cssi/SciSciGPT-SciSciNet huggingface dataset:
ProductNet: a Collection of High-Quality Datasets for Product Representation Learning

ProductNet is a collection of high-quality product datasets for better product understanding. Motivated by ImageNet, ProductNet aims at supporting product representation learning by curating product datasets of high quality with properly chosen taxonomy. In this paper, the two goals of building high-quality product datasets and learning product representation support each other in an iterative fashion: the product embedding is obtained via a multi-modal deep neural network (master model) designed to leverage product image and catalog information; and in return, the embedding is utilized via active learning (local model) to vastly accelerate the annotation process. For the labeled data, the proposed master model yields high categorization accuracy (94.7% top-1 accuracy for 1240 classes), which can be used as search indices, partition keys, and input features for machine learning models. The product embedding, as well as the fined-tuned master model for a specific business task, can also be used for various transfer learning tasks.
The benefit of being flexible in distributed computation

In wireless distributed computing, networked nodes perform intermediate computations over data placed in their memory and exchange these intermediate values to calculate function values. In this paper we consider an asymmetric setting where each node has access to a random subset of the data, i.e., we cannot control the data placement. The paper makes a simple point: we can realize significant benefits if we are allowed to be “flexible”, and decide which node computes which function, in our system. We make this argument in the case where each function depends on only two of the data messages, as is the case in similarity searches. We establish a percolation in the behaviour of the system, where, depending on the amount of observed data, by being flexible, we may need no communication at all.
Regularization with stochastic transformations and perturbations for deep semi-supervised learning

Effective convolutional neural networks are trained on large sets of labeled data. However, creating large labeled datasets is a very costly and time-consuming task. Semi-supervised learning uses unlabeled data to train a model with higher accuracy when there is a limited set of labeled data available. In this paper, we consider the problem of semi-supervised learning with convolutional neural networks. Techniques such as randomized data augmentation, dropout and random max-pooling provide better generalization and stability for classifiers that are trained using gradient descent. Multiple passes of an individual sample through the network might lead to different predictions due to the non-deterministic behavior of these techniques. We propose an unsupervised loss function that takes advantage of the stochastic nature of these methods and minimizes the difference between the predictions of multiple passes of a training sample through the network. We evaluate the proposed method on several benchmark datasets.
To Trust Or Not To Trust A Classifier

Knowing when a classifier's prediction can be trusted is useful in many applications and critical for safely using AI. While the bulk of the effort in machine learning research has been towards improving classifier performance, understanding when a classifier's predictions should and should not be trusted has received far less attention. The standard approach is to use the classifier's discriminant or confidence score; however, we show there exists an alternative that is more effective in many situations. We propose a new score, called the {\it trust score}, which measures the agreement between the classifier and a modified nearest-neighbor classifier on the testing example. We show empirically that high (low) trust scores produce surprisingly high precision at identifying correctly (incorrectly) classified examples, consistently outperforming the classifier's confidence score as well as many other baselines. Further, under some mild distributional assumptions, we show that if the trust score for an example is high (low), the classifier will likely agree (disagree) with the Bayes-optimal classifier. Our guarantees consist of non-asymptotic rates of statistical consistency under various nonparametric settings and build on recent developments in topological data analysis.
On the image of a noncommutative polynomial

Abstract Let F be an algebraically closed field of characteristic zero. We consider the question which subsets of M n ( F ) can be images of noncommutative polynomials. We prove that a noncommutative polynomial f has only finitely many similarity orbits modulo nonzero scalar multiplication in its image if and only if f is power-central. The union of the zero matrix and a standard open set closed under conjugation by GL n ( F ) and nonzero scalar multiplication is shown to be the image of a noncommutative polynomial. We investigate the density of the images with respect to the Zariski topology. We also answer Lvovʼs conjecture for multilinear Lie polynomials of degree at most 4 affirmatively.
The Ihara Zeta Function of the Infinite Grid

The infinite grid is the Cayley graph of $\mathbb{Z} \times \mathbb{Z}$ with the usual generators. In this paper, the Ihara zeta function for the infinite grid is computed using elliptic integrals and theta functions. The zeta function of the grid extends to an analytic, multivalued function which satisfies a functional equation. The set of singularities in its domain is finite. The grid zeta function is the first computed example which is non-elementary, and which takes infinitely many values at each point of its domain. It is also the limiting value of the normalized sequence of Ihara zeta functions for square grid graphs and torus graphs.
Sublinear Time Low-Rank Approximation of Positive Semidefinite Matrices

