arXiv subjects

Pierre Baldi

Publications and source records attributed to Pierre Baldi.

At least 91 records · Page 5Linked to original sources

arXiv2019

The capacity of feedforward neural networks

A long standing open problem in the theory of neural networks is the development of quantitative methods to estimate and compare the capabilities of different architectures. Here we define the capacity of an architecture by the binary logarithm of the number of functions it can compute, as the synaptic weights are varied. The capacity provides an upper bound on the number of bits that can be extracted from the training data and stored in the architecture during learning. We study the capacity of layered, fully-connected, architectures of linear threshold neurons with $L$ layers of size $n_1,n_2, \ldots, n_L$ and show that in essence the capacity is given by a cubic polynomial in the layer sizes: $C(n_1,\ldots, n_L)=\sum_{k=1}^{L-1} \min(n_1,\ldots,n_k)n_kn_{k+1}$, where layers that are smaller than all previous layers act as bottlenecks. In proving the main result, we also develop new techniques (multiplexing, enrichment, and stacking) as well as new bounds on the capacity of finite sets. We use the main result to identify architectures with maximal or minimal capacity under a number of natural constraints. This leads to the notion of structural regularization for deep architectures. While in general, everything else being equal, shallow networks compute more functions than deep networks, the functions computed by deep networks are more regular and "interesting".

cs.LG↗

arXiv2019

Improved Energy Reconstruction in NOvA with Regression Convolutional Neural Networks

In neutrino experiments, neutrino energy reconstruction is crucial because neutrino oscillations and differential cross-sections are functions of neutrino energy. It is also challenging due to the complexity in the detector response and kinematics of final state particles. We propose a regression Convolutional Neural Network (CNN) based method to reconstruct electron neutrino energy and electron energy in the NOvA neutrino experiment. We demonstrate that with raw detector pixel inputs, a regression CNN can reconstruct event energy even with complicated final states involving lepton and hadrons. Compared with kinematics-based energy reconstruction, this method shows a significantly better energy resolution. The reconstructed to true energy ratio shows comparable or less dependence on true energy, hadronic energy fractions, and interaction modes. The regression CNN also shows smaller systematic uncertainties from the simulation of neutrino interactions. The proposed energy estimator provides improvements of $16\%$ and $12\%$ in RMS for $ν_e$ CC and electron, respectively. This method can also be extended to solve other regression problems in HEP, taking over kinematics-based reconstruction tasks.

physics.ins-det↗

arXiv2018

Towards Automating Precision Studies of Clone Detectors

Current research in clone detection suffers from poor ecosystems for evaluating precision of clone detection tools. Corpora of labeled clones are scarce and incomplete, making evaluation labor intensive and idiosyncratic, and limiting inter tool comparison. Precision-assessment tools are simply lacking. We present a semi-automated approach to facilitate precision studies of clone detection tools. The approach merges automatic mechanisms of clone classification with manual validation of clone pairs. We demonstrate that the proposed automatic approach has a very high precision and it significantly reduces the number of clone pairs that need human validation during precision experiments. Moreover, we aggregate the individual effort of multiple teams into a single evolving dataset of labeled clone pairs, creating an important asset for software clone research.

cs.SE↗

arXiv2018

Neural Network Gradient Hamiltonian Monte Carlo

Hamiltonian Monte Carlo is a widely used algorithm for sampling from posterior distributions of complex Bayesian models. It can efficiently explore high-dimensional parameter spaces guided by simulated Hamiltonian flows. However, the algorithm requires repeated gradient calculations, and these computations become increasingly burdensome as data sets scale. We present a method to substantially reduce the computation burden by using a neural network to approximate the gradient. First, we prove that the proposed method still maintains convergence to the true distribution though the approximated gradient no longer comes from a Hamiltonian system. Second, we conduct experiments on synthetic examples and real data sets to validate the proposed method.

