Nonlinear Encoding Research Articles

Polytopic autoencoders with smooth clustering for reduced-order modeling of flows

With the advancement of neural networks, there has been a notable increase, both in terms of quantity and variety, in research publications concerning the application of autoencoders to reduced-order models. We propose a polytopic autoencoder architecture that includes a lightweight nonlinear encoder, a convex combination decoder, and a smooth clustering network. Supported by several proofs, the model architecture ensures that all reconstructed states lie within a polytope, accompanied by a metric indicating the quality of the constructed polytopes, referred to as polytope error. Additionally, it offers a minimal number of convex coordinates for polytopic linear-parameter varying systems while achieving acceptable reconstruction errors compared to proper orthogonal decomposition (POD). To validate our proposed model, we conduct simulations involving two flow scenarios with the incompressible Navier-Stokes equation. Numerical results demonstrate the guaranteed properties of the model, low reconstruction errors compared to POD, and the improvement in error using a clustering network.

Broadband infrared imaging governed by guided-mode resonance in dielectric metasurfaces

Nonlinear metasurfaces have experienced rapid growth recently due to their potential in various applications, including infrared imaging and spectroscopy. However, due to the low conversion efficiencies of metasurfaces, several strategies have been adopted to enhance their performances, including employing resonances at signal or nonlinear emission wavelengths. This strategy results in a narrow operational band of the nonlinear metasurfaces, which has bottlenecked many applications, including nonlinear holography, image encoding, and nonlinear metalenses. Here, we overcome this issue by introducing a new nonlinear imaging platform utilizing a pump beam to enhance signal conversion through four-wave mixing (FWM), whereby the metasurface is resonant at the pump wavelength rather than the signal or nonlinear emissions. As a result, we demonstrate broadband nonlinear imaging for arbitrary objects using metasurfaces. A silicon disk-on-slab metasurface is introduced with an excitable guided-mode resonance at the pump wavelength. This enabled direct conversion of a broad IR image ranging from >1000 to 4000 nm into visible. Importantly, adopting FWM substantially reduces the dependence on high-power signal inputs or resonant features at the signal beam of nonlinear imaging by utilizing the quadratic relationship between the pump beam intensity and the signal conversion efficiency. Our results, therefore, unlock the potential for broadband infrared imaging capabilities with metasurfaces, making a promising advancement for next-generation all-optical infrared imaging techniques with chip-scale photonic devices.

Nonlinear encoding in diffractive information processing using linear optical materials

Nonlinear encoding of optical information can be achieved using various forms of data representation. Here, we analyze the performances of different nonlinear information encoding strategies that can be employed in diffractive optical processors based on linear materials and shed light on their utility and performance gaps compared to the state-of-the-art digital deep neural networks. For a comprehensive evaluation, we used different datasets to compare the statistical inference performance of simpler-to-implement nonlinear encoding strategies that involve, e.g., phase encoding, against data repetition-based nonlinear encoding strategies. We show that data repetition within a diffractive volume (e.g., through an optical cavity or cascaded introduction of the input data) causes the loss of the universal linear transformation capability of a diffractive optical processor. Therefore, data repetition-based diffractive blocks cannot provide optical analogs to fully connected or convolutional layers commonly employed in digital neural networks. However, they can still be effectively trained for specific inference tasks and achieve enhanced accuracy, benefiting from the nonlinear encoding of the input information. Our results also reveal that phase encoding of input information without data repetition provides a simpler nonlinear encoding strategy with comparable statistical inference accuracy to data repetition-based diffractive processors. Our analyses and conclusions would be of broad interest to explore the push-pull relationship between linear material-based diffractive optical systems and nonlinear encoding strategies in visual information processors.

Subcortical origin of nonlinear sound encoding in auditory cortex

A major challenge in neuroscience is to understand how neural representations of sensory information are transformed by the network of ascending and descending connections in each sensory system. By recording from neurons at several levels of the auditory pathway, we show that much of the nonlinear encoding of complex sounds in auditory cortex can be explained by transformations in the midbrain and thalamus. Modeling cortical neurons in terms of their inputs across these subcortical populations enables their responses to be predicted with unprecedented accuracy. By contrast, subcortical responses cannot be predicted from descending cortical inputs, indicating that ascending transformations are irreversible, resulting in increasingly lossy, higher-order representations across the auditory pathway. Rather, auditory cortex selectively modulates the nonlinear aspects of thalamic auditory responses and the functional coupling between subcortical neurons without affecting the linear encoding of sound. These findings reveal the fundamental role of subcortical transformations in shaping cortical responses.

