We present a novel methodology for convex optimization algorithm design using ideas from electric RLC circuits. Given an optimization problem, the first stage of the methodology is to design an appropriate electric circuit whose continuous-time dynamics converge to the solution of the optimization problem at hand. Then, the second stage is an automated, computer-assisted discretization of the continuous-time dynamics, yielding a provably convergent discrete-time algorithm. Our methodology recovers many classical (distributed) optimization algorithms and enables users to quickly design and explore a wide range of new algorithms with convergence guarantees.

We present two new classes of algorithms for efficient field integration on graphs encoding point cloud data. The first class, $\mathrm{SeparatorFactorization}$ (SF), leverages the bounded genus of point cloud mesh graphs, while the second class, $\mathrm{RFDiffusion}$ (RFD), uses popular $\epsilon$-nearest-neighbor graph representations for point clouds. Both can be viewed as providing the functionality of Fast Multipole Methods (FMMs), which have had a tremendous impact on efficient integration, but for non-Euclidean spaces. We focus on geometries induced by distributions of walk lengths between points (e.g. shortest-path distance). We provide an extensive theoretical analysis of our algorithms, obtaining new results in structural graph theory as a byproduct. We also perform exhaustive empirical evaluation, including on-surface interpolation for rigid and deformable objects (in particular for mesh-dynamics modeling) as well as Wasserstein distance computations for point clouds, including the Gromov-Wasserstein variant.

Standard autoregressive seq2seq models are easily trained by max-likelihood, but tend to show poor results under small-data conditions.We introduce a class of seq2seq models, GAMs (Global Autoregressive Models), which combine an autoregressive component with a log-linear component, allowing the use of global a priori features to compensate for lack of data.We train these models in two steps.In the first step, we obtain an unnormalized GAM that maximizes the likelihood of the data, but is improper for fast inference or evaluation.In the second step, we use this GAM to train (by distillation) a second autoregressive model that approximates the normalized distribution associated with the GAM, and can be used for fast inference and evaluation.Our experiments focus on language modelling under synthetic conditions and show a strong perplexity reduction of using the second autoregressive model over the standard one.

Most artificial neural network models for question-answering rely on complex attention mechanisms. These techniques demonstrate high performance on existing datasets; however, they are limited in their ability to capture natural language variability, and to generate diverse relevant answers. To address this limitation, we propose a model that learns multiple interpretations of a given question. This diversity is ensured by our interpretation policy module which automatically adapts the parameters of a question-answering model with respect to a discrete latent variable. This variable follows the distribution of interpretations learned by the interpretation policy through a semi-supervised variational inference framework. To boost the performance further, the resulting policy is fine-tuned using the rewards from the answer accuracy with a policy gradient. We demonstrate the relevance and efficiency of our model through a large panel of experiments. Qualitative results, in particular, underline the ability of the proposed architecture to discover multiple interpretations of a question. When tested using the Stanford Question Answering Dataset 1.1, our model outperforms the baseline methods in finding multiple and diverse answers. To assess our strategy from a human standpoint, we also conduct a large-scale user study. This study highlights the ability of our network to produce diverse and coherent answers compared to existing approaches. Our Pytorch implementation is available as open source.11github.com/parshakova/APIP.