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25th ACM International Workshop on Formal Techniques for Java-like Programs (FTfJP)

作者： Boehler, Timon Richter, David Mezini, Mira Tech Univ Darmstadt Darmstadt Germany Hessian AI Darmstadt Germany

ISBN: (纸本)9798400702464

Automatic Differentiation (AD) has become a dominant technique in ML. AD frameworks have first been implemented for imperative languages using tapes. Meanwhile, functional implementations of AD have been developed, often based on dual numbers, which are close to the formal specification of differentiation and hence easier to prove correct. But these papers have focussed on correctness not efficiency. Recently, it was shown how an approach using dual numbers could be made efficient through the right optimizations. Optimizations are highly dependent on order, as one optimization can enable another. It can therefore be useful to have fine-grained control over the scheduling of optimizations. One method expresses compiler optimizations as rewrite rules, whose application can be combined and controlled using strategy languages. Previous work describes the use of term rewriting and strategies to generate high-performance code in a compiler for a functional language. In this work, we implement dual numbers AD in a functional array programming language using rewrite rules and strategy combinators for optimization. We aim to combine the elegance of differentiation using dual numbers with a succinct expression of the optimization schedule using a strategy language. We give preliminary evidence suggesting the viability of the approach on a micro-benchmark.

关键词： differentiable programming domain-specific language optimization term rewriting

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Fast Auto-differentiable Digitally Reconstructed Radiographs for Solving Inverse Problems in Intraoperative Imaging 1

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11th International Workshop on Clinical Image-Based Procedures - Towards Holistic Patient Models for Personalised Healthcare (CLIP)

作者： Gopalakrishnan, Vivek Golland, Polina MIT Harvard MIT Hlth Sci & Technol 77 Massachusetts Ave Cambridge MA 02139 USA MIT Comp Sci & Artificial Intelligence Lab 77 Massachusetts Ave Cambridge MA 02139 USA

ISBN: (数字)9783031231797

ISBN: (纸本)9783031231780;9783031231797

The use of digitally reconstructed radiographs (DRRs) to solve inverse problems such as slice-to-volume registration and 3D reconstruction is well-studied in preoperative settings. In intraoperative imaging, the utility of DRRs is limited by the challenges in generating them in real-time and supporting optimization procedures that rely on repeated DRR synthesis. While immense progress has been made in accelerating the generation of DRRs through algorithmic refinements and GPU implementations, DRR-based optimization remains slow because most DRR generators do not offer a straightforward way to obtain gradients with respect to the imaging parameters. To make DRRs interoperable with gradient-based optimization and deep learning frameworks, we have reformulated Siddon's method, the most popular ray-tracing algorithm used in DRR generation, as a series of vectorized tensor operations. We implemented this vectorized version of Siddon's method in PyTorch, taking advantage of the library's strong automatic differentiation engine to make this DRR generator fully differentiable with respect to its parameters. Additionally, using GPU-accelerated tensor computation enables our vectorized implementation to achieve rendering speeds equivalent to state-of-the-art DRR generators implemented in CUDA and C++. We illustrate the resulting method in the context of slice-to-volume registration. Moreover, our simulations suggest that the loss landscapes for the slice-to-volume registration problem are convex in the neighborhood of the optimal solution, and gradient-based registration promises a much faster solution than prevailing gradient-free optimization strategies. The proposed DRR generator enables fast computer vision algorithms to support image guidance in minimally invasive procedures. Our implementation is publically available at https://***/v715/DiffDRR.

关键词： DRRs differentiable programming Inverse problems

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A differentiable IMAGE SOURCE MODEL FOR ROOM ACOUSTICS OPTIMIZATION

A DIFFERENTIABLE IMAGE SOURCE MODEL FOR ROOM ACOUSTICS OPTIM...

