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Source author record

Barak A. Pearlmutter

Barak A. Pearlmutter appears in the imported research catalog. Authorship, coauthor and topic links are available while profile ownership is still unclaimed.

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Machine LearningMathematical SoftwareProgramming LanguagesNumerical AnalysisNeurons and CognitionDigital LibrariesLogic in Computer ScienceMethodologyQuantitative MethodsSymbolic Computation

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Published work

18 published item(s)

preprint2026arXiv

OSSMM: An Open-Source Sleep Monitor and Modulator

We present the Open-Source Sleep Monitor and Modulator (OSSMM), an open-source hardware and software platform for accessible sleep research. The OSSMM comprises a small wearable headband built from 3D prints and affordable commercial-off-the-shelf (COTS) components at a material cost under 40 euros, supported by a companion Android application. The system requires no conductive gels, disposable electrodes, or specialized equipment, and captures multiple biosignals movement, pulse, electrooculography (EOG), and putative electroencephalography (EEG) with wireless connectivity for data storage and potential sleep modulation capability via an onboard vibration motor. A proof-of-concept single-participant evaluation across 15 nights demonstrated that the captured biosignals support four-stage sleep classification (Wake, Light Sleep, Deep Sleep, REM) using conventional machine learning methods, with the best-performing model achieving a Macro F1-score of 0.770 and accuracy of 0.776 against a validated non-contact sleep monitor ($κ$=0.63 with PSG). Two technical findings are of particular note. First, inexpensive, reusable conductive thermoplastic polyurethane (CTPU) electrodes from commercial fitness chest straps captured a differential signal whose spectral properties in canonical EEG frequency bands, including signatures consistent with sleep spindles, are the principal features driving classification. Second, this signal is obtained from just two frontal electrodes without a dedicated ground reference, suggesting that practical sleep staging is achievable with simpler configurations than typically employed. All hardware designs, software, and build instructions are openly available to support replication and modification by the research community.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

ECG synthesis with Neural ODE and GAN models

Continuous medical time series data such as ECG is one of the most complex time series due to its dynamic and high dimensional characteristics. In addition, due to its sensitive nature, privacy concerns and legal restrictions, it is often even complex to use actual data for different medical research. As a result, generating continuous medical time series is a very critical research area. Several research works already showed that the ability of generative adversarial networks (GANs) in the case of continuous medical time series generation is promising. Most medical data generation works, such as ECG synthesis, are mainly driven by the GAN model and its variation. On the other hand, Some recent work on Neural Ordinary Differential Equation (Neural ODE) demonstrates its strength against informative missingness, high dimension as well as dynamic nature of continuous time series. Instead of considering continuous-time series as a discrete-time sequence, Neural ODE can train continuous time series in real-time continuously. In this work, we used Neural ODE based model to generate synthetic sine waves and synthetic ECG. We introduced a new technique to design the generative adversarial network with Neural ODE based Generator and Discriminator. We developed three new models to synthesise continuous medical data. Different evaluation metrics are then used to quantitatively assess the quality of generated synthetic data for real-world applications and data analysis. Another goal of this work is to combine the strength of GAN and Neural ODE to generate synthetic continuous medical time series data such as ECG. We also evaluated both the GAN model and the Neural ODE model to understand the comparative efficiency of models from the GAN and Neural ODE family in medical data synthesis.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Gradients without Backpropagation

Using backpropagation to compute gradients of objective functions for optimization has remained a mainstay of machine learning. Backpropagation, or reverse-mode differentiation, is a special case within the general family of automatic differentiation algorithms that also includes the forward mode. We present a method to compute gradients based solely on the directional derivative that one can compute exactly and efficiently via the forward mode. We call this formulation the forward gradient, an unbiased estimate of the gradient that can be evaluated in a single forward run of the function, entirely eliminating the need for backpropagation in gradient descent. We demonstrate forward gradient descent in a range of problems, showing substantial savings in computation and enabling training up to twice as fast in some cases.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Neural ODEs for Informative Missingness in Multivariate Time Series