Cognitive Thinking Differences in E-C Translation Driven by Temporal/Spatial Preferences: A Case Study of the Translation of “The Proceedings of the International Military Tribunal for the Far East”

This study, grounded in the interdisciplinary integration of cognitive science and translation studies known as translation cognition, examines how differing temporal-spatial cognitive orientations in English and Chinese influence translation processes. English exhibits a temporality preference, explicitly linking semantic logic through grammatical and lexical devices, while Chinese demonstrates a spatiality preference with nonlinear, chunked, and discrete language encoding. During translation, translators must cognitively reconstruct the source language to align with the target language's cognitive and expressive conventions. Analyzing English-Chinese translation cases from "The Proceedings of the International Military Tribunal For the Far East," the research reveals cognitive strategies in semantic processing and sentence restructuring. It emphasizes the importance of understanding and applying temporal-spatial cognitive differences in cross-linguistic and cross-cultural communication.

Bifurcation investigation, phase synchronization and FPGA implementation of a new photosensitive Fitz Hugh Nagumo neuron based meminductor

Abstract This paper focuses on the estimation of the nonlinear encoding and responses of a photosensitive Fitz Hugh Nagumo (FHN) neuron-based-meminductor and provides a relevant analysis of its phase synchronization. In the pattern, a Fitz Hugh–Nagumo neuron connected to a meminductor is activated by a photocell, and a time-varying current source is generated by the presence of external optical signals. This coupling is a benchmark circuit with memory similar to artificial eyes with the ability to capture and encode external signals. It is designed with the aim of studying the dynamics of a neuron with a memory effect highlighted through the meminductor. An appropriate dynamical analysis is provided using standard indicators such as bifurcations to point out thorough transitions and the nature of the electrical neuronal activities. Some couplings between two FHN neurons with meminductor using hybrid synapses composed of passive electronic components are achieved. Relevant tools are used to analyze the stability of the synchronization which gives prominent details on the selection of the appropriate coupling. The energy balance of the external system is evaluated which gives the effort to achieve encoding signals and also proves the feasibility of the proposal in real-time implementation. Simulations are performed on FPGA. The results present a good agreement. In many engineering applications, the detection of optical signals is inescapable as well as the synchronization of its signals for the transmission of the stimuli. These results could be useful for the designer.

MUSE-XAE: MUtational Signature Extraction with eXplainable AutoEncoder enhances tumour types classification.

Mutational signatures are a critical component in deciphering the genetic alterations that underlie cancer development and have become a valuable resource to understand the genomic changes during tumorigenesis. Therefore, it is essential to employ precise and accurate methods for their extraction to ensure that the underlying patterns are reliably identified and can be effectively utilized in new strategies for diagnosis, prognosis, and treatment of cancer patients. We present MUSE-XAE, a novel method for mutational signature extraction from cancer genomes using an explainable autoencoder. Our approach employs a hybrid architecture consisting of a nonlinear encoder that can capture nonlinear interactions among features, and a linear decoder which ensures the interpretability of the active signatures. We evaluated and compared MUSE-XAE with other available tools on both synthetic and real cancer datasets and demonstrated that it achieves superior performance in terms of precision and sensitivity in recovering mutational signature profiles. MUSE-XAE extracts highly discriminative mutational signature profiles by enhancing the classification of primary tumour types and subtypes in real world settings. This approach could facilitate further research in this area, with neural networks playing a critical role in advancing our understanding of cancer genomics. MUSE-XAE software is freely available at https://github.com/compbiomed-unito/MUSE-XAE.

Practical utilization of nonlinear spatial encoding: Fast field mapping and FRONSAC-wave.