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IEEE Workshop on Applications of Signal Processing to Audio and Acoustics (WASPAA)

作者： Zhi, Bowen Sharma, Alisha Zotkin, Dmitry M. Duraiswami, Ramani Univ Maryland Perceptual Interfaces & Real Lab Comp Sci & UMIACS College Pk MD 20742 USA Naval Res Lab Washington DC 20375 USA

ISBN: (纸本)9798350323726

The geometry and material properties of a room dictate its acoustic behavior, which in turn heavily influences the perception of sounds within. Room acoustics models have thus seen use in a broad range of application areas including architecture and interior design, video games, as well as virtual and augmented reality. With recent advances in the development of machine learning, automatic differentiation frameworks have appeared. These frameworks open a promising avenue for research in acoustical signal processing. We investigate the feasibility of using differentiable physics in determining room shape and material to achieve desired acoustical listening characteristics. We present a simple fully differentiable room acoustics simulator and explore its use for gradient-based optimization of room geometry and material properties in proof-of-concept scenarios. Results and applications in various design and inverse problem scenarios are promising.

关键词： Geometric acoustics room and material optimization differentiable programming inverse problems

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A General Construction for Abstract Interpretation of Higher-Order Automatic Differentiation

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PROCEEDINGS OF THE ACM ON programming LANGUAGES-PACMPL 2022年第OOPSLA期6卷 1007–1035页

作者： Laurel, Jacob Yang, Rem Ugare, Shubham Nagel, Robert Singh, Gagandeep Misailovic, Sasa Univ Illinois Champaign IL USA Univ Illinois VMware Res Champaign IL USA

We present a novel, general construction to abstractly interpret higher-order automatic differentiation (AD). Our construction allows one to instantiate an abstract interpreter for computing derivatives up to a chosen order. Furthermore, since our construction reduces the problem of abstractly reasoning about derivatives to abstractly reasoning about real-valued straight-line programs, it can be instantiated with almost any numerical abstract domain, both relational and non-relational. We formally establish the soundness of this construction. We implement our technique by instantiating our construction with both the non-relational interval domain and the relational zonotope domain to compute both first and higher-order derivatives. In the latter case, we are the first to apply a relational domain to automatic differentiation for abstracting higher-order derivatives, and hence we are also the first abstract interpretation work to track correlations across not only different variables, but different orders of derivatives. We evaluate these instantiations on multiple case studies, namely robustly explaining a neural network and more precisely computing a neural network's Lipschitz constant. For robust interpretation, first and second derivatives computed via zonotope AD are up to 4.76x and 6.98x more precise, respectively, compared to interval AD. For Lipschitz certification, we obtain bounds that are up to 11,850x more precise with zonotopes, compared to the state-of-the-art interval-based tool.

关键词： Abstract Interpretation differentiable programming

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A Dual Number Abstraction for Static Analysis of Clarke Jacobians

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PROCEEDINGS OF THE ACM ON programming LANGUAGES-PACMPL 2022年第POPL期6卷 1–30页

作者： Laurel, Jacob Yang, Rem Singh, Gagandeep Misailovic, Sasa Univ Illinois Urbana IL 61801 USA VMware Res Palo Alto CA USA

We present a novel abstraction for bounding the Clarke Jacobian of a Lipschitz continuous, but not necessarily differentiable function over a local input region. To do so, we leverage a novel abstract domain built upon dual numbers, adapted to soundly over-approximate all first derivatives needed to compute the Clarke Jacobian. We formally prove that our novel forward-mode dual interval evaluation produces a sound, interval domain-based over-approximation of the true Clarke Jacobian for a given input region. Due to the generality of our formalism, we can compute and analyze interval Clarke Jacobians for a broader class of functions than previous works supported - specifically, arbitrary compositions of neural networks with Lipschitz, but non-differentiable perturbations. We implement our technique in a tool called DeepJ and evaluate it on multiple deep neural networks and non-differentiable input perturbations to showcase both the generality and scalability of our analysis. Concretely, we can obtain interval Clarke Jacobians to analyze Lipschitz robustness and local optimization landscapes of both fully-connected and convolutional neural networks for rotational, contrast variation, and haze perturbations, as well as their compositions.