Informative missingness is unavoidable in the digital processing of continuous time series, where the value for one or more observations at different time points are missing. Such missing observations are one of the major limitations of time series processing using deep learning. Practical applications, e.g., sensor data, healthcare, weather, generates data that is in truth continuous in time, and informative missingness is a common phenomenon in these datasets. These datasets often consist of multiple variables, and often there are missing values for one or many of these variables. This characteristic makes time series prediction more challenging, and the impact of missing input observations on the accuracy of the final output can be significant. A recent novel deep learning model called GRU-D is one early attempt to address informative missingness in time series data. On the other hand, a new family of neural networks called Neural ODEs (Ordinary Differential Equations) are natural and efficient for processing time series data which is continuous in time. In this paper, a deep learning model is proposed that leverages the effective imputation of GRU-D, and the temporal continuity of Neural ODEs. A time series classification task performed on the PhysioNet dataset demonstrates the performance of this architecture.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Neural Ordinary Differential Equation based Recurrent Neural Network Model

Neural differential equations are a promising new member in the neural network family. They show the potential of differential equations for time series data analysis. In this paper, the strength of the ordinary differential equation (ODE) is explored with a new extension. The main goal of this work is to answer the following questions: (i)~can ODE be used to redefine the existing neural network model? (ii)~can Neural ODEs solve the irregular sampling rate challenge of existing neural network models for a continuous time series, i.e., length and dynamic nature, (iii)~how to reduce the training and evaluation time of existing Neural ODE systems? This work leverages the mathematical foundation of ODEs to redesign traditional RNNs such as Long Short-Term Memory (LSTM) and Gated Recurrent Unit (GRU). The main contribution of this paper is to illustrate the design of two new ODE-based RNN models (GRU-ODE model and LSTM-ODE) which can compute the hidden state and cell state at any point of time using an ODE solver. These models reduce the computation overhead of hidden state and cell state by a vast amount. The performance evaluation of these two new models for learning continuous time series with irregular sampling rate is then demonstrated. Experiments show that these new ODE based RNN models require less training time than Latent ODEs and conventional Neural ODEs. They can achieve higher accuracy quickly, and the design of the neural network is simpler than, previous neural ODE systems.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Binomial Checkpointing for Arbitrary Programs with No User Annotation

Heretofore, automatic checkpointing at procedure-call boundaries, to reduce the space complexity of reverse mode, has been provided by systems like Tapenade. However, binomial checkpointing, or treeverse, has only been provided in Automatic Differentiation (AD) systems in special cases, e.g., through user-provided pragmas on DO loops in Tapenade, or as the nested taping mechanism in adol-c for time integration processes, which requires that user code be refactored. We present a framework for applying binomial checkpointing to arbitrary code with no special annotation or refactoring required. This is accomplished by applying binomial checkpointing directly to a program trace. This trace is produced by a general-purpose checkpointing mechanism that is orthogonal to AD.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

DiffSharp: An AD Library for .NET Languages

DiffSharp is an algorithmic differentiation or automatic differentiation (AD) library for the .NET ecosystem, which is targeted by the C# and F# languages, among others. The library has been designed with machine learning applications in mind, allowing very succinct implementations of models and optimization routines. DiffSharp is implemented in F# and exposes forward and reverse AD operators as general nestable higher-order functions, usable by any .NET language. It provides high-performance linear algebra primitives---scalars, vectors, and matrices, with a generalization to tensors underway---that are fully supported by all the AD operators, and which use a BLAS/LAPACK backend via the highly optimized OpenBLAS library. DiffSharp currently uses operator overloading, but we are developing a transformation-based version of the library using F#'s "code quotation" metaprogramming facility. Work on a CUDA-based GPU backend is also underway.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Efficient Implementation of a Higher-Order Language with Built-In AD

We show that Automatic Differentiation (AD) operators can be provided in a dynamic language without sacrificing numeric performance. To achieve this, general forward and reverse AD functions are added to a simple high-level dynamic language, and support for them is included in an aggressive optimizing compiler. Novel technical mechanisms are discussed, which have the ability to migrate the AD transformations from run-time to compile-time. The resulting system, although only a research prototype, exhibits startlingly good performance. In fact, despite the potential inefficiencies entailed by support of a functional-programming language and a first-class AD operator, performance is competitive with the fastest available preprocessor-based Fortran AD systems. On benchmarks involving nested use of the AD operators, it can even dramatically exceed their performance.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Evolving the Incremental λ Calculus into a Model of Forward Automatic Differentiation (AD)

