arXiv subjects

Yan Ru Pei

Publications and source records attributed to Yan Ru Pei.

24 records · Page 2Linked to original sources

arXiv2022

A Finite-temperature Phase Transition for the Ising Spin-glass in $d\geq 2$

It is believed that the $\pm J$ Ising spin-glass does not order at finite temperatures in dimension $d=2$. However, using a graphical representation and a contour argument, we prove rigorously the existence of a finite-temperature phase transition in $d\geq 2$ with $T_c \geq 0.4$. In the graphical representation, the low-temperature phase allows for the coexistence of multiple infinite clusters each with a rigidly aligned spin-overlap state. These clusters correlate negatively with each other, and are entropically stable without breaking any global symmetry. They can emerge in most graph structures and disorder measures.

cond-mat.dis-nn↗

arXiv2021

Non-equilibrium criticality and efficient exploration of glassy landscapes with memory dynamics

Spin glasses are notoriously difficult to study both analytically and numerically due to the presence of frustration and metastability. Their highly non-convex landscapes require collective updates to explore efficiently. Currently, most state-of-the-art algorithms rely on stochastic spin clusters to perform non-local updates, but such "cluster algorithms" lack general efficiency. Here, we introduce a non-equilibrium approach for simulating spin glasses based on classical dynamics with memory. By simulating various classes of 3d spin glasses (Edwards-Anderson, partially-frustrated, and fully-frustrated models), we find that memory dynamically promotes critical spin clusters during time evolution, in a self-organizing manner. This facilitates an efficient exploration of the low-temperature phases of spin glasses.

cond-mat.dis-nn↗

arXiv2020

Generating Weighted MAX-2-SAT Instances of Tunable Difficulty with Frustrated Loops

Many optimization problems can be cast into the maximum satisfiability (MAX-SAT) form, and many solvers have been developed for tackling such problems. To evaluate a MAX-SAT solver, it is convenient to generate hard MAX-SAT instances with known solutions. Here, we propose a method of generating weighted MAX-2-SAT instances inspired by the frustrated-loop algorithm used by the quantum annealing community. We extend the algorithm for instances of general bipartite couplings, with the associated optimization problem being the minimization of the restricted Boltzmann machine (RBM) energy over the nodal values, which is useful for effectively pre-training the RBM. The hardness of the generated instances can be tuned through a central parameter known as the frustration index. Two versions of the algorithm are presented: the random- and structured-loop algorithms. For the random-loop algorithm, we provide a thorough theoretical and empirical analysis on its mathematical properties from the perspective of frustration, and observe empirically a double phase transition behavior in the hardness scaling behavior driven by the frustration index. For the structured-loop algorithm, we show that it offers an improvement in hardness over the random-loop algorithm in the regime of high loop density, with the variation of hardness tunable through the concentration of frustrated weights.

cs.LG↗

arXiv2020

Mode-Assisted Unsupervised Learning of Restricted Boltzmann Machines

Restricted Boltzmann machines (RBMs) are a powerful class of generative models, but their training requires computing a gradient that, unlike supervised backpropagation on typical loss functions, is notoriously difficult even to approximate. Here, we show that properly combining standard gradient updates with an off-gradient direction, constructed from samples of the RBM ground state (mode), improves their training dramatically over traditional gradient methods. This approach, which we call mode training, promotes faster training and stability, in addition to lower converged relative entropy (KL divergence). Along with the proofs of stability and convergence of this method, we also demonstrate its efficacy on synthetic datasets where we can compute KL divergences exactly, as well as on a larger machine learning standard, MNIST. The mode training we suggest is quite versatile, as it can be applied in conjunction with any given gradient method, and is easily extended to more general energy-based neural network structures such as deep, convolutional and unrestricted Boltzmann machines.

cs.LG↗

arXiv2019

The Optimal Deterrence of Crime: A Focus on the Time Preference of DWI Offenders

We develop a general model for finding the optimal penal strategy based on the behavioral traits of the offenders. We focus on how the discount rate (level of time discounting) affects criminal propensity on the individual level, and how the aggregation of these effects influences criminal activities on the population level. The effects are aggregated based on the distribution of discount rate among the population. We study this distribution empirically through a survey with 207 participants, and we show that it follows zero-inflated exponential distribution. We quantify the effectiveness of the penal strategy as its net utility for the population, and show how this quantity can be maximized. When we apply the maximization procedure on the offense of impaired driving (DWI), we discover that the effectiveness of DWI deterrence depends critically on the amount of fine and prison condition.

econ.GN↗

arXiv2019

On the Universality of Memcomputing Machines

Universal memcomputing machines (UMMs) [IEEE Trans. Neural Netw. Learn. Syst. 26, 2702 (2015)] represent a novel computational model in which memory (time non-locality) accomplishes both tasks of storing and processing of information. UMMs have been shown to be Turing-complete, namely they can simulate any Turing machine. In this paper, using set theory and cardinality arguments, we compare them with liquid-state machines (or "reservoir computing") and quantum machines ("quantum computing"). We show that UMMs can simulate both types of machines, hence they are both "liquid-" or "reservoir-complete" and "quantum-complete". Of course, these statements pertain only to the type of problems these machines can solve, and not to the amount of resources required for such simulations. Nonetheless, the method presented here provides a general framework in which to describe the relation between UMMs and any other type of computational model.

cs.NE↗