关键词： Abstract Interpretation differentiable programming Robustness

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differentiable self-supervised clustering with intrinsic interpretability

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NEURAL NETWORKS 2024年 179卷 106542页

作者： Yan, Xiaoqiang Jin, Zhixiang Mao, Yiqiao Ye, Yangdong Yu, Hui Zhengzhou Univ Sch Comp & Artificial Intelligence 100 Sci Ave Zhengzhou 450000 Peoples R China Univ Glasgow cSCAN Ctr Glasgow City G12 8QB Scotland

Self-supervised clustering has garnered widespread attention due to its ability to discover latent clustering structures without the need for external labels. However, most existing approaches on self-supervised clustering lack of inherent interpretability in the data clustering process. In this paper, we propose a differentiable self-supervised clustering method with intrinsic interpretability (DSC2I), which provides an interpretable data clustering mechanism by reformulating clustering process based on differentiable programming. To be specific, we first design a differentiable mutual information measurement to explicitly train a neural network with analytical gradients, which avoids variational inference and learns a discriminative and compact representation. Then, an interpretable clustering mechanism based on differentiable programming is devised to transform fundamental clustering process (i.e., minimum intra-cluster distance, maximum inter-cluster distance) into neural networks and convert cluster centers to learnable neural parameters, which allows us to obtain a transparent and interpretable clustering layer. Finally, a unified optimization method is designed, in which the differentiable representation learning and interpretable clustering can be optimized simultaneously in a self-supervised manner. Extensive experiments demonstrate the effectiveness of the proposed DSC2I method compared with 16 clustering approaches.

关键词： Interpretable clustering differentiable programming Mutual information measurement Self-supervised clustering

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TOMOPT: differential optimisation for task- and constraint-aware design of particle detectors in the context of muon tomography

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MACHINE LEARNING-SCIENCE AND TECHNOLOGY 2024年第3期5卷 035002页

作者： Strong, Giles C. Lagrange, Maxime Orio, Aitor Bordignon, Anna Bury, Florian Dorigo, Tommaso Giammanco, Andrea Heikal, Mariam Kieseler, Jan Lamparth, Max del Arbol, Pablo Martinez Ruiz Nardi, Federico Vischia, Pietro Zaraket, Haitham MODE Collaborat Padua Italy Ist Nazl Fis Nucl Sez Padova Padua Italy Catholic Univ Louvain Ctr Cosmol Particle Phys & Phenomenol CP3 Louvain La Neuve Belgium Muon Tomog Syst SL Bilbao Spain Univ Cantabria UC Santander Spain Univ Padua Dept Stat Sci Padua Italy Univ Bristol Bristol England Lulea Univ Technol S-97187 Lulea Sweden Amer Univ Beirut Beirut Lebanon Karlsruhe Inst Technol Karlsruhe Germany Tech Univ Munich Phys Dept Munich Germany Inst Fis Cantabria Santander Spain Univ Padua Dipartimento Fis & Astron Padua Italy Univ Clermont Auvergne Clermont Ferrand France Univ Oviedo Oviedo Spain ICTEA Oviedo Spain Lebanese Univ Fac Sci Multidisciplinary Phys Lab Opt & Fiber Opt Grp Beirut Lebanon Univ Grenoble Alpes Lab Phys Subatom & Cosmologie Grenoble France

We describe a software package, TomOpt, developed to optimise the geometrical layout and specifications of detectors designed for tomography by scattering of cosmic-ray muons. The software exploits differentiable programming for the modeling of muon interactions with detectors and scanned volumes, the inference of volume properties, and the optimisation cycle performing the loss minimisation. In doing so, we provide the first demonstration of end-to-end-differentiable and inference-aware optimisation of particle physics instruments. We study the performance of the software on a relevant benchmark scenario and discuss its potential applications. Our code is available on Github (Strong et al 2024 available at: https://***/GilesStrong/tomopt).

关键词： detector design differentiable programming differentiable optimisation end-to-end optimisation muon tomography inference aware learning automatic differentiation

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Making It Simple? Training Deep Learning Models Toward Simplicity

Making It Simple? Training Deep Learning Models Toward Simpl...