We show how to compute a relative-error low-rank approximation to any positive semidefinite (PSD) matrix in sublinear time, i.e., for any n x n PSD matrix A, in &#xd5;(n &#x22C5; poly(k/&#x03B5;)) time we output a rank-k matrix B, in factored form, for which kA &#x2013; B&#x2551; 2 F &#x2264; (1 + &#x03B5;)&#x2551;A &#x2013; Ak&#x2551;2 F , where Ak is the best rank-k approximation to A. When k and 1/&#x03B5; are not too large compared to the sparsity of A, our algorithm does not need to read all entries of the matrix. Hence, we significantly improve upon previous nnz(A) time algorithms based on oblivious subspace embeddings, and bypass an nnz(A) time lower bound for general matrices (where nnz(A) denotes the number of non-zero entries in the matrix). We prove time lower bounds for low-rank approximation of PSD matrices, showing that our algorithm is close to optimal. Finally, we extend our techniques to give sublinear time algorithms for lowrank approximation of A in the (often stronger) spectral norm metric &#x2551;A &#x2013; B&#x2551;2 2 and for ridge regression on PSD matrices.
Physics and Astrophysics Opportunities with Supernova Neutrinos

Neutrinos emitted from a supernova encode useful information about neutrino physics and astrophysics. Interpreting the neutrino signal depends crucial ly on understanding neutrino production, flavor mixing during propagation, and detection. In this tal k, we review the physics potential of a SN neutrino observation.
Using Programmable Graphene Channels as Weights in Spin-Diffusive Neuromorphic Computing

A graphene-based spin-diffusive neural network is presented in this paper that takes advantage of the locally tunable spin transport of graphene and the non-volatility of nanomagnets. By using electrostatically gated graphene as spintronic synapses, a weighted summation operation can be performed in the spin domain while the weights can be programmed using circuits in the charge domain. Four-component spin/charge circuit simulations coupled to magnetic dynamics are used to show the feasibility of the neuron-synapse functionality and quantify the analog weighting capability of the graphene under different spin-relaxation mechanisms. This spin-diffusive neural network using a graphene-based synapse design achieves total energy consumption of 0.55–0.97 fJ per cell $\cdot $ synapse and attains significantly better scalability compared to its digital counterparts, particularly as the number and bit accuracy of the synapses increases.
Rigidity of the three-dimensional hierarchical Coulomb gas

A random set of points in Euclidean space is called ‘rigid’ or ‘hyperuniform’ if the number of points falling inside any given region has significantly smaller fluctuations than the corresponding number for a set of i.i.d. random points. This phenomenon has received considerable attention in recent years, due to its appearance in random matrix theory, the theory of Coulomb gases and zeros of random analytic functions. However, most of the published results are in dimensions one and two. This paper gives the first proof of hyperuniformity in a Coulomb type system in dimension three, known as the hierarchical Coulomb gas. This is a simplified version of the actual 3D Coulomb gas. The interaction potential in this model, inspired by Dyson’s hierarchical model of the Ising ferromagnet, has a hierarchical structure and is locally an approximation of the Coulomb potential. Hyperuniformity is proved at both macroscopic and microscopic scales, with upper and lower bounds for the order of fluctuations that match up to logarithmic factors. The fluctuations have cube-root behavior, in agreement with a well-known prediction for the 3D Coulomb gas. For completeness, analogous results are also proved for the 2D hierarchical Coulomb gas and the 1D hierarchical log gas.
A strictly stationary, N-tuplewise independent counterexample to the Central Limit Theorem

Abstract For an arbitrary integer N ≥ 2 , this paper gives the construction of a strictly stationary (and ergodic), N -tuplewise independent sequence of (nondegenerate) bounded random variables such that the Central Limit Theorem fails to hold. The sequence is in part an adaptation of a nonstationary example with similar properties constructed by one of the authors (ARP) in a paper published in 1998.
The fast Slepian transform

Abstract The discrete prolate spheroidal sequences (DPSS's) provide an efficient representation for discrete signals that are perfectly timelimited and nearly bandlimited. Due to the high computational complexity of projecting onto the DPSS basis – also known as the Slepian basis – this representation is often overlooked in favor of the fast Fourier transform (FFT). We show that there exist fast constructions for computing approximate projections onto the leading Slepian basis elements. The complexity of the resulting algorithms is comparable to the FFT, and scales favorably as the quality of the desired approximation is increased. In the process of bounding the complexity of these algorithms, we also establish new nonasymptotic results on the eigenvalue distribution of discrete time–frequency localization operators. We then demonstrate how these algorithms allow us to efficiently compute the solution to certain least-squares problems that arise in signal processing. We also provide simulations comparing these fast, approximate Slepian methods to exact Slepian methods as well as the traditional FFT based methods.
Staggered t-Structures on Derived Categories of Equivariant Coherent Sheaves

Let X be a scheme, and let G be an affine group scheme acting on X. Under reasonable hypotheses on X and G, we construct a t-structure on the derived category of G-equivariant coherent sheaves that in many ways resembles the perverse coherent t-structure, but which incorporates additional information from the G-action. Under certain circumstances, the heart of this t-structure, called the “staggered t-structure,” is a finite-length category, and its simple objects are particularly easy to describe. We also exhibit two small examples in which the staggered t-structure is better-behaved than the perverse coherent t-structure.
Improved Deep Learning of Object Category Using Pose Information