To study the additional value of FRONSAC encoding in 2D and 3D wave sequences, implementing a simple strategy to trajectory mapping for FRONSAC encoding gradients. The nonlinear gradient trajectory for each voxel was estimated by exploiting the sparsity of the point spread function in the frequency domain. Simulations and in-vivo experiments were used to analyze the performance of combinations of wave and FRONSAC encoding. Field mapping using the simplified approach produced similar image quality with much shorter calibration time than the comprehensive mapping schemes utilized in previous work. In-vivo human brain images showed that the addition of FRONSAC encoding could improve wave image quality, particularly at very high undersampling factors and in the context of limited wave amplitudes. These results were further supported by g-factor maps. Results show that FRONSAC can be used to improve image quality of wave at very high undersampling rates or in slew-limited acquisitions. Our study illustrates the potential of the proposed fast field mapping approach.

A nonlinear recurrent encoders for early detection of strep throat infection to prevent acute rheumatic fever

A nonlinear recurrent encoders for early detection of strep throat infection to prevent acute rheumatic fever

Gravity from holomorphic discs and celestial Lw1+∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Lw_{1+\\infty }$$\\end{document} symmetries

The study of physical theories in various signatures has been important for uncovering structures not easily visible or definable in Lorentz signature. In split signature, global twistor constructions for conformally self-dual (SD) gravity and Yang–Mills construct solutions from twistor data that can be expressed in terms of free data without gauge freedom. This is developed for asymptotically flat SD gravity to give a fully nonlinear encoding of the asymptotic gravitational data in terms of a real homogeneous generating function h on the real twistor space. The recently discovered Lw1+∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Lw_{1+\\infty }$$\\end{document} celestial symmetries, when real, act locally as passive Poisson diffeomorphisms on the real twistor space. The twistor data, h, generates an imaginary such Poisson transformation that then generates the gravitational field by shifting the real slice of the twistor space. The twistor chiral sigma models, whose correlators yield the Einstein gravity tree-level S-matrix, are reformulated as theories of holomorphic discs in twistor space whose boundaries lie on the deformed real slice determined by h. The real Lw1+∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Lw_{1+\\infty }$$\\end{document} symmetries act on the corresponding formula for the S-matrix geometrically with vanishing Noether currents, but imaginary generators yield graviton vertex operators that generate gravitons in the perturbative expansion. A generating function for the all plus 1-loop amplitude, the analogous framework for Yang–Mills, possible interpretations in Lorentz signature and similar open string formulations of twistor and ambitwistor strings in 4d in split signature, are briefly discussed.

Accelerated 2D Cartesian MRI with an 8-channel local B0 coil array combined with parallel imaging.

In MRI, the magnetization of nuclear spins is spatially encoded with linear gradients and radiofrequency receiverssensitivity profiles to produce images, which inherently leads to a long scan time. Cartesian MRI, as widely adopted for clinical scans, can be accelerated with parallel imaging and rapid magnetic field modulation during signal readout. Here, by using an 8-channel local coil array, the modulation scheme optimized for sampling efficiency is investigated to speed up 2D Cartesian scans. An 8-channel local coil array is made to carry sinusoidal currents during signal readout to accelerate 2D Cartesian scans. An MRI sampling theory based on reproducing kernel Hilbert space is exploited to visualize the efficiency of nonlinear encoding in arbitrary sampling duration. A field calibration method using current monitors for local coils and the ESPIRiT algorithm is proposed to facilitate image reconstruction. Image acceleration with various modulation field shapes, aliasing control, and distinct modulation frequencies are scrutinized to find an optimized modulation scheme. A safety evaluation is conducted. In vivo 2D Cartesian scans are accelerated by the local coils. For 2D Cartesian MRI, the optimal modulation field by this local array converges to a nearly linear gradient field. With the field calibration technique, it accelerates the in vivo scans (i.e., proved safe) by threefold and eightfold free of visible artifacts, without and with SENSE, respectively. The nonlinear encoding analysis tool, the field calibration method, the safety evaluation procedures, and the in vivo reconstructed scans make significant steps to push MRI speed further with the local coil array.

A Fast Magnetic Flux Density Measurement Method With Skip-Echo Acquired Turbo Spin Echo (SATE).