stat.CO↗

arXiv2018

Oreo: Detection of Clones in the Twilight Zone

Source code clones are categorized into four types of increasing difficulty of detection, ranging from purely textual (Type-1) to purely semantic (Type-4). Most clone detectors reported in the literature work well up to Type-3, which accounts for syntactic differences. In between Type-3 and Type-4, however, there lies a spectrum of clones that, although still exhibiting some syntactic similarities, are extremely hard to detect -- the Twilight Zone. Most clone detectors reported in the literature fail to operate in this zone. We present Oreo, a novel approach to source code clone detection that not only detects Type-1 to Type-3 clones accurately, but is also capable of detecting harder-to-detect clones in the Twilight Zone. Oreo is built using a combination of machine learning, information retrieval, and software metrics. We evaluate the recall of Oreo on BigCloneBench, and perform manual evaluation for precision. Oreo has both high recall and precision. More importantly, it pushes the boundary in detection of clones with moderate to weak syntactic similarity in a scalable manner.

cs.SE↗

arXiv2018

Solving the Rubik's Cube Without Human Knowledge

A generally intelligent agent must be able to teach itself how to solve problems in complex domains with minimal human supervision. Recently, deep reinforcement learning algorithms combined with self-play have achieved superhuman proficiency in Go, Chess, and Shogi without human data or domain knowledge. In these environments, a reward is always received at the end of the game, however, for many combinatorial optimization environments, rewards are sparse and episodes are not guaranteed to terminate. We introduce Autodidactic Iteration: a novel reinforcement learning algorithm that is able to teach itself how to solve the Rubik's Cube with no human assistance. Our algorithm is able to solve 100% of randomly scrambled cubes while achieving a median solve length of 30 moves -- less than or equal to solvers that employ human domain knowledge.

cs.AI↗

arXiv2017

Learning in the Machine: Random Backpropagation and the Deep Learning Channel

Random backpropagation (RBP) is a variant of the backpropagation algorithm for training neural networks, where the transpose of the forward matrices are replaced by fixed random matrices in the calculation of the weight updates. It is remarkable both because of its effectiveness, in spite of using random matrices to communicate error information, and because it completely removes the taxing requirement of maintaining symmetric weights in a physical neural system. To better understand random backpropagation, we first connect it to the notions of local learning and learning channels. Through this connection, we derive several alternatives to RBP, including skipped RBP (SRPB), adaptive RBP (ARBP), sparse RBP, and their combinations (e.g. ASRBP) and analyze their computational complexity. We then study their behavior through simulations using the MNIST and CIFAR-10 bechnmark datasets. These simulations show that most of these variants work robustly, almost as well as backpropagation, and that multiplication by the derivatives of the activation functions is important. As a follow-up, we study also the low-end of the number of bits required to communicate error information over the learning channel. We then provide partial intuitive explanations for some of the remarkable properties of RBP and its variations. Finally, we prove several mathematical results, including the convergence to fixed points of linear chains of arbitrary length, the convergence to fixed points of linear autoencoders with decorrelated data, the long-term existence of solutions for linear systems with a single hidden layer and convergence in special cases, and the convergence to fixed points of non-linear chains, when the derivative of the activation functions is included.

cs.LG↗

arXiv2017

Learning in the Machine: the Symmetries of the Deep Learning Channel

In a physical neural system, learning rules must be local both in space and time. In order for learning to occur, non-local information must be communicated to the deep synapses through a communication channel, the deep learning channel. We identify several possible architectures for this learning channel (Bidirectional, Conjoined, Twin, Distinct) and six symmetry challenges: 1) symmetry of architectures; 2) symmetry of weights; 3) symmetry of neurons; 4) symmetry of derivatives; 5) symmetry of processing; and 6) symmetry of learning rules. Random backpropagation (RBP) addresses the second and third symmetry, and some of its variations, such as skipped RBP (SRBP) address the first and the fourth symmetry. Here we address the last two desirable symmetries showing through simulations that they can be achieved and that the learning channel is particularly robust to symmetry variations. Specifically, random backpropagation and its variations can be performed with the same non-linear neurons used in the main input-output forward channel, and the connections in the learning channel can be adapted using the same algorithm used in the forward channel, removing the need for any specialized hardware in the learning channel. Finally, we provide mathematical results in simple cases showing that the learning equations in the forward and backward channels converge to fixed points, for almost any initial conditions. In symmetric architectures, if the weights in both channels are small at initialization, adaptation in both channels leads to weights that are essentially symmetric during and after learning. Biological connections are discussed.

