Inductive benchmarking for purely functional data structures

Every designer of a new data structure wants to know how well it performs in comparison with others. But finding, coding and testing applications as benchmarks can be tedious and time-consuming. Besides, how a benchmark uses a data structure may considerably affect its apparent efficiency, so the choice of applications may bias the results. We address these problems by developing a tool for inductive benchmarking. This tool, Auburn, can generate benchmarks across a wide distribution of uses. We precisely define 'the use of a data structure', upon which we build the core algorithms of Auburn: how to generate a benchmark from a description of use, and how to extract a description of use from an application. We then apply inductive classification techniques to obtain decision trees for the choice between competing data structures. We test Auburn by benchmarking several implementations of three common data structures: queues, random-access lists and heaps. These and other results show Auburn to be a useful and accurate tool, but they also reveal some limitations of the approach

A principled approach to programming with nested types in Haskell

Initial algebra semantics is one of the cornerstones of the theory of modern functional programming languages. For each inductive data type, it provides a Church encoding for that type, a build combinator which constructs data of that type, a fold combinator which encapsulates structured recursion over data of that type, and a fold/build rule which optimises modular programs by eliminating from them data constructed using the buildcombinator, and immediately consumed using the foldcombinator, for that type. It has long been thought that initial algebra semantics is not expressive enough to provide a similar foundation for programming with nested types in Haskell. Specifically, the standard folds derived from initial algebra semantics have been considered too weak to capture commonly occurring patterns of recursion over data of nested types in Haskell, and no build combinators or fold/build rules have until now been defined for nested types. This paper shows that standard folds are, in fact, sufficiently expressive for programming with nested types in Haskell. It also defines buildcombinators and fold/build fusion rules for nested types. It thus shows how initial algebra semantics provides a principled, expressive, and elegant foundation for programming with nested types in Haskell

Graph Networks as a Universal Machine Learning Framework for Molecules and Crystals

Graph networks are a new machine learning (ML) paradigm that supports both relational reasoning and combinatorial generalization. Here, we develop universal MatErials Graph Network (MEGNet) models for accurate property prediction in both molecules and crystals. We demonstrate that the MEGNet models outperform prior ML models such as the SchNet in 11 out of 13 properties of the QM9 molecule data set. Similarly, we show that MEGNet models trained on $\sim 60,000$ crystals in the Materials Project substantially outperform prior ML models in the prediction of the formation energies, band gaps and elastic moduli of crystals, achieving better than DFT accuracy over a much larger data set. We present two new strategies to address data limitations common in materials science and chemistry. First, we demonstrate a physically-intuitive approach to unify four separate molecular MEGNet models for the internal energy at 0 K and room temperature, enthalpy and Gibbs free energy into a single free energy MEGNet model by incorporating the temperature, pressure and entropy as global state inputs. Second, we show that the learned element embeddings in MEGNet models encode periodic chemical trends and can be transfer-learned from a property model trained on a larger data set (formation energies) to improve property models with smaller amounts of data (band gaps and elastic moduli)

Extending Coq with Imperative Features and its Application to SAT Verification

This work was supported in part by the french ANR DECERT initiativeInternational audienceCoq has within its logic a programming language that can be used to replace many deduction steps into a single computation, this is the so-called reflection. In this paper, we present two extensions of the evaluation mechanism that preserve its correctness and make it possible to deal with cpu-intensive tasks such as proof checking of SAT traces

Neurosymbolic Programming for Science

Neurosymbolic Programming (NP) techniques have the potential to accelerate scientific discovery. These models combine neural and symbolic components to learn complex patterns and representations from data, using high-level concepts or known constraints. NP techniques can interface with symbolic domain knowledge from scientists, such as prior knowledge and experimental context, to produce interpretable outputs. We identify opportunities and challenges between current NP models and scientific workflows, with real-world examples from behavior analysis in science: to enable the use of NP broadly for workflows across the natural and social sciences.Comment: Neural Information Processing Systems 2022 - AI for science worksho

A simple approach to the visible-light photoactivation of molecular metal oxides

This study explores a new method to maximize the visible-light-driven photocatalytic performance of organic–inorganic hybrid polyoxometalates (POMs). Experimental and theoretical investigations of a family of phosphonate-substituted POMs show that modification of grafted organic moieties can be used to tune the electronic structure and photoactivity of the metal oxide component. Unlike fully inorganic polyoxotungstates, these organic–inorganic hybrid species are responsive to visible light and function as photocatalysts (λ > 420 nm) in the decomposition of a model environmental pollutant. The degree of photoactivation is shown to be dependent on the nature of the inductive effect exerted by the covalently grafted substituent groups. This study emphasizes the untapped potential that lies in an orbital engineering approach to hybrid-POM design and helps to underpin the next generation of bespoke, robust, and cost-effective molecular metal oxide photoactive materials and catalysts