Despite significant recent progress, the best available computer vision algorithms still lag far behind human capabilities, even for recognizing individual discrete objects under various poses, illuminations, and backgrounds. Here we present a new approach to using object pose information to improve deep network learning. While existing large-scale datasets, e.g. ImageNet, do not have pose information, we leverage the newly published turntable dataset, iLab-20M, which has 22M images of 704 object instances shot under different lightings, camera viewpoints and turntable rotations, to do more controlled object recognition experiments. We introduce a new convolutional neural network architecture, what/where CNN (2W-CNN), built on a linear-chain feedforward CNN (e.g., AlexNet), augmented by hierarchical layers regularized by object poses. Pose information is only used as feedback signal during training, in addition to category information, but is not needed during test. To validate the approach, we train both 2W-CNN and AlexNet using a fraction of the dataset, and 2W-CNN achieves 6% performance improvement in category prediction. We show mathematically that 2W-CNN has inherent advantages over AlexNet under the stochastic gradient descent (SGD) optimization procedure. Furthermore, we fine-tune object recognition on ImageNet by using the pretrained 2W-CNN and AlexNet features on iLab-20M, results show significant improvement compared with training AlexNet from scratch. Moreover, fine-tuning 2W-CNN features performs even better than fine-tuning the pretrained AlexNet features. These results show that pretrained features on iLab-20M generalize well to natural image datasets, and 2W-CNN learns better features for object recognition than AlexNet.
Noise-induced stabilization of planar flows ii

We show that the complex-valued ODE ($n\geq 1$, $a_{n+1} \neq 0$): $$\dot z = a_{n+1} z^{n+1} + a_n z^n+\cdots+a_0 , $$ which necessarily has trajectories along which the dynamics blows up in finite time, can be stabilized by the addition of an arbitrarily small elliptic, additive Brownian stochastic term. We also show that the stochastic perturbation has a unique invariant probability measure which is heavy-tailed yet is uniformly, exponentially attracting. The methods turn on the construction of Lyapunov functions. The techniques used in the construction are general and can likely be used in other settings where a Lyapunov function is needed. This is a two-part paper. This paper, Part I, focuses on general Lyapunov methods as applied to a special, simplified version of the problem. Part II extends the main results to the general setting.
Extracting gravitational waves induced by plasma turbulence in the early Universe through an averaging process

This work is a follow-up to the paper, "Numerical Relativity as a Tool for Studying the Early Universe". In this article, we determine if cosmological gravitational waves can be accurately extracted from a dynamical spacetime using an averaging process as opposed to conventional methods of gravitational wave extraction using a complex Weyl scalar. We calculate the normalized energy density, strain and degree of polarization of gravitational waves produced by a simulated turbulent plasma similar to what was believed to have existed shortly after the electroweak scale. This calculation is completed using two numerical codes, one which utilizes full General Relativity calculations based on modified BSSN equations while the other utilizes a linearized approximation of General Relativity. Our results show that the spectrum of gravitational waves calculated from the nonlinear code using an averaging process are nearly indistinguishable from those calculated from the linear code. This result validates the use of the averaging process for gravitational wave extraction of cosmological systems.
Wall-crossing functors for quantized symplectic resolutions: perversity and partial Ringel dualities

In this paper we study wall-crossing functors between categories of modules over quantizations of symplectic resolutions. We prove that wall-crossing functors through faces are perverse equivalences and use this to verify an Etingof type conjecture for quantizations of Nakajima quiver varieties associated to affine quivers. In the case when there is a Hamiltonian torus action on the resolution with finitely many fixed points so that it makes sense to speak about categories $\mathcal{O}$ over quantizations, we introduce new standardly stratified structures on these categories $\mathcal{O}$ and relate the wall-crossing functors to the Ringel duality functors associated to these standardly stratified structures.
Regret Bounds for Robust Adaptive Control of the Linear Quadratic Regulator

We consider adaptive control of the Linear Quadratic Regulator (LQR), where an unknown linear system is controlled subject to quadratic costs. Leveraging recent developments in the estimation of linear systems and in robust controller synthesis, we present the first provably polynomial time algorithm that achieves sub-linear regret on this problem. We further study the interplay between regret minimization and parameter estimation by proving a lower bound on the expected regret in terms of the exploration schedule used by any algorithm. Finally, we conduct a numerical study comparing our robust adaptive algorithm to other methods from the adaptive LQR literature, and demonstrate the flexibility of our proposed method by extending it to a demand forecasting problem subject to state constraints.
On model-theoretic tree properties

We study model theoretic tree properties (TP,TP1,TP2) and their associated cardinal invariants (κcdt,κsct,κinp, respectively). In particular, we obtain a quantitative refinement of Shelah’s theorem...
FastGCN: Fast Learning with Graph Convolutional Networks via Importance Sampling