Formal transformations somehow resembling the usual derivative are surprisingly common in computer science, with two notable examples being derivatives of regular expressions and derivatives of types. A newcomer to this list is the incremental $λ$-calculus, or ILC, a "theory of changes" that deploys a formal apparatus allowing the automatic generation of efficient update functions which perform incremental computation. The ILC is not only defined, but given a formal machine-understandable definition---accompanied by mechanically verifiable proofs of various properties, including in particular correctness of various sorts. Here, we show how the ILC can be mutated into propagating tangents, thus serving as a model of Forward Accumulation Mode Automatic Differentiation. This mutation is done in several steps. These steps can also be applied to the proofs, resulting in machine-checked proofs of the correctness of this model of forward AD.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Tricks from Deep Learning

The deep learning community has devised a diverse set of methods to make gradient optimization, using large datasets, of large and highly complex models with deeply cascaded nonlinearities, practical. Taken as a whole, these methods constitute a breakthrough, allowing computational structures which are quite wide, very deep, and with an enormous number and variety of free parameters to be effectively optimized. The result now dominates much of practical machine learning, with applications in machine translation, computer vision, and speech recognition. Many of these methods, viewed through the lens of algorithmic differentiation (AD), can be seen as either addressing issues with the gradient itself, or finding ways of achieving increased efficiency using tricks that are AD-related, but not provided by current AD systems. The goal of this paper is to explain not just those methods of most relevance to AD, but also the technical constraints and mindset which led to their discovery. After explaining this context, we present a "laundry list" of methods developed by the deep learning community. Two of these are discussed in further mathematical detail: a way to dramatically reduce the size of the tape when performing reverse-mode AD on a (theoretically) time-reversible process like an ODE integrator; and a new mathematical insight that allows for the implementation of a stochastic Newton's method.

0 citations0 reviewsNo code linkedOpen access
preprint2015arXiv

DiffSharp: Automatic Differentiation Library

In this paper we introduce DiffSharp, an automatic differentiation (AD) library designed with machine learning in mind. AD is a family of techniques that evaluate derivatives at machine precision with only a small constant factor of overhead, by systematically applying the chain rule of calculus at the elementary operator level. DiffSharp aims to make an extensive array of AD techniques available, in convenient form, to the machine learning community. These including arbitrary nesting of forward/reverse AD operations, AD with linear algebra primitives, and a functional API that emphasizes the use of higher-order functions and composition. The library exposes this functionality through an API that provides gradients, Hessians, Jacobians, directional derivatives, and matrix-free Hessian- and Jacobian-vector products. Bearing the performance requirements of the latest machine learning techniques in mind, the underlying computations are run through a high-performance BLAS/LAPACK backend, using OpenBLAS by default. GPU support is currently being implemented.

0 citations0 reviewsNo code linkedOpen access
preprint2015arXiv

The Compositional Nature of Event Representations in the Human Brain

How does the human brain represent simple compositions of constituents: actors, verbs, objects, directions, and locations? Subjects viewed videos during neuroimaging (fMRI) sessions from which sentential descriptions of those videos were identified by decoding the brain representations based only on their fMRI activation patterns. Constituents (e.g., "fold" and "shirt") were independently decoded from a single presentation. Independent constituent classification was then compared to joint classification of aggregate concepts (e.g., "fold-shirt"); results were similar as measured by accuracy and correlation. The brain regions used for independent constituent classification are largely disjoint and largely cover those used for joint classification. This allows recovery of sentential descriptions of stimulus videos by composing the results of the independent constituent classifiers. Furthermore, classifiers trained on the words one set of subjects think of when watching a video can recognise sentences a different subject thinks of when watching a different video.

0 citations0 reviewsNo code linkedOpen access
preprint2014arXiv

An Analysis of Publication Venues for Automatic Differentiation Research

We present the results of our analysis of publication venues for papers on automatic differentiation (AD), covering academic journals and conference proceedings. Our data are collected from the AD publications database maintained by the autodiff.org community website. The database is purpose-built for the AD field and is expanding via submissions by AD researchers. Therefore, it provides a relatively noise-free list of publications relating to the field. However, it does include noise in the form of variant spellings of journal and conference names. We handle this by manually correcting and merging these variants under the official names of corresponding venues. We also share the raw data we get after these corrections.

