xDNN: Inference for Deep Convolutional Neural Networks

We present xDNN, an end-to-end system for deep-learning inference based on a family of specialized hardware processors synthesized on Field-Programmable Gate Array (FPGAs) and Convolution Neural Networks (CNN). We present a design optimized for low latency, high throughput, and high compute efficiency with no batching. The design is scalable and a parametric function of the number of multiply-accumulate units, on-chip memory hierarchy, and numerical precision. The design can produce a scale-down processor for embedded devices, replicated to produce more cores for larger devices, or resized to optimize efficiency. On Xilinx Virtex Ultrascale+ VU13P FPGA, we achieve 800 MHz that is close to the Digital Signal Processing maximum frequency and above 80% efficiency of on-chip compute resources. On top of our processor family, we present a runtime system enabling the execution of different networks for different input sizes (i.e., from 224× 224 to 2048× 1024). We present a compiler that reads CNNs from native frameworks (i.e., MXNet, Caffe, Keras, and Tensorflow), optimizes them, generates codes, and provides performance estimates. The compiler combines quantization information from the native environment and optimizations to feed the runtime with code as efficient as any hardware expert could write. We present tools partitioning a CNN into subgraphs for the division of work to CPU cores and FPGAs. Notice that the software will not change when or if the FPGA design becomes an ASIC, making our work vertical and not just a proof-of-concept FPGA project. We show experimental results for accuracy, latency, and power for several networks: In summary, we can achieve up to 4 times higher throughput, 3 times better power efficiency than the GPUs, and up to 20 times higher throughput than the latest CPUs. To our knowledge, we provide solutions faster than any previous FPGA-based solutions and comparable to any other top-of-the-shelves solutions.

Entropy considerations in improved circuits for a biologically-inspired random pulse computer

We present five novel or modified circuits intended for building a universal computer based on random pulse computing (RPC) paradigm, a biologically-inspired way of computation in which variable is represented by a frequency of a random pulse train (RPT) rather than by a logic state. For the first time we investigate operation of RPC circuits from the point of entropy. In particular, we introduce entropy budget criterion (EBC) to reliably predict whether it is even possible to create a deterministic circuit for a given mathematical operation and show its relevance to numerical precision of calculations. Based on insights gained from the EBC, unlike in the previous art, where randomness is obtained from electronics noise or a pseudorandom shift register while processing circuitry is deterministic, in our approach both variable generation and signal processing rely on the random flip-flop (RFF) whose randomness is derived from a fundamentally random quantum process. This approach offers an advantage in higher precision, better randomness of the output and conceptual simplicity of circuits.

Some Critical Reflections on the Measurement of Social Sustainability and Well-Being in Complex Societies

The aim of this discussion paper is to raise awareness of the conceptual and practical limits of mainstream practices in social measurement and to suggest possible directions for social indicator construction, in view of effectively supporting policies for social sustainability and well-being promotion. We start with a review of the epistemological issues raised by the measurement of social phenomena, investigate the notion of social complexity, and discuss the critical link between it and measurement. We then suggest that social indicators should be primarily designed to build structural syntheses of the data, unfolding the patterns and stylizing the complexity of social phenomena, rather than computed pursuing numerical precision, through hardly interpretable aggregated measures. This calls for tools and algorithms capable of rendering structural information, preserving the essential traits of complexity and overcoming the limitations of classical aggregation procedures. We provide some examples along this line, using real data pertaining to regional well-being in OECD countries.

Hilbert curve vs Hilbert space: exploiting fractal 2D covering to increase tensor network efficiency

We present a novel mapping for studying 2D many-body quantum systems by solving an effective, one-dimensional long-range model in place of the original two-dimensional short-range one. In particular, we address the problem of choosing an efficient mapping from the 2D lattice to a 1D chain that optimally preserves the locality of interactions within the TN structure. By using Matrix Product States (MPS) and Tree Tensor Network (TTN) algorithms, we compute the ground state of the 2D quantum Ising model in transverse field with lattice size up to 64×64, comparing the results obtained from different mappings based on two space-filling curves, the snake curve and the Hilbert curve. We show that the locality-preserving properties of the Hilbert curve leads to a clear improvement of numerical precision, especially for large sizes, and turns out to provide the best performances for the simulation of 2D lattice systems via 1D TN structures.

Explicit asymptotic secret key rate of continuous-variable quantum key distribution with an arbitrary modulation

We establish an analytical lower bound on the asymptotic secret key rate of continuous-variable quantum key distribution with an arbitrary modulation of coherent states. Previously, such bounds were only available for protocols with a Gaussian modulation, and numerical bounds existed in the case of simple phase-shift-keying modulations. The latter bounds were obtained as a solution of convex optimization problems and our new analytical bound matches the results of Ghorai et al. (2019), up to numerical precision. The more relevant case of quadrature amplitude modulation (QAM) could not be analyzed with the previous techniques, due to their large number of coherent states. Our bound shows that relatively small constellation sizes, with say 64 states, are essentially sufficient to obtain a performance close to a true Gaussian modulation and are therefore an attractive solution for large-scale deployment of continuous-variable quantum key distribution. We also derive similar bounds when the modulation consists of arbitrary states, not necessarily pure.

Dark matter relic abundance beyond kinetic equilibrium

We introduce , a numerical precision tool for predicting the dark matter relic abundance also in situations where the standard assumption of kinetic equilibrium during the freeze-out process may not be satisfied. comes with a set of three dedicated Boltzmann equation solvers that implement, respectively, the traditionally adopted equation for the dark matter number density, fluid-like equations that couple the evolution of number density and velocity dispersion, and a full numerical evolution of the phase-space distribution. We review the general motivation for these approaches and, for illustration, highlight three concrete classes of models where kinetic and chemical decoupling are intertwined in a way that quantitatively impacts the relic density: (i) dark matter annihilation via a narrow resonance, (ii) Sommerfeld-enhanced annihilation and (iii) ‘forbidden’ annihilation to final states that are kinematically inaccessible at threshold. We discuss all these cases in some detail, demonstrating that the commonly adopted, traditional treatment can result in an estimate of the relic density that is wrong by up to an order of magnitude. The public release of , along with several examples of how to calculate the relic density in concrete models, is provided at drake.hepforge.org

Analytic structure of all loop banana integrals

Using the Gelfand-Kapranov-Zelevinskĭ system for the primitive cohomology of an infinite series of complete intersection Calabi-Yau manifolds, whose dimension is the loop order minus one, we completely clarify the analytic structure of all banana integrals with arbitrary masses. In particular, we find that the leading logarithmic structure in the high energy regime, which corresponds to the point of maximal unipotent monodromy, is determined by a novel $$ \hat{\Gamma}\hbox{-} \mathrm{class} $$ Γ ̂ ‐ class evaluation in the ambient spaces of the mirror, while the imaginary part of the integral in this regime is determined by the $$ \hat{\Gamma}\hbox{-} \mathrm{class} $$ Γ ̂ ‐ class of the mirror Calabi-Yau manifold itself. We provide simple closed all loop formulas for the former as well as for the Frobenius κ-constants, which determine the behaviour of the integrals when the momentum square equals the sum of the masses squared, in terms of zeta values. We extend our previous work from three to four loops by providing for the latter case a complete set of (inhomogeneous) Picard-Fuchs differential equations for arbitrary masses. This allows to evaluate the banana integral in very short time to very high numerical precision for all values of the physical parameters. Using modular properties of the periods we determine the value of the maximal cut equal mass four-loop integral at the attractor points in terms of periods of modular weight two and four Hecke eigenforms and the quasiperiods of their meromorphic cousins.