The graph convolutional networks (GCN) recently proposed by Kipf and Welling are an effective graph model for semi-supervised learning. This model, however, was originally designed to be learned with the presence of both training and test data. Moreover, the recursive neighborhood expansion across layers poses time and memory challenges for training with large, dense graphs. To relax the requirement of simultaneous availability of test data, we interpret graph convolutions as integral transforms of embedding functions under probability measures. Such an interpretation allows for the use of Monte Carlo approaches to consistently estimate the integrals, which in turn leads to a batched training scheme as we propose in this work---FastGCN. Enhanced with importance sampling, FastGCN not only is efficient for training but also generalizes well for inference. We show a comprehensive set of experiments to demonstrate its effectiveness compared with GCN and related models. In particular, training is orders of magnitude more efficient while predictions remain comparably accurate.
Transitivity of surface dynamics lifted to Abelian covers

A homeomorphism f of a manifold M is called H1-transitive if there is a transitive lift of an iterate of f to the universal Abelian cover . Roughly speaking, this means that f has orbits which repeatedly and densely explore all elements of H1(M). For a rel pseudo-Anosov map ϕ of a compact surface M we show that the following are equivalent: (a) ϕ is H1-transitive, (b) the action of ϕ on H1(M) has spectral radius one and (c) the lifts of the invariant foliations of ϕ to have dense leaves. The proof relies on a characterization of transitivity for twisted ℤd-extensions of a transitive subshift of finite type.
Derived resolution property for stacks, Euler classes and applications

By resolving an arbitrary perfect derived object over a Deligne-Mumford stack, we define its Euler class. We then apply it to define the Euler numbers for a smooth Calabi-Yau threefold in the 4-dimensional projective space. These numbers are conjectured to be the reduced Gromov-Witten invariants and to determine the usual Gromov-Witten numbers of the smooth quintic as speculated by J. Li and A. Zinger.
Teaching Categories to Human Learners with Visual Explanations

We study the problem of computer-assisted teaching with explanations. Conventional approaches for machine teaching typically only provide feedback at the instance level e.g., the category or label of the instance. However, it is intuitive that clear explanations from a knowledgeable teacher can significantly improve a student's ability to learn a new concept. To address these existing limitations, we propose a teaching framework that provides interpretable explanations as feedback and models how the learner incorporates this additional information. In the case of images, we show that we can automatically generate explanations that highlight the parts of the image that are responsible for the class label. Experiments on human learners illustrate that, on average, participants achieve better test set performance on challenging categorization tasks when taught with our interpretable approach compared to existing methods.
Real-time stochastic kinodynamic motion planning via multiobjective search on GPUs

In this paper we present the PUMP (Parallel Uncertainty-aware Multiobjective Planning) algorithm for addressing the stochastic kinodynamic motion planning problem, whereby one seeks a low-cost, dynamically-feasible motion plan subject to a constraint on collision probability (CP). To ensure exhaustive evaluation of candidate motion plans (as needed to tradeoff the competing objectives of performance and safety), PUMP incrementally builds the Pareto front of the problem, accounting for the optimization objective and an approximation of CP. This is performed by a massively parallel multiobjective search, here implemented with a focus on GPUs. Upon termination of the exploration phase, PUMP searches the Pareto set of motion plans to identify the lowest cost solution that is certified to satisfy the CP constraint (according to an asymptotically exact estimator). We introduce a novel particle-based CP approximation scheme, designed for efficient GPU implementation, which accounts for dependencies over the history of a trajectory execution. We present numerical experiments for quadrotor planning wherein PUMP identifies solutions in ∼100 ms, evaluating over one hundred thousand partial plans through the course of its exploration phase. The results show that this multiobjective search achieves a lower motion plan cost, for the same CP constraint, compared to a safety buffer-based search heuristic and repeated RRT trials.
Millimeter Wave Communications with Reconfigurable Antennas

The highly sparse nature of propagation channels and the restricted use of radio frequency (RF) chains at transceivers limit the performance of millimeter wave (mmWave) multiple-input multiple- output (MIMO) systems. Introducing reconfigurable antennas to mmWave can offer an additional degree of freedom on designing mmWave MIMO systems. This paper provides a theoretical framework for studying the mmWave MIMO with reconfigurable antennas. We present an architecture of reconfigurable mmWave MIMO with beamspace hybrid analog-digital beamformers and reconfigurable antennas at both the transmitter and the receiver. We show that employing reconfigurable antennas can provide throughput gain for the mmWave MIMO. We derive the expression for the average throughput gain of using reconfigurable antennas, and further simplify the expression by considering the case of large number of reconfiguration states. In addition, we propose a low-complexity algorithm for the reconfiguration state and beam selection, which achieves nearly the same throughput performance as the optimal selection of reconfiguration state and beams by exhaustive search.
A digraph fourier transform with spread frequency components

