No Arabic abstract
We describe a purely image-based method for finding geometric constructions with a ruler and compass in the Euclidea geometric game. The method is based on adapting the Mask R-CNN state-of-the-art image processing neural architecture and adding a tree-based search procedure to it. In a supervised setting, the method learns to solve all 68 kinds of geometric construction problems from the first six level packs of Euclidea with an average 92% accuracy. When evaluated on new kinds of problems, the method can solve 31 of the 68 kinds of Euclidea problems. We believe that this is the first time that a purely image-based learning has been trained to solve geometric construction problems of this difficulty.
For the task of face verification, we explore the utility of harnessing auxiliary facial emotion labels to impose explicit geometric constraints on the embedding space when training deep embedding models. We introduce several novel loss functions that, in conjunction with a standard Triplet Loss [43], or ArcFace loss [10], provide geometric constraints on the embedding space; the labels for our loss functions can be provided using either manually annotated or automatically detected auxiliary emotion labels. Our method is implemented purely in terms of the loss function and does not require any changes to the neural network backbone of the embedding function.
We propose ScheduleNet, a RL-based real-time scheduler, that can solve various types of multi-agent scheduling problems. We formulate these problems as a semi-MDP with episodic reward (makespan) and learn ScheduleNet, a decentralized decision-making policy that can effectively coordinate multiple agents to complete tasks. The decision making procedure of ScheduleNet includes: (1) representing the state of a scheduling problem with the agent-task graph, (2) extracting node embeddings for agent and tasks nodes, the important relational information among agents and tasks, by employing the type-aware graph attention (TGA), and (3) computing the assignment probability with the computed node embeddings. We validate the effectiveness of ScheduleNet as a general learning-based scheduler for solving various types of multi-agent scheduling tasks, including multiple salesman traveling problem (mTSP) and job shop scheduling problem (JSP).
The last decade has witnessed an experimental revolution in data science and machine learning, epitomised by deep learning methods. Indeed, many high-dimensional learning tasks previously thought to be beyond reach -- such as computer vision, playing Go, or protein folding -- are in fact feasible with appropriate computational scale. Remarkably, the essence of deep learning is built from two simple algorithmic principles: first, the notion of representation or feature learning, whereby adapted, often hierarchical, features capture the appropriate notion of regularity for each task, and second, learning by local gradient-descent type methods, typically implemented as backpropagation. While learning generic functions in high dimensions is a cursed estimation problem, most tasks of interest are not generic, and come with essential pre-defined regularities arising from the underlying low-dimensionality and structure of the physical world. This text is concerned with exposing these regularities through unified geometric principles that can be applied throughout a wide spectrum of applications. Such a geometric unification endeavour, in the spirit of Felix Kleins Erlangen Program, serves a dual purpose: on one hand, it provides a common mathematical framework to study the most successful neural network architectures, such as CNNs, RNNs, GNNs, and Transformers. On the other hand, it gives a constructive procedure to incorporate prior physical knowledge into neural architectures and provide principled way to build future architectures yet to be invented.
We show that generative models can be used to capture visual geometry constraints statistically. We use this fact to infer the 3D shape of object categories from raw single-view images. Differently from prior work, we use no external supervision, nor do we use multiple views or videos of the objects. We achieve this by a simple reconstruction task, exploiting the symmetry of the objects shape and albedo. Specifically, given a single image of the object seen from an arbitrary viewpoint, our model predicts a symmetric canonical view, the corresponding 3D shape and a viewpoint transformation, and trains with the goal of reconstructing the input view, resembling an auto-encoder. Our experiments show that this method can recover the 3D shape of human faces, cat faces, and cars from single view images, without supervision. On benchmarks, we demonstrate superior accuracy compared to other methods that use supervision at the level of 2D image correspondences.
This paper introduces R2D3, an agent that makes efficient use of demonstrations to solve hard exploration problems in partially observable environments with highly variable initial conditions. We also introduce a suite of eight tasks that combine these three properties, and show that R2D3 can solve several of the tasks where other state of the art methods (both with and without demonstrations) fail to see even a single successful trajectory after tens of billions of steps of exploration.