The measurements of magnetic flux density ( Bz) needed in magnetic resonance electrical impedance tomography (MREIT) and magnetic resonance current density imaging (MRCDI) techniques often utilize spin echo (SE)-based sequences for data acquisition. The low imaging speed of SE-based methods significantly hampers the clinical applications of MREIT and MRCDI. Here, we propose a new sequence for substantially accelerating the acquisition of Bz measurements. A skip-echo acquired turbo spin echo (SATE) imaging sequence based on the conventional turbo spin echo (TSE) technique was proposed by adding a skip-echo module in front of the TSE acquisition module. The skip-echo module consisted of a series of refocusing pulses without acquisition. In SATE, amplitude-modulated crusher gradients were used to remove the stimulated echo pathways, and the radiofrequency (RF) pulse shape was specially selected to preserve more signals. In efficiency evaluation experiments performed on a spherical gel phantom, we demonstrated that SATE had improved measurement efficiency compared to the conventional TSE sequence via skipping one echo before acquiring signals. The accuracy of the Bz measurements by SATE was validated against those by the multi-echo injection current nonlinear encoding (ME-ICNE) method, while SATE was able to accelerate the data acquisition up to 10-fold. Volumetric coverage of Bz maps obtained in the phantom, pork, and human calf illustrated that SATE can reliably measure volumetric Bz distributions within clinically acceptable time. The proposed SATE sequence provides a fast and effective approach for volumetric coverage of Bz measurements, greatly facilitating the clinical applications of MREIT and MRCDI techniques.

The Neural Basis for Biased Behavioral Responses Evoked by Galvanic Vestibular Stimulation in Primates.

Noninvasive electrical stimulation of the vestibular system in humans has become an increasingly popular tool with a broad range of research and clinical applications. However, common assumptions regarding the neural mechanisms that underlie the activation of central vestibular pathways through such stimulation, known as galvanic vestibular stimulation (GVS), have not been directly tested. Here, we show that GVS is encoded by VIIIth nerve vestibular afferents with nonlinear dynamics that differ markedly from those predicted by current models. GVS produced asymmetric activation of both semicircular canal and otolith afferents to the onset versus offset and cathode versus anode of applied current, that in turn produced asymmetric eye movement responses in three awake-behaving male monkeys. Additionally, using computational methods, we demonstrate that the experimentally observed nonlinear neural response dynamics lead to an unexpected directional bias in the net population response when the information from both vestibular nerves is centrally integrated. Together our findings reveal the neural basis by which GVS activates the vestibular system, establish that neural response dynamics differ markedly from current predictions, and advance our mechanistic understanding of how asymmetric activation of the peripheral vestibular system alters vestibular function. We suggest that such nonlinear encoding is a general feature of neural processing that will be common across different noninvasive electrical stimulation approaches.SIGNIFICANCE STATEMENT Here, we show that the application of noninvasive electrical currents to the vestibular system (GVS) induces more complex responses than commonly assumed. We recorded vestibular afferent activity in macaque monkeys exposed to GVS using a setup analogous to human studies. GVS evoked notable asymmetries in irregular afferent responses to cathodal versus anodal currents. We developed a nonlinear model explaining these GVS-evoked afferent responses. Our model predicts that GVS induces directional biases in centrally integrated head motion signals and establishes electrical stimuli that recreate physiologically plausible sensations of motion. Altogether, our findings provide new insights into how GVS activates the vestibular system, which will be vital to advancing new clinical and biomedical applications.

Generating Robust DNN With Resistance to Bit-Flip Based Adversarial Weight Attack

Rowhammer Attack, a new DRAM-based attack, was developed exploiting weak cells to alter their content. Such attacks can be launched at the user level without requiring access permission to the victim memory cells. Leveraging such attacks, a new bit-flip-based adversarial weights attack (BFA) was developed targeting deep neural network models. When BFA attackers acquire a DNN model, they manipulate the existing DNN adversarial attack into locating vulnerable bits in the target DNN model. By flipping a subset of them using Rowhammer, they can crash that model within 30 trails. In this paper, we propose a lightweight and easy-to-deploy defense mechanism in the bit-level, Randomized Rotated and Nonlinear Encoding (RREC), which generates both robustness and fault-tolerant against BFA. Since flipping the most significant bit (MSB) in quantized data is too dangerous, we introduce randomized Rotation to obfuscate the bit order of model data and efficiently hide truly vulnerable bits with less vulnerable ones. Further, RREC reduces the average bit-flipped distance by more than 3x from the nonlinear encoding. It decreases the bit-flip distance among the majority of bits (including those vulnerable bits). Theoretically, RREC minimized the impact of a single bit BFA to 1/24 compared with baseline. Experimentally, RREC tolerates more than 17x flipped bits versus baseline model and 4.8x and 5.7x more bits compared with the existing BFA defenses (4B QAT and WR) with 0.01x to 0.08x of runtime latency. Moreover, we evaluate RREC against a newly emerged attack, Targeted-BFA, and it improves the defense rate from <inline-formula><tex-math notation="LaTeX">$5\%$</tex-math></inline-formula> to <inline-formula><tex-math notation="LaTeX">$95\%$</tex-math></inline-formula> .