We study the problem of constructing a graph Fourier transform (GFT) for directed graphs (digraphs), which decomposes graph signals into different modes of variation with respect to the underlying network. Accordingly, to capture low, medium and high frequencies we seek a digraph (D)GFT such that the orthonormal frequency components are as spread as possible in the graph spectral domain. This specification gives rise to a challenging nonconvex optimization problem, so we resort to a simple yet efficient heuristic to construct the DGFT basis from Laplacian eigenvectors of an undirected version of the digraph. To select frequency components which are as spread as possible, we define a spectral dispersion function and show that it is supermodular. Moreover, we show that orthonormality can be enforced via a matroid basis constraint, which motivates adopting a scalable greedy algorithm to obtain an approximate solution with provable performance guarantee. The effectiveness of the novel DGFT is illustrated through numerical tests on synthetic and real-world graphs.
Towards Real-Time Detection and Tracking of Spatio-Temporal Features: Blob-Filaments in Fusion Plasma

A novel algorithm and implementation of real-time identification and tracking of blob-filaments in fusion reactor data is presented. Similar spatio-temporal features are important in many other applications, for example, ignition kernels in combustion and tumor cells in a medical image. This work presents an approach for extracting these features by dividing the overall task into three steps: local identification of feature cells, grouping feature cells into extended feature, and tracking movement of feature through overlapping in space. Through our extensive work in parallelization, we demonstrate that this approach can effectively make use of a large number of compute nodes to detect and track blob-filaments in real time in fusion plasma. On a set of 30 GB fusion simulation data, we observed linear speedup on 1,024 processes and completed blob detection in less than three milliseconds using Edison, a Cray XC30 system at NERSC.
Estimating distribution grid topologies: A graphical learning based approach

Distribution grids represent the final tier in electric networks consisting of medium and low voltage lines that connect the distribution substations to the end-users/loads. Traditionally, distribution networks have been operated in a radial topology that may be changed from time to time. Due to absence of a significant number of real-time line monitoring devices in the distribution grid, estimation of the topology/structure is a problem critical for its observability and control. This paper develops a novel graphical learning based approach to estimate the radial operational grid structure using voltage measurements collected from the grid loads. The learning algorithm is based on conditional independence tests for continuous variables over chordal graphs and has wide applicability. It is proven that the scheme can be used for several power flow laws (DC or AC approximations) and more importantly is independent of the specific probability distribution controlling individual bus's power usage. The complexity of the algorithm is discussed and its performance is demonstrated by simulations on distribution test cases.
Neural Programmer: Inducing Latent Programs with Gradient Descent

Abstract: Deep neural networks have achieved impressive supervised classification performance in many tasks including image recognition, speech recognition, and sequence to sequence learning. However, this success has not been translated to applications like question answering that may involve complex arithmetic and logic reasoning. A major limitation of these models is in their inability to learn even simple arithmetic and logic operations. For example, it has been shown that neural networks fail to learn to add two binary numbers reliably. In this work, we propose Neural Programmer, an end-to-end differentiable neural network augmented with a small set of basic arithmetic and logic operations. Neural Programmer can call these augmented operations over several steps, thereby inducing compositional programs that are more complex than the built-in operations. The model learns from a weak supervision signal which is the result of execution of the correct program, hence it does not require expensive annotation of the correct program itself. The decisions of what operations to call, and what data segments to apply to are inferred by Neural Programmer. Such decisions, during training, are done in a differentiable fashion so that the entire network can be trained jointly by gradient descent. We find that training the model is difficult, but it can be greatly improved by adding random noise to the gradient. On a fairly complex synthetic table-comprehension dataset, traditional recurrent networks and attentional models perform poorly while Neural Programmer typically obtains nearly perfect accuracy.
The Asymptotic Distribution of Symbols on Diagonals of Random Weighted Staircase Tableaux

Staircase tableaux are combinatorial objects that were first introduced due to a connection with the asymmetric simple exclusion process (ASEP) and Askey-Wilson polynomials. Since their introduction, staircase tableaux have been the object of study in many recent papers. Relevant to this paper, Hitczenko and Janson proved that distribution of parameters on the first diagonal is asymptotically normal. In addition, they conjectured that other diagonals would be asymptotically Poisson. Since then, only the second and the third diagonal were proven to follow the conjecture. This paper builds upon those results to prove the conjecture for the kth diagonal where k is fixed. In particular, we prove that the distribution of the number of α's (β's) on the kth diagonal, k > 1, is asymptotically Poisson with parameter 1/2. In addition, we prove that symbols on the kth diagonal are asymptotically independent and thus, collectively follow the Poisson distribution with parameter 1. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 49, 795–818, 2016
Deep exploration via bootstrapped DQN

