of real-world codes. We develop ATC, a compiler that uses program synthesis to map regions of code to specific APIs. The mapping space that ATC explores is combinatorially large, requiring the development of program classification, dynamic analysis, variable constraint generation and lexical distance matching techniques to make it tractable. We apply ATC to real-world tensor and linear algebra codes and evaluate them against four state-of-the-art approaches. We accelerate between 2.6x and 7x more programs, leading to over an order of magnitude performance improvement.

This paper presents a framework to represent high-fidelity pointcloud sensor observations for efficient communication and storage. The proposed approach exploits Sparse Gaussian Process to encode pointcloud into a compact form. Our approach represents both the free space and the occupied space using only one model (one 2D Sparse Gaussian Process) instead of the existing two-model framework (two 3D Gaussian Mixture Models). We achieve this by proposing a variance-based sampling technique that effectively discriminates between the free and occupied space. The new representation requires less memory footprint and can be transmitted across limitedbandwidth communication channels. The framework is extensively evaluated in simulation and it is also demonstrated using a real mobile robot equipped with a 3D LiDAR. Our method results in a 70 to 100 times reduction in the communication rate compared to sending the raw pointcloud.

Since hardware resources are limited, the objective of training deep learning models is typically to maximize accuracy subject to the time and memory constraints of training and inference. We study the impact of model size in this setting, focusing on Transformer models for NLP tasks that are limited by compute: self-supervised pretraining and high-resource machine translation. We first show that even though smaller Transformer models execute faster per iteration, wider and deeper models converge in significantly fewer steps. Moreover, this acceleration in convergence typically outpaces the additional computational overhead of using larger models. Therefore, the most compute-efficient training strategy is to counterintuitively train extremely large models but stop after a small number of iterations. This leads to an apparent trade-off between the training efficiency of large Transformer models and the inference efficiency of small Transformer models. However, we show that large models are more robust to compression techniques such as quantization and pruning than small models. Consequently, one can get the best of both worlds: heavily compressed, large models achieve higher accuracy than lightly compressed, small models.

With the rapid increase of large-scale, real-world datasets, it becomes critical to address the problem of long-tailed data distribution (i.e., a few classes account for most of the data, while most classes are under-represented). Existing solutions typically adopt class re-balancing strategies such as re-sampling and re-weighting based on the number of observations for each class. In this work, we argue that as the number of samples increases, the additional benefit of a newly added data point will diminish. We introduce a novel theoretical framework to measure data overlap by associating with each sample a small neighboring region rather than a single point. The effective number of samples is defined as the volume of samples and can be calculated by a simple formula $(1-\beta^{n})/(1-\beta)$, where $n$ is the number of samples and $\beta \in [0,1)$ is a hyperparameter. We design a re-weighting scheme that uses the effective number of samples for each class to re-balance the loss, thereby yielding a class-balanced loss. Comprehensive experiments are conducted on artificially induced long-tailed CIFAR datasets and large-scale datasets including ImageNet and iNaturalist. Our results show that when trained with the proposed class-balanced loss, the network is able to achieve significant performance gains on long-tailed datasets.

We advocate the use of implicit fields for learning generative models of shapes and introduce an implicit field decoder for shape generation, aimed at improving the visual quality of the generated shapes. An implicit field assigns a value to each point in 3D space, so that a shape can be extracted as an iso-surface. Our implicit field decoder is trained to perform this assignment by means of a binary classifier. Specifically, it takes a point coordinate, along with a feature vector encoding a shape, and outputs a value which indicates whether the point is outside the shape or not. By replacing conventional decoders by our decoder for representation learning and generative modeling of shapes, we demonstrate superior results for tasks such as shape autoencoding, generation, interpolation, and single-view 3D reconstruction, particularly in terms of visual quality.