The roles of Kerr nonlinearity in a bosonic quantum neural network

The emerging technology of quantum neural networks (QNNs) offers a quantum advantage over classical artificial neural networks (ANNs) in terms of speed or efficiency of information processing tasks. It is well established that nonlinear mapping between input and output is an indispensable feature of classical ANNs, while in a QNN the roles of nonlinearity are not yet fully understood. As one tends to think of QNNs as physical systems, it is natural to think of nonlinear mapping originating from a physical nonlinearity of the system, such as Kerr nonlinearity. Here we investigate the effect of Kerr nonlinearity on a bosonic QNN in the context of both classical (simulating an XOR gate) and quantum (generating Schrödinger cat states) tasks. Aside offering a mechanism of nonlinear input-output mapping, Kerr nonlinearity reduces the effect of noise or losses, which are particularly important to consider in the quantum setting. We note that nonlinear mapping may also be introduced through a nonlinear input-output encoding rather than a physical nonlinearity: for example, an output intensity is already a nonlinear function of input amplitude. While in such cases Kerr nonlinearity is not strictly necessary, it still increases the performance in the face of noise or losses.

Multivariate curve resolution with autoencoders for CARS microspectroscopy

Coherent anti-Stokes Raman scattering (CARS) microspectroscopy is a powerful tool for label-free cell imaging thanks to its ability to acquire a rich amount of information. An important family of operations applied to such data is multivariate curve resolution (MCR). It aims to find main components of a dataset and compute their spectra and concentrations in each pixel. Recently, autoencoders began to be studied to accomplish MCR with dense and convolutional models. However, many questions, like the results variability or the reconstruction metric, remain open and applications are limited to hyperspectral imaging. In this article, we present a nonlinear convolutional encoder combined with a linear decoder to apply MCR to CARS microspectroscopy. We conclude with a study of the result variability induced by the encoder initialization.

Nonlinear cortical encoding of color predicts enhanced McCollough effects in anomalous trichromats

Nonlinear encoding of chromatic contrast by the early visual cortex predicts that anomalous trichromats will show a larger McCollough effect than normal trichromats. In Experiment 1 we employed the McCollough effect to probe the cortical representation of saturation in normal trichromats, and used the results to predict enhanced McCollough effects for anomalous trichromats, which we measured in Experiment 2. In Experiment 1 three participants adapted to red and green orthogonal gratings of four different saturations. Using nulling to measure aftereffect strength, we found that halving the saturation of the inducing gratings decreased aftereffect strength only slightly, consistent with a compressive coding of saturation in early visual cortex. In anomalous trichromats, cone contrasts between red and green are greatly decreased from those of normal trichromats, but induced aftereffects are only slightly decreased, because of the non-linearity in the cortical encoding of saturation. To null the aftereffect, however, the retinal color deficiency must be overcome by adding more color to the null than required by normal trichromats. We confirmed this prediction in Experiment 2 where four anomalous trichromats required nulling stimuli approximately four times more saturated than did normal trichromats. We consider two competing models to explain our results: in a ‘pigment swap’ model anomalous trichromats have an altered photopigment but process color postreceptorally in the same way as normal trichromats; in a ‘postreceptoral compensation’ model the cortical representation of red-green contrasts is amplified to compensate for reduced cone contrasts. The latter provided a better fit to our data.

Wear patterns in knee OA correlate with native limb geometry.

Background: To date, the amount of cartilage loss is graded by means of discrete scoring systems on artificially divided regions of interest (ROI). However, optimal statistical comparison between and within populations requires anatomically standardized cartilage thickness assessment. Providing anatomical standardization relying on non-rigid registration, we aim to compare morphotypes of a healthy control