Efficient exploration remains a major challenge for reinforcement learning (RL). Common dithering strategies for exploration, such as '-greedy, do not carry out temporally-extended (or deep) exploration; this can lead to exponentially larger data requirements. However, most algorithms for statistically efficient RL are not computationally tractable in complex environments. Randomized value functions offer a promising approach to efficient exploration with generalization, but existing algorithms are not compatible with nonlinearly parameterized value functions. As a first step towards addressing such contexts we develop bootstrapped DQN. We demonstrate that bootstrapped DQN can combine deep exploration with deep neural networks for exponentially faster learning than any dithering strategy. In the Arcade Learning Environment bootstrapped DQN substantially improves learning speed and cumulative performance across most games.
Operator Calculus of Differential Chains and Differential Forms

We describe a subspace of de Rham currents called “differential chains,” given as an inductive limit of Banach spaces. We make use of the viewpoint introduced by Mackey and developed by Whitney in which currents are treated as chains instead of cochains. This approach gives our space and its topology an intrinsic geometric definition. Moreover, our sequence of norms gives fine control over convergence and compactness, providing viable alternatives to the weak and flat topologies on currents. Boundary is a continuous operator, as are operators that dualize to Hodge star, Lie derivative, pullback and interior product. Partitions of unity exist in this setting, and we are also able to define a Cartesian wedge product. We conclude with an application of this framework, generalizing the Reynolds’ Transport Theorem to nonsmooth domains.
STDP-Based Pruning of Connections and Weight Quantization in Spiking Neural Networks for Energy-Efficient Recognition

Spiking neural networks (SNNs) with a large number of weights and varied weight distribution can be difficult to implement in emerging in-memory computing hardware due to the limitations on crossbar size (implementing dot product), the constrained number of conductance states in non-CMOS devices and the power budget. We present a sparse SNN topology where noncritical connections are pruned to reduce the network size, and the remaining critical synapses are weight quantized to accommodate for limited conductance states. Pruning is based on the power law weight-dependent spike timing dependent plasticity model; synapses between pre- and post-neuron with high spike correlation are retained, whereas synapses with low correlation or uncorrelated spiking activity are pruned. The weights of the retained connections are quantized to the available number of conductance states. The process of pruning noncritical connections and quantizing the weights of critical synapses is performed at regular intervals during training. We evaluated our sparse and quantized network on MNIST dataset and on a subset of images from Caltech-101 dataset. The compressed topology achieved a classification accuracy of 90.1% (91.6%) on the MNIST (Caltech-101) dataset with 3.1X (2.2X) and 4X (2.6X) improvement in energy and area, respectively. The compressed topology is energy and area efficient while maintaining the same classification accuracy of a 2-layer fully connected SNN topology.
On a uniformly random chord diagram and its intersection graph

Abstract A chord diagram refers to a set of chords with distinct endpoints on a circle. The intersection graph of a chord diagram C is defined by substituting the chords of C with vertices and by adding edges between two vertices whenever the corresponding two chords cross each other. Let C n and G n denote the chord diagram chosen uniformly at random from all chord diagrams with n chords and the corresponding intersection graph, respectively. We analyze C n and G n as n tends to infinity. In particular, we study the degree of a random vertex in G n , the k -core of G n , and the number of strong components of the directed graph obtained from G n by orienting edges by flipping a fair coin for each edge. We also give two equivalent evolutions of a random chord diagram and show that, with probability approaching 1 , a chord diagram produced after m steps of these evolutions becomes monolithic as m tends to infinity and stays monolithic afterward forever.
Slow motion for the nonlocal Allen-Cahn equation in n-dimensions

The goal of this paper is to study the slow motion of solutions of the nonlocal Allen–Cahn equation in a bounded domain \(\Omega \subset \mathbb {R}^n\), for \(n > 1\). The initial data is assumed to be close to a configuration whose interface separating the states minimizes the surface area (or perimeter); both local and global perimeter minimizers are taken into account. The evolution of interfaces on a time scale \(\varepsilon ^{-1}\) is deduced, where \(\varepsilon \) is the interaction length parameter. The key tool is a second-order \(\Gamma \)-convergence analysis of the energy functional, which provides sharp energy estimates. New regularity results are derived for the isoperimetric function of a domain. Slow motion of solutions for the Cahn–Hilliard equation starting close to global perimeter minimizers is proved as well.
On the head and the tail of the colored Jones polynomial

The colored Jones polynomial is a function JK : N !" Z[t,t ! 1 ] associated with a knot K in 3-space. We will show that for an alternating knot K the absolute values of the first and the last three leading coe!cients of JK(n) are independent of n when n is su!ciently large. Computation of sample knots indicates that this should be true for any fixed leading coe!cient of the colored Jones polynomial for alternating knots. As a corollary we get a volume-ish theorem for the colored Jones polynomial.
Graph based Neural Networks for Event Factuality Prediction using Syntactic and Semantic Structures

Event factuality prediction (EFP) is the task of assessing the degree to which an event mentioned in a sentence has happened. For this task, both syntactic and semantic information are crucial to identify the important context words. The previous work for EFP has only combined these information in a simple way that cannot fully exploit their coordination. In this work, we introduce a novel graph-based neural network for EFP that can integrate the semantic and syntactic information more effectively. Our experiments demonstrate the advantage of the proposed model for EFP.
Continuity of minimizers to weighted least gradient problems

