No Arabic abstract
Resampling is a key component of sample-based recursive state estimation in particle filters. Recent work explores differentiable particle filters for end-to-end learning. However, resampling remains a challenge in these works, as it is inherently non-differentiable. We address this challenge by replacing traditional resampling with a learned neural network resampler. We present a novel network architecture, the particle transformer, and train it for particle resampling using a likelihood-based loss function over sets of particles. Incorporated into a differentiable particle filter, our model can be end-to-end optimized jointly with the other particle filter components via gradient descent. Our results show that our learned resampler outperforms traditional resampling techniques on synthetic data and in a simulated robot localization task.
Intelligent agents need a physical understanding of the world to predict the impact of their actions in the future. While learning-based models of the environment dynamics have contributed to significant improvements in sample efficiency compared to model-free reinforcement learning algorithms, they typically fail to generalize to system states beyond the training data, while often grounding their predictions on non-interpretable latent variables. We introduce Interactive Differentiable Simulation (IDS), a differentiable physics engine, that allows for efficient, accurate inference of physical properties of rigid-body systems. Integrated into deep learning architectures, our model is able to accomplish system identification using visual input, leading to an interpretable model of the world whose parameters have physical meaning. We present experiments showing automatic task-based robot design and parameter estimation for nonlinear dynamical systems by automatically calculating gradients in IDS. When integrated into an adaptive model-predictive control algorithm, our approach exhibits orders of magnitude improvements in sample efficiency over model-free reinforcement learning algorithms on challenging nonlinear control domains.
In many robotic applications, it is crucial to maintain a belief about the state of a system, which serves as input for planning and decision making and provides feedback during task execution. Bayesian Filtering algorithms address this state estimation problem, but they require models of process dynamics and sensory observations and the respective noise characteristics of these models. Recently, multiple works have demonstrated that these models can be learned by end-to-end training through differentiab
Graph neural networks (GNNs), which learn the representation of a node by aggregating its neighbors, have become an effective computational tool in downstream applications. Over-smoothing is one of the key issues which limit the performance of GNNs as the number of layers increases. It is because the stacked aggregators would make node representations converge to indistinguishable vectors. Several attempts have been made to tackle the issue by bringing linked node pairs close and unlinked pairs distinct. However, they often ignore the intrinsic community structures and would result in sub-optimal performance. The representations of nodes within the same community/class need be similar to facilitate the classification, while different classes are expected to be separated in embedding space. To bridge the gap, we introduce two over-smoothing metrics and a novel technique, i.e., differentiable group normalization (DGN). It normalizes nodes within the same group independently to increase their smoothness, and separates node distributions among different groups to significantly alleviate the over-smoothing issue. Experiments on real-world datasets demonstrate that DGN makes GNN models more robust to over-smoothing and achieves better performance with deeper GNNs.
Recent work has shown how to embed differentiable optimization problems (that is, problems whose solutions can be backpropagated through) as layers within deep learning architectures. This method provides a useful inductive bias for certain problems, but existing software for differentiable optimization layers is rigid and difficult to apply to new settings. In this paper, we propose an approach to differentiating through disciplined convex programs, a subclass of convex optimization problems used by domain-specific languages (DSLs) for convex optimization. We introduce disciplined parametrized programming, a subset of disciplined convex programming, and we show that every disciplined parametrized program can be represented as the composition of an affine map from parameters to problem data, a solver, and an affine map from the solvers solution to a solution of the original problem (a new form we refer to as affine-solver-affine form). We then demonstrate how to efficiently differentiate through each of these components, allowing for end-to-end analytical differentiation through the entire convex program. We implement our methodology in version 1.1 of CVXPY, a popular Python-embedded DSL for convex optimization, and additionally implement differentiable layers for disciplined convex programs in PyTorch and TensorFlow 2.0. Our implementation significantly lowers the barrier to using convex optimization problems in differentiable programs. We present applications in linear machine learning models and in stochastic control, and we show that our layer is competitive (in execution time) compared to specialized differentiable solvers from past work.
We propose a new gradient-based approach for extracting sub-architectures from a given large model. Contrarily to existing pruning methods, which are unable to disentangle the network architecture and the corresponding weights, our architecture-pruning scheme produces transferable new structures that can be successfully retrained to solve different tasks. We focus on a transfer-learning setup where architectures can be trained on a large data set but very few data points are available for fine-tuning them on new tasks. We define a new gradient-based algorithm that trains architectures of arbitrarily low complexity independently from the attached weights. Given a search space defined by an existing large neural model, we reformulate the architecture search task as a complexity-penalized subset-selection problem and solve it through a two-temperature relaxation scheme. We provide theoretical convergence guarantees and validate the proposed transfer-learning strategy on real data.