0 citations0 reviewsNo code linkedOpen access
preprint2014arXiv

Automatic Differentiation of Algorithms for Machine Learning

Automatic differentiation---the mechanical transformation of numeric computer programs to calculate derivatives efficiently and accurately---dates to the origin of the computer age. Reverse mode automatic differentiation both antedates and generalizes the method of backwards propagation of errors used in machine learning. Despite this, practitioners in a variety of fields, including machine learning, have been little influenced by automatic differentiation, and make scant use of available tools. Here we review the technique of automatic differentiation, describe its two main modes, and explain how it can benefit machine learning practitioners. To reach the widest possible audience our treatment assumes only elementary differential calculus, and does not assume any knowledge of linear algebra.

0 citations0 reviewsNo code linkedOpen access
preprint2013arXiv

Block Coordinate Descent for Sparse NMF

Nonnegative matrix factorization (NMF) has become a ubiquitous tool for data analysis. An important variant is the sparse NMF problem which arises when we explicitly require the learnt features to be sparse. A natural measure of sparsity is the L$_0$ norm, however its optimization is NP-hard. Mixed norms, such as L$_1$/L$_2$ measure, have been shown to model sparsity robustly, based on intuitive attributes that such measures need to satisfy. This is in contrast to computationally cheaper alternatives such as the plain L$_1$ norm. However, present algorithms designed for optimizing the mixed norm L$_1$/L$_2$ are slow and other formulations for sparse NMF have been proposed such as those based on L$_1$ and L$_0$ norms. Our proposed algorithm allows us to solve the mixed norm sparsity constraints while not sacrificing computation time. We present experimental evidence on real-world datasets that shows our new algorithm performs an order of magnitude faster compared to the current state-of-the-art solvers optimizing the mixed norm and is suitable for large-scale datasets.

0 citations0 reviewsNo code linkedOpen access
preprint2013arXiv

The Compositional Nature of Verb and Argument Representations in the Human Brain

How does the human brain represent simple compositions of objects, actors,and actions? We had subjects view action sequence videos during neuroimaging (fMRI) sessions and identified lexical descriptions of those videos by decoding (SVM) the brain representations based only on their fMRI activation patterns. As a precursor to this result, we had demonstrated that we could reliably and with high probability decode action labels corresponding to one of six action videos (dig, walk, etc.), again while subjects viewed the action sequence during scanning (fMRI). This result was replicated at two different brain imaging sites with common protocols but different subjects, showing common brain areas, including areas known for episodic memory (PHG, MTL, high level visual pathways, etc.,i.e. the 'what' and 'where' systems, and TPJ, i.e. 'theory of mind'). Given these results, we were also able to successfully show a key aspect of language compositionality based on simultaneous decoding of object class and actor identity. Finally, combining these novel steps in 'brain reading' allowed us to accurately estimate brain representations supporting compositional decoding of a complex event composed of an actor, a verb, a direction, and an object.

0 citations0 reviewsNo code linkedOpen access
preprint2012arXiv

AD in Fortran, Part 1: Design

We propose extensions to Fortran which integrate forward and reverse Automatic Differentiation (AD) directly into the programming model. Irrespective of implementation technology, embedding AD constructs directly into the language extends the reach and convenience of AD while allowing abstraction of concepts of interest to scientific-computing practice, such as root finding, optimization, and finding equilibria of continuous games. Multiple different subprograms for these tasks can share common interfaces, regardless of whether and how they use AD internally. A programmer can maximize a function F by calling a library maximizer, XSTAR=ARGMAX(F,X0), which internally constructs derivatives of F by AD, without having to learn how to use any particular AD tool. We illustrate the utility of these extensions by example: programs become much more concise and closer to traditional mathematical notation. A companion paper describes how these extensions can be implemented by a program that generates input to existing Fortran-based AD tools.

0 citations0 reviewsNo code linkedOpen access
preprint2012arXiv

AD in Fortran, Part 2: Implementation via Prepreprocessor

We describe an implementation of the Farfel Fortran AD extensions. These extensions integrate forward and reverse AD directly into the programming model, with attendant benefits to flexibility, modularity, and ease of use. The implementation we describe is a "prepreprocessor" that generates input to existing Fortran-based AD tools. In essence, blocks of code which are targeted for AD by Farfel constructs are put into subprograms which capture their lexical variable context, and these are closure-converted into top-level subprograms and specialized to eliminate EXTERNAL arguments, rendering them amenable to existing AD preprocessors, which are then invoked, possibly repeatedly if the AD is nested.

0 citations0 reviewsNo code linkedOpen access