Pedro Gonnet

Oleksandr Ferludin, Arno Eigenwillig, Martin Blais et al. · deepmind

TensorFlow-GNN (TF-GNN) is a scalable library for Graph Neural Networks in TensorFlow. It is designed from the bottom up to support the kinds of rich heterogeneous graph data that occurs in today's information ecosystems. In addition to enabling machine learning researchers and advanced developers, TF-GNN offers low-code solutions to empower the broader developer community in graph learning. Many production models at Google use TF-GNN, and it has been recently released as an open source project. In this paper we describe the TF-GNN data model, its Keras message passing API, and relevant capabilities such as graph sampling and distributed training.

Pedro Gonnet

The most critical component of any adaptive numerical quadrature routine is the estimation of the integration error. Since the publication of the first algorithms in the 1960s, many error estimation schemes have been presented, evaluated and discussed. This paper presents a review of existing error estimation techniques and discusses their differences and their common features. Some common shortcomings of these algorithms are discussed and a new general error estimation technique is presented.

Pedro Gonnet

We present two new adaptive quadrature routines. Both routines differ from previously published algorithms in many aspects, most significantly in how they represent the integrand, how they treat non-numerical values of the integrand, how they deal with improper divergent integrals and how they estimate the integration error. The main focus of these improvements is to increase the reliability of the algorithms without significantly impacting their efficiency. Both algorithms are implemented in Matlab and tested using both the "families" suggested by Lyness and Kaganove and the battery test used by Gander and Gautschi and Kahaner. They are shown to be more reliable, albeit in some cases less efficient, than other commonly-used adaptive integrators.

Pedro Gonnet

In this paper, we consider methods to compute the coefficients of interpolants relative to a basis of polynomials satisfying a three-term recurrence relation. Two new algorithms are presented: the first constructs the coefficients of the interpolation incrementally and can be used to update the coefficients whenever a nodes is added to or removed from the interpolation. The second algorithm, which constructs the interpolation coefficients by decomposing the Vandermonde-like matrix iteratively, can not be used to update or downdate an interpolation, yet is more numerically stable than the first algorithm and is more efficient when the coefficients of multiple interpolations are to be computed over the same set of nodes.

Pedro Gonnet, Thomas Deselaers

We introduce Independently Recurrent Long Short-term Memory cells: IndyLSTMs. These differ from regular LSTM cells in that the recurrent weights are not modeled as a full matrix, but as a diagonal matrix, i.e.\ the output and state of each LSTM cell depends on the inputs and its own output/state, as opposed to the input and the outputs/states of all the cells in the layer. The number of parameters per IndyLSTM layer, and thus the number of FLOPS per evaluation, is linear in the number of nodes in the layer, as opposed to quadratic for regular LSTM layers, resulting in potentially both smaller and faster models. We evaluate their performance experimentally by training several models on the popular \iamondb and CASIA online handwriting datasets, as well as on several of our in-house datasets. We show that IndyLSTMs, despite their smaller size, consistently outperform regular LSTMs both in terms of accuracy per parameter, and in best accuracy overall. We attribute this improved performance to the IndyLSTMs being less prone to overfitting.

Victor Carbune, Pedro Gonnet, Thomas Deselaers et al.

We describe an online handwriting system that is able to support 102 languages using a deep neural network architecture. This new system has completely replaced our previous Segment-and-Decode-based system and reduced the error rate by 20%-40% relative for most languages. Further, we report new state-of-the-art results on IAM-OnDB for both the open and closed dataset setting. The system combines methods from sequence recognition with a new input encoding using Bézier curves. This leads to up to 10x faster recognition times compared to our previous system. Through a series of experiments we determine the optimal configuration of our models and report the results of our setup on a number of additional public datasets.