Abstract We revisit the question of existence and regularity of minimizers to the weighted least gradient problem with Dirichlet boundary condition inf ∫ Ω a ( x ) | D u | : u ∈ B V ( Ω ) , u | ∂ Ω = g , where g ∈ C ( ∂ Ω ) , and a ∈ C 2 ( Ω ) is a weight function that is bounded away from zero. Under suitable geometric conditions on the domain Ω ⊂ R n , we construct continuous solutions of the above problem for any dimension n ≥ 2 , by extending the Sternberg–Williams–Ziemer technique (Sternberg et al., 1992) to this setting of inhomogeneous variations. We show that the level sets of the constructed minimizer are minimal surfaces in the conformal metric a 2 ∕ ( n − 1 ) I n . This result complements the approach in Jerrard et al. (2018) since it provides a continuous solution even in high dimensions where the possibility exists for level sets to develop singularities. The proof relies on an application of a strict maximum principle for sets with area minimizing boundary established by Leon Simon in Simon (1987).
Joint Modeling of Accents and Acoustics for Multi-Accent Speech Recognition

The performance of automatic speech recognition systems degrades with increasing mismatch between the training and testing scenarios. Differences in speaker accents are a significant source of such mismatch. The traditional approach to deal with multiple accents involves pooling data from several accents during training and building a single model in multi-task fashion, where tasks correspond to individual accents. In this paper, we explore an alternate model where we jointly learn an accent classifier and a multi-task acoustic model. Experiments on the American English Wall Street Journal and British English Cambridge corpora demonstrate that our joint model outperforms the strong multi-task acoustic model baseline. We obtain a 5.94% relative improvement in word error rate on British English, and 9.47% relative improvement on American English. This illustrates that jointly modeling with accent information improves acoustic model performance.
Sequential Nonparametric Regression

We present algorithms for nonparametric regression in settings where the data are obtained sequentially. While traditional estimators select bandwidths that depend upon the sample size, for sequential data the effective sample size is dynamically changing. We propose a linear time algorithm that adjusts the bandwidth for each new data point, and show that the estimator achieves the optimal minimax rate of convergence. We also propose the use of online expert mixing algorithms to adapt to unknown smoothness of the regression function. We provide simulations that confirm the theoretical results, and demonstrate the effectiveness of the methods.
Analyzing and mitigating the impact of permanent faults on a systolic array based neural network accelerator

Due to their growing popularity and computational cost, deep neural networks (DNNs) are being targeted for hardware acceleration. A popular architecture for DNN acceleration, adopted by the Google Tensor Processing Unit (TPU), utilizes a systolic array based matrix multiplication unit at its core. This paper deals with the design of fault-tolerant, systolic array based DNN accelerators for high defect rate technologies. To this end, we empirically show that the classification accuracy of a baseline TPU drops significantly even at extremely low fault rates (as low as 0.006%). We then propose two novel strategies, fault-aware pruning (FAP) and fault-aware pruning+retraining (FAP+T), that enable the TPU to operate at fault rates of up to 50%, with negligible drop in classification accuracy (as low as 0.1%) and no run-time performance overhead. The FAP+T does introduce a one-time retraining penalty per TPU chip before it is deployed, but we propose optimizations that reduce this one-time penalty to under 12 minutes. The penalty is then amortized over the entire lifetime of the TPU's operation.
Common greedy wiring and rewiring heuristics do not guarantee maximum assortative graphs of given degree

Abstract We examine two greedy heuristics — wiring and rewiring — for constructing maximum assortative graphs over all simple connected graphs with a target degree sequence. Counterexamples show that natural greedy rewiring heuristics do not necessarily return a maximum assortative graph, even though it is known that the meta-graph of all simple connected graphs with given degree is connected under rewiring. Counterexamples show an elegant greedy graph wiring heuristic from the literature may fail to achieve the target degree sequence or may fail to wire a maximally assortative graph.
The singular set of mean curvature flow with generic singularities

A mean curvature flow starting from a closed embedded hypersurface in $$\mathbf{R}^{n+1}$$ must develop singularities. We show that if the flow has only generic singularities, then the space-time singular set is contained in finitely many compact embedded $$(n-1)$$ -dimensional Lipschitz submanifolds plus a set of dimension at most $$n-2$$ . If the initial hypersurface is mean convex, then all singularities are generic and the results apply. In $$\mathbf{R}^3$$ and $$\mathbf{R}^4$$ , we show that for almost all times the evolving hypersurface is completely smooth and any connected component of the singular set is entirely contained in a time-slice. For 2 or 3-convex hypersurfaces in all dimensions, the same arguments lead to the same conclusion: the flow is completely smooth at almost all times and connected components of the singular set are contained in time-slices. A key technical point is a strong parabolic Reifenberg property that we show in all dimensions and for all flows with only generic singularities. We also show that the entire flow clears out very rapidly after a generic singularity. These results are essentially optimal.
On the quotient of $\mathbb{C}^4$ by a finite primitive group of Type (I)

