In large-scale distributed matrix-vector multiplications, e.g., for generative AI, straggling nodes can slow down or even jeopardize the whole operation. Coded distributed computing (CDC) uses erasure codes to create redundant computations and combat stragglers. This requires encoding very large matrices. Moreover, encoding must be repeated whenever system parameters (e.g., weight matrices in AI models) evolve. This paper introduces a general framework for reducing encoding complexity in CDC. We propose the notion of an encoding blueprint, a construction schedule that specifies how each coded symbol is constructed from data and previously computed coded symbols. An optimal blueprint minimizes the number of arithmetic operations required for a given code. We first design blueprints using addition-only operations. We then extend the framework to also allow subtraction, which further decreases the number of required operations. The optimization problem is cast as a mixed-integer program (MIP), and solved. Numerical results on matrix–vector multiplication show that optimized blueprints reduce encoding operations by up to 60 percent compared to standard methods, saving billions of operations in large-scale applications. Our techniques can be used for efficient decoding as well.

In high-rate or long-haul optical fiber transmissions, correcting chromatic dispersion (CD) is critical but challenging and energy-intensive due to the large filter tap size required for CD compensation (CDC). Overlap-save (OLS) is a common frequency-domain CDC technique that uses fast Fourier transform (FFT). However, hardware constraints-such as power, memory, latency, and chip area-limit the FFT size. This limitation makes OLS too complex or even infeasible in dispersive channels where the number of taps approaches or exceeds the FFT size. We introduce the time-segmented overlap-free (TS-OLF) technique, a novel frequency-domain block filtering method to enable low-complexity CDC under FFT-size limitations. TS-OLF divides the signal into non-overlapping blocks and segments the filter accordingly to enable filtering operations with any FFT size. It aggregates the results of different filter segments directly in the frequency domain, therefore, using a minimum number of FFT operations. We show that TS-OLF achieves consistently lower complexity than OLS when the filter size is more than half the FFT size, and unlike OLS, can handle filter sizes that exceed the FFT size. TS-OLF also outperforms other filter segmenting methods, providing significant complexity improvements.

Dragonfly visual systems intrinsically incorporate a variety of motion‐sensitive neurons able to be well contributed to probe into bio‐inspired computational models. However, it remains unclear how their visual response mechanisms can be borrowed to construct neurocomputational models for solving optimization problems. Hereby, a feedforward dragonfly visual attention–merged neural network (DVAMNN) with presynaptic and postsynaptic subnetworks is developed to output two types of online activities named learning rates in terms of the dragonfly visual information‐processing and attention mechanisms. Integrated such learning rates into a new‐type and metaheuristics‐inspired state transition strategy, a dragonfly visual attention–merged evolutionary neural network (DVAMENN) with the unique parameter of input resolution is developed to solve ultrahigh dimensional global optimization (UHDGO) problems. The theoretical analysis implicates that the DVAMENN’s complexity is mainly decided by the optimization problem itself. Experimental results have confirmed that DVAMENN can successfully optimize the structures of two sixth‐order active filters and discover the global or approximate solutions of the CEC’ 2010 and CEC’ 2013 benchmark suites with dimension 20,000 per example. Nevertheless, the compared metaheuristics encounter unprecedented troubles in the case of UHDGO.

According to the Gaussian noise (GN) model, nonlinear interference noise (NLIN) in fiber depends on the signal power spectral density (PSD). Consequently, optimizing the PSD of the pulse that modulates data, as the main factor influencing the PSD of the launched signal into the fiber, can effectively minimize fiber NLIN. In this study, we first employ the calculus of variations to identify the optimal band-limited pulse PSD that minimizes fiber NLIN. Next, we add other communication requirements, such as zero inter-symbol interference (ISI) and fast decay over time, as constraints to our design problem. For this case, we develop a general pulse model and formulate the design problem as an optimization problem. By solving this optimization problem, we find the optimal pulse PSD that not only minimizes NLIN power in fiber but also meets practical requirements. We study the time-domain impact of the designed modulating pulse PSD on the launched signal properties to gain insights into the nonlinearity benefits we achieve. We further analytically demonstrate that our designed pulse has favorable properties for the Godard timing recovery method. Through extensive simulations using the split-step Fourier method on a fiber with typical parameters and considering practical transmitter/receiver limitations, we illustrate the superior system reach and achievable data rate of our optimized pulses compared to existing pulse shapes.