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International Conference on Decision Aid Sciences and Applications (DASA)

作者： Repetto, Marco La Torre, Davide Siemens Italy Digital Ind Milan Italy Univ Milano Bicocca Dept Econ Management & Stat Milan Italy SKEMA Business Sch Artificial Intelligence Inst Sophia Antipolis France

ISBN: (纸本)9781665495011

Deep Learning aims to achieve high performances at the expense of explainability. Explainable Artificial Intelligence consists of all the methods addressing this problem. These methods do not provide interpretability right away, and their usage is limited to model debugging. Furthermore, it's unclear when an explanation qualifies as understandable. This paper aims at creating a double backpropagation technique restricting the model's feature effects. The approach ensures interpretable Deep Learning models' explanations during the learning phase. The problem is framed as a Multicriteria one allowing the stakeholders to control the degree of regularization. As a result, the Deep Learning model embodies simple interpretability from the start and is compliant with recent regulations. A series of numerical examples show that our method produces performant yet flexible models that can generalize even when data is scarce.

关键词： Deep Learning Multiple Criteria Decision Making differentiable programming

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differentiable and accelerated spherical harmonic and Wigner transforms

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JOURNAL OF COMPUTATIONAL PHYSICS 2024年 510卷

作者： Price, Matthew A. McEwen, Jason D. Univ Coll London Mullard Space Sci Lab Dorking RH5 6NT Surrey England Alan Turing Inst London NW1 2DB England

Many areas of science and engineering encounter data defined on spherical manifolds. Modelling and analysis of spherical data often necessitates spherical harmonic transforms, at high degrees, and increasingly requires efficient computation of gradients for machine learning or other differentiable programming tasks. We develop novel algorithmic structures for accelerated and differentiable computation of generalised Fourier transforms on the sphere S-2 and rotation group SO(3), i.e. spherical harmonic and Wigner transforms, respectively. We present a recursive algorithm for the calculation of Wigner-functions that is both stable to high harmonic degrees and extremely parallelisable. By tightly coupling this with separable spherical transforms, we obtain algorithms that exhibit an extremely parallelisable structure that is well-suited for the high throughput computing of modern hardware accelerators ( e.g. GPUs). We also develop a hybrid automatic and manual differentiation approach so that gradients can be computed efficiently. Our algorithms are implemented within the JAX differentiable programming framework in the S2FFT I.1 software code. Numerous samplings of the sphere are supported, including equiangular and HEALPix sampling. Computational errors are at the order of machine precision for spherical samplings that admit a sampling theorem. When benchmarked against alternative C codes we observe up to a 400-fold acceleration. Furthermore, when distributing over multiple GPUs we achieve very close to optimal linear scaling with increasing number of GPUs due to the highly parallelised and balanced nature of our algorithms. Provided access to sufficiently many GPUs our transforms thus exhibit an unprecedented effective linear time complexity.

关键词： Harmonic analysis differentiable programming Spherical harmonic transform Wigner transform Machine learning Geometric deep learning

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Robust Counterexample-guided Optimization for Planning from differentiable Temporal Logic

Robust Counterexample-guided Optimization for Planning from ...

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IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)

作者： Dawson, Charles Fan, Chuchu MIT Dept Aeronaut & Astronaut Cambridge MA 02139 USA

ISBN: (数字)9781665479271

ISBN: (纸本)9781665479271

Signal temporal logic (STL) provides a powerful, flexible framework for specifying complex autonomy tasks;however, existing methods for planning based on STL specifications have difficulty scaling to long-horizon tasks and are not robust to external disturbances. In this paper, we present an algorithm for finding robust plans that satisfy STL specifications. Our method alternates between local optimization and local falsification, using automatically differentiable temporal logic to iteratively optimize its plan in response to counterexamples found during the falsification process. We benchmark our counterexample-guided planning method against state-of-the-art planning methods on two long-horizon satellite rendezvous missions, showing that our method finds high-quality plans that satisfy STL specifications despite adversarial disturbances. We find that our method consistently finds plans that are robust to adversarial disturbances and requires less than half the time of competing methods. We provide an implementation of our planner at https://***/MIT-REALM/architect.

关键词： formal methods differentiable programming temporal logic

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