**QRkit**

Embedded computer vision applications increasingly require the speed and power benefits of single-precision (32 bit) floating point. However, applications which make use of Levenberg-like optimization can lose significant accuracy when reducing to single precision, sometimes unrecoverably so. This accuracy can be regained using solvers based on QR rather than Cholesky decomposition, but the absence of sparse QR solvers for common sparsity patterns found in computer vision means that many applications cannot benefit. We introduce an open-source suite of solvers for Eigen, which efficiently compute the QR decomposition for matrices with some common sparsity patterns (block diagonal, horizontal and vertical concatenation, and banded). For problems with very particular sparsity structures, these elements can be composed together in ‘kit’ form, hence the name QRkit. We apply our methods to several computer vision problems, showing competitive performance and suitability especially in single precision arithmetic. … **Biregular Irreducible Functions (BRI)**

It is investigated how to achieve semantic security for the wiretap channel. It is shown that asymptotically, every rate achievable with strong secrecy is also achievable with semantic security if the strong secrecy information leakage decreases sufficiently fast. If the decrease is slow, this continues to hold with a weaker formulation of semantic security. A new type of functions called biregular irreducible (BRI) functions, similar to universal hash functions, is introduced. BRI functions provide a universal method of establishing secrecy. It is proved that the known secrecy rates of any discrete and Gaussian wiretap channel are achievable with semantic security by modular wiretap codes constructed from a BRI function and an error-correcting code. A concrete universal hash function given by finite-field arithmetic can be converted into a BRI function for certain parameters. A characterization of BRI functions in terms of edge-disjoint biregular graphs on a common vertex set is derived. New BRI functions are constructed from families of Ramanujan graphs. It is shown that BRI functions used in modular schemes which achieve the semantic security capacity of discrete or Gaussian wiretap channels should be nearly Ramanujan. Moreover, BRI functions are universal hash functions on average. … **Stochastic Penalty**

The last decade witnessed a rise in the importance of supervised learning applications involving {\em big data} and {\em big models}. Big data refers to situations where the amounts of training data available and needed causes difficulties in the training phase of the pipeline. Big model refers to situations where large dimensional and over-parameterized models are needed for the application at hand. Both of these phenomena lead to a dramatic increase in research activity aimed at taming the issues via the design of new sophisticated optimization algorithms. In this paper we turn attention to the {\em big constraints} scenario and argue that elaborate machine learning systems of the future will necessarily need to account for a large number of real-world constraints, which will need to be incorporated in the training process. This line of work is largely unexplored, and provides ample opportunities for future work and applications. To handle the {\em big constraints} regime, we propose a {\em stochastic penalty} formulation which {\em reduces the problem to the well understood big data regime}. Our formulation has many interesting properties which relate it to the original problem in various ways, with mathematical guarantees. We give a number of results specialized to nonconvex loss functions, smooth convex functions, strongly convex functions and convex constraints. We show through experiments that our approach can beat competing approaches by several orders of magnitude when a medium accuracy solution is required. … **TinBiNN**

Reduced-precision arithmetic improves the size, cost, power and performance of neural networks in digital logic. In convolutional neural networks, the use of 1b weights can achieve state-of-the-art error rates while eliminating multiplication, reducing storage and improving power efficiency. The BinaryConnect binary-weighted system, for example, achieves 9.9% error using floating-point activations on the CIFAR-10 dataset. In this paper, we introduce TinBiNN, a lightweight vector processor overlay for accelerating inference computations with 1b weights and 8b activations. The overlay is very small — it uses about 5,000 4-input LUTs and fits into a low cost iCE40 UltraPlus FPGA from Lattice Semiconductor. To show this can be useful, we build two embedded ‘person detector’ systems by shrinking the original BinaryConnect network. The first is a 10-category classifier with a 89% smaller network that runs in 1,315ms and achieves 13.6% error. The other is a 1-category classifier that is even smaller, runs in 195ms, and has only 0.4% error. In both classifiers, the error can be attributed entirely to training and not reduced precision. …

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