We introduce Centaurus, a class of networks composed of generalized state-space model (SSM) blocks, where the SSM operations can be treated as tensor contractions during training. The optimal order of tensor contractions can then be systematically determined for every SSM block to maximize training efficiency. This allows more flexibility in designing SSM blocks beyond the depthwise-separable configuration commonly implemented. The new design choices will take inspiration from classical convolutional blocks including group convolutions, full convolutions, and bottleneck blocks. We architect the Centaurus network with a mixture of these blocks, to balance between network size and performance, as well as memory and computational efficiency during both training and inference. We show that this heterogeneous network design outperforms its homogeneous counterparts in raw audio processing tasks including keyword spotting, speech denoising, and automatic speech recognition (ASR). For ASR, Centaurus is the first network with competitive performance that can be made fully state-space based, without using any nonlinear recurrence (LSTMs), explicit convolutions (CNNs), or (surrogate) attention mechanism.

We introduce a class of neural networks named PLEIADES (PoLynomial Expansion In Adaptive Distributed Event-based Systems), which contains temporal convolution kernels generated from orthogonal polynomial basis functions. We focus on interfacing these networks with event-based data to perform online spatiotemporal classification and detection with low latency. By virtue of using structured temporal kernels and event-based data, we have the freedom to vary the sample rate of the data along with the discretization step-size of the network without additional finetuning. We experimented with three event-based benchmarks and obtained state-of-the-art results on all three by large margins with significantly smaller memory and compute costs. We achieved: 1) 99.59% accuracy with 192K parameters on the DVS128 hand gesture recognition dataset and 100\% with a small additional output filter; 2) 99.58% test accuracy with 277K parameters on the AIS 2024 eye tracking challenge; and 3) 0.556 mAP with 576k parameters on the PROPHESEE 1 Megapixel Automotive Detection Dataset.

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 MAXSAT 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.

Universal memcomputing machines (UMMs) represent a novel computational model in which memory (time nonlocality) 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, we first introduce a novel set theory approach to compare different computational models and use it to recover the previous results on Turing-completeness of UMMs. We then relate UMMs directly to 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 set-theoretic method presented here provides a general framework which describes the relationship between any computational models.