cs.NE↗

arXiv2017

Efficient Antihydrogen Detection in Antimatter Physics by Deep Learning

Antihydrogen is at the forefront of antimatter research at the CERN Antiproton Decelerator. Experiments aiming to test the fundamental CPT symmetry and antigravity effects require the efficient detection of antihydrogen annihilation events, which is performed using highly granular tracking detectors installed around an antimatter trap. Improving the efficiency of the antihydrogen annihilation detection plays a central role in the final sensitivity of the experiments. We propose deep learning as a novel technique to analyze antihydrogen annihilation data, and compare its performance with a traditional track and vertex reconstruction method. We report that the deep learning approach yields significant improvement, tripling event coverage while simultaneously improving performance by over 5% in terms of Area Under Curve (AUC).

physics.ins-det↗

arXiv2017

Decorrelated Jet Substructure Tagging using Adversarial Neural Networks

We describe a strategy for constructing a neural network jet substructure tagger which powerfully discriminates boosted decay signals while remaining largely uncorrelated with the jet mass. This reduces the impact of systematic uncertainties in background modeling while enhancing signal purity, resulting in improved discovery significance relative to existing taggers. The network is trained using an adversarial strategy, resulting in a tagger that learns to balance classification accuracy with decorrelation. As a benchmark scenario, we consider the case where large-radius jets originating from a boosted resonance decay are discriminated from a background of nonresonant quark and gluon jets. We show that in the presence of systematic uncertainties on the background rate, our adversarially-trained, decorrelated tagger considerably outperforms a conventionally trained neural network, despite having a slightly worse signal-background separation power. We generalize the adversarial training technique to include a parametric dependence on the signal hypothesis, training a single network that provides optimized, interpolatable decorrelated jet tagging across a continuous range of hypothetical resonance masses, after training on discrete choices of the signal mass.

hep-ex↗

arXiv2016

Revealing Fundamental Physics from the Daya Bay Neutrino Experiment using Deep Neural Networks

Experiments in particle physics produce enormous quantities of data that must be analyzed and interpreted by teams of physicists. This analysis is often exploratory, where scientists are unable to enumerate the possible types of signal prior to performing the experiment. Thus, tools for summarizing, clustering, visualizing and classifying high-dimensional data are essential. In this work, we show that meaningful physical content can be revealed by transforming the raw data into a learned high-level representation using deep neural networks, with measurements taken at the Daya Bay Neutrino Experiment as a case study. We further show how convolutional deep neural networks can provide an effective classification filter with greater than 97% accuracy across different classes of physics events, significantly better than other machine learning approaches.

stat.ML↗

arXiv2016

A Theory of Local Learning, the Learning Channel, and the Optimality of Backpropagation

In a physical neural system, where storage and processing are intimately intertwined, the rules for adjusting the synaptic weights can only depend on variables that are available locally, such as the activity of the pre- and post-synaptic neurons, resulting in local learning rules. A systematic framework for studying the space of local learning rules is obtained by first specifying the nature of the local variables, and then the functional form that ties them together into each learning rule. Such a framework enables also the systematic discovery of new learning rules and exploration of relationships between learning rules and group symmetries. We study polynomial local learning rules stratified by their degree and analyze their behavior and capabilities in both linear and non-linear units and networks. Stacking local learning rules in deep feedforward networks leads to deep local learning. While deep local learning can learn interesting representations, it cannot learn complex input-output functions, even when targets are available for the top layer. Learning complex input-output functions requires local deep learning where target information is communicated to the deep layers through a backward learning channel. The nature of the communicated information about the targets and the structure of the learning channel partition the space of learning algorithms. We estimate the learning channel capacity associated with several algorithms and show that backpropagation outperforms them by simultaneously maximizing the information rate and minimizing the computational cost, even in recurrent networks. The theory clarifies the concept of Hebbian learning, establishes the power and limitations of local learning rules, introduces the learning channel which enables a formal analysis of the optimality of backpropagation, and explains the sparsity of the space of learning rules discovered so far.

cs.LG↗

arXiv2016

Jet Flavor Classification in High-Energy Physics with Deep Neural Networks

Classification of jets as originating from light-flavor or heavy-flavor quarks is an important task for inferring the nature of particles produced in high-energy collisions. The large and variable dimensionality of the data provided by the tracking detectors makes this task difficult. The current state-of-the-art tools require expert data-reduction to convert the data into a fixed low-dimensional form that can be effectively managed by shallow classifiers. We study the application of deep networks to this task, attempting classification at several levels of data, starting from a raw list of tracks. We find that the highest-level lowest-dimensionality expert information sacrifices information needed for classification, that the performance of current state-of-the-art taggers can be matched or slightly exceeded by deep-network-based taggers using only track and vertex information, that classification using only lowest-level highest-dimensionality tracking information remains a difficult task for deep networks, and that adding lower-level track and vertex information to the classifiers provides a significant boost in performance compared to the state-of-the-art.