We study rationality problem for the quotient of $\mathbb{C}^4$ by a finite primitive group $G$ of Type (I). We prove that this quotient is a rational variety for any such $G$.
A Marketplace for Data: An Algorithmic Solution

In this work, we aim to design a data marketplace; a robust real-time matching mechanism to efficiently buy and sell training data for Machine Learning tasks. While the monetization of data and pre-trained models is an essential focus of industry today, there does not exist a market mechanism to price training data and match buyers to sellers while still addressing the associated (computational and other) complexity. The challenge in creating such a market stems from the very nature of data as an asset: (i) it is freely replicable; (ii) its value is inherently combinatorial due to correlation with signal in other data; (iii) prediction tasks and the value of accuracy vary widely; (iv) usefulness of training data is difficult to verify a priori without first applying it to a prediction task. As our main contributions we: (i) propose a mathematical model for a two-sided data market and formally define the key associated challenges; (ii) construct algorithms for such a market to function and analyze how they meet the challenges defined. We highlight two technical contributions: (i) a new notion of "fairness" required for cooperative games with freely replicable goods; (ii) a truthful, zero regret mechanism to auction a class of combinatorial goods based on utilizing Myerson's payment function and the Multiplicative Weights algorithm. These might be of independent interest.
Fluidic Bypass Structures for Improving the Robustness of Liquid Scanning Probes

Objective: We aim to improve operational robustness of liquid scanning probes. Two main failure modes to be addressed are an obstruction of the flow path of the processing liquid and a deviation from the desired gap distance between probe and sample. Methods: We introduce a multi-functional design element, a microfluidic bypass channel, which can be operated in dc and in ac mode, each preventing one of the two main failure modes. Results: In dc mode, the bypass channel is filled with liquid and exhibits resistive behavior, enabling the probe to passively react to an obstruction. In the case of an obstruction of the flow path, the processing liquid is passively diverted through the bypass to prevent its leakage and to limit the buildup of high pressure levels. In ac mode, the bypass is filled with gas and has capacitive characteristics, allowing the gap distance between the probe and the sample to be monitored by observing a phase shift in the motion of two gas–liquid interfaces. For a modulation of the input pressure at 4 Hz, significant changes of the phase shift were observed up to a gap distance of 25 μm. Conclusion: The presented passive design element counters both failure modes in a simple and highly compatible manner. Significance: Liquid scanning probes enabling targeted interfacing with biological surfaces are compatible with a wide range of workflows and bioanalytical applications. An improved operational robustness would facilitate rapid and widespread adoption of liquid scanning probes in research as well as in diagnostics.
Graph-based active learning: A new look at expected error minimization

In graph-based active learning, algorithms based on expected error minimization (EEM) have been popular and yield good empirical performance. The exact computation of EEM optimally balances exploration and exploitation. In practice, however, EEM-based algorithms employ various approximations due to the computational hardness of exact EEM. This can result in a lack of either exploration or exploitation, which can negatively impact the effectiveness of active learning. We propose a new algorithm TSA (Two-Step Approximation) that balances between exploration and exploitation efficiently while enjoying the same computational complexity as existing approximations. Finally, we empirically show the value of balancing between exploration and exploitation in both toy and real-world datasets where our method outperforms several state-of-the-art methods.
Extremal Rays and Automorphisms of Holomorphic Symplectic Varieties

For the last fifteen years, numerous authors have studied the birational geometry of projective irreducible holomorphic symplectic varieties X, seeking to relate extremal contractions \( X \to X ^\prime \) to properties of the Hodge structures on \( H^2 \left( {X,{\Bbb Z}} \right)\,and \,H_2 \left({X,{\Bbb Z}} \right) \), regarded as lattices under the Beauville-Bogomolov form. Significant contributions have been made by Huybrechts, Markman, O’Grady, Verbitsky, and many others [Huy99], [Mar08], [O’G99], [Ver13], see also [Huy11].
Mbps experimental acoustic through-tissue communications: MEAT-COMMS

Methods for digital, phase-coherent acoustic communication date to at least the work of Stojanjovic, et al [20], and the added robustness afforded by improved phase tracking and compensation of Johnson, et al [21]. This work explores the use of such methods for communications through tissue for potential biomedical applications, using the tremendous bandwidth available in commercial medical ultrasound transducers. While long-range ocean acoustic experiments have been at rates of under 100kbps, typically on the order of 1–10kbps, data rates in excess of 120Mb/s have been achieved over cm-scale distances in ultrasonic testbeds [19]. This paper describes experimental transmission of digital communication signals through samples of real pork tissue and beef liver, achieving data rates of 20–30Mbps, demonstrating the possibility of real-time video-rate data transmission through tissue for in-body ultrasonic communications with implanted medical devices.