Biological systems have a great number of visual motion detection neurons, some of which can preferentially react to specific visual regions. Nevertheless, little work has been performed about how they can be used to develop neural network models for omnidirectional collision detection. Hereby, an artificial fly visual brain neural network with presynaptic and postsynaptic subnetworks, for the first time, is developed to detect the changes of visual motion in panoramic scenes. Herein, the presynaptic subnetwork, which originates from the preferential response characteristics of five fly visual neurons, responds to all the moving objects in the panoramic field; the postsynaptic network, which is based on the properties of the angle and height detection neurons in the fly’s brain system, collects the excitatory intensities of the visual neurons, and outputs the real‐time activities of the main object closest to the panoramic camera. Hereafter, a computational model is constructed to implement omnidirectional collision detection, relying upon the artificial visual brain neural network and three functional neurons. The theoretical analysis has verified that the collision detection model’s computational complexity depends mainly on the image input resolution. Three experimental conclusions can be clearly drawn: (i) the motion characteristics of the main object in the panoramic environment can be clearly exhibited in the neural network; (ii) the collision detection model can not only outperform the compared models but also successfully perform omnidirectional collision detection; and (iii) it spends 0.24 s or so to execute visual information processing per frame with the resolution of 120 × 80.

Neurophysiologic achievements claimed that the fly visual system could naturally contribute to a type of artificial computation model which used motion-sensitive neurons to detect the local movement direction changes of moving objects. It, however, still remains open how the neurons' information-processing mechanisms and the inspirations of swarm intelligence can be integrated to serve an interdisciplinary topic between computer vision and intelligence optimization-visual evolutionary neural networks. Hereby, a fly visual evolutionary neural network is developed to solve large-scale global optimization (LSGO), inspired by swarm evolution and the characteristics of fly visual perception. It includes two functional modules, of which one is to generate global and local motion direction activities of visual neural nodes, and the other takes the activities as learning rates to update the nodes' states by a population-like evolutionary strategy. Also, it is used to optimize the structure of a multilayer perceptron to acquire a sample classification model. The theoretical results indicate that the network is convergent and meanwhile the computational complexity mainly depends on the size of the input layer and the dimension of LSGO. The comparative experiments have verified that the network is an extremely competitive optimizer for LSGO problems.

All complex motion patterns can be decomposed into several elements, including translation, expansion/contraction, and rotational motion. In biological vision systems, scientists have found that specific types of visual neurons have specific preferences to each of the three motion elements. There are computational models on translation and expansion/contraction perceptions; however, little has been done in the past to create computational models for rotational motion perception. To fill this gap, we proposed a neural network that utilizes a specific spatiotemporal arrangement of asymmetric lateral inhibited direction selective neural networks (DSNNs) for rotational motion perception. The proposed neural network consists of two parts-presynaptic and postsynaptic parts. In the presynaptic part, there are a number of lateral inhibited DSNNs to extract directional visual cues. In the postsynaptic part, similar to the arrangement of the directional columns in the cerebral cortex, these direction selective neurons are arranged in a cyclic order to perceive rotational motion cues. In the postsynaptic network, the delayed excitation from each direction selective neuron is multiplied by the gathered excitation from this neuron and its unilateral counterparts depending on which rotation, clockwise (cw) or counter-cw (ccw), to perceive. Systematic experiments under various conditions and settings have been carried out and validated the robustness and reliability of the proposed neural network in detecting cw or ccw rotational motion. This research is a critical step further toward dynamic visual information processing.All complex motion patterns can be decomposed into several elements, including translation, expansion/contraction, and rotational motion. In biological vision systems, scientists have found that specific types of visual neurons have specific preferences to each of the three motion elements. There are computational models on translation and expansion/contraction perceptions; however, little has been done in the past to create computational models for rotational motion perception. To fill this gap, we proposed a neural network that utilizes a specific spatiotemporal arrangement of asymmetric lateral inhibited direction selective neural networks (DSNNs) for rotational motion perception. The proposed neural network consists of two parts-presynaptic and postsynaptic parts. In the presynaptic part, there are a number of lateral inhibited DSNNs to extract directional visual cues. In the postsynaptic part, similar to the arrangement of the directional columns in the cerebral cortex, these direction selective neurons are arranged in a cyclic order to perceive rotational motion cues. In the postsynaptic network, the delayed excitation from each direction selective neuron is multiplied by the gathered excitation from this neuron and its unilateral counterparts depending on which rotation, clockwise (cw) or counter-cw (ccw), to perceive. Systematic experiments under various conditions and settings have been carried out and validated the robustness and reliability of the proposed neural network in detecting cw or ccw rotational motion. This research is a critical step further toward dynamic visual information processing.

In this letter, we address the design of fractionally spaced adaptive equalizers when the input signal is sampled with noninteger, subsymbol sampling. We consider the problem of joint equalization and sample rate conversion and derive a stochastic gradient-based weight update algorithm for the equalizer. This enables us to decouple the equalization of channel impairments from that of fixed (periodic) distortion arising from noninteger, subsymbol sampling. This decoupling leads to a novel low-complexity architecture for the equalizer that shows superior or equal performance as compared to the existing architectures with higher complexity.