hep-ex↗

arXiv2016

Jet Substructure Classification in High-Energy Physics with Deep Neural Networks

At the extreme energies of the Large Hadron Collider, massive particles can be produced at such high velocities that their hadronic decays are collimated and the resulting jets overlap. Deducing whether the substructure of an observed jet is due to a low-mass single particle or due to multiple decay objects of a massive particle is an important problem in the analysis of collider data. Traditional approaches have relied on expert features designed to detect energy deposition patterns in the calorimeter, but the complexity of the data make this task an excellent candidate for the application of machine learning tools. The data collected by the detector can be treated as a two-dimensional image, lending itself to the natural application of image classification techniques. In this work, we apply deep neural networks with a mixture of locally-connected and fully-connected nodes. Our experiments demonstrate that without the aid of expert features, such networks match or modestly outperform the current state-of-the-art approach for discriminating between jets from single hadronic particles and overlapping jets from pairs of collimated hadronic particles, and that such performance gains persist in the presence of pileup interactions.

hep-ex↗

arXiv2016

Parameterized Machine Learning for High-Energy Physics

We investigate a new structure for machine learning classifiers applied to problems in high-energy physics by expanding the inputs to include not only measured features but also physics parameters. The physics parameters represent a smoothly varying learning task, and the resulting parameterized classifier can smoothly interpolate between them and replace sets of classifiers trained at individual values. This simplifies the training process and gives improved performance at intermediate values, even for complex problems requiring deep learning. Applications include tools parameterized in terms of theoretical model parameters, such as the mass of a particle, which allow for a single network to provide improved discrimination across a range of masses. This concept is simple to implement and allows for optimized interpolatable results.

hep-ex↗

arXiv2015

Learning Activation Functions to Improve Deep Neural Networks

Artificial neural networks typically have a fixed, non-linear activation function at each neuron. We have designed a novel form of piecewise linear activation function that is learned independently for each neuron using gradient descent. With this adaptive activation function, we are able to improve upon deep neural network architectures composed of static rectified linear units, achieving state-of-the-art performance on CIFAR-10 (7.51%), CIFAR-100 (30.83%), and a benchmark from high-energy physics involving Higgs boson decay modes.

cs.NE↗

arXiv2014

Enhanced Higgs to $τ^+τ^-$ Searches with Deep Learning

The Higgs boson is thought to provide the interaction that imparts mass to the fundamental fermions, but while measurements at the Large Hadron Collider (LHC) are consistent with this hypothesis, current analysis techniques lack the statistical power to cross the traditional 5$σ$ significance barrier without more data. \emph{Deep learning} techniques have the potential to increase the statistical power of this analysis by \emph{automatically} learning complex, high-level data representations. In this work, deep neural networks are used to detect the decay of the Higgs to a pair of tau leptons. A Bayesian optimization algorithm is used to tune the network architecture and training algorithm hyperparameters, resulting in a deep network of eight non-linear processing layers that improves upon the performance of shallow classifiers even without the use of features specifically engineered by physicists for this application. The improvement in discovery significance is equivalent to an increase in the accumulated dataset of 25\%.

hep-ph↗

arXiv2014

Searching for Exotic Particles in High-Energy Physics with Deep Learning

Collisions at high-energy particle colliders are a traditionally fruitful source of exotic particle discoveries. Finding these rare particles requires solving difficult signal-versus-background classification problems, hence machine learning approaches are often used. Standard approaches have relied on `shallow' machine learning models that have a limited capacity to learn complex non-linear functions of the inputs, and rely on a pain-staking search through manually constructed non-linear features. Progress on this problem has slowed, as a variety of techniques have shown equivalent performance. Recent advances in the field of deep learning make it possible to learn more complex functions and better discriminate between signal and background classes. Using benchmark datasets, we show that deep learning methods need no manually constructed inputs and yet improve the classification metric by as much as 8\% over the best current approaches. This demonstrates that deep learning approaches can improve the power of collider searches for exotic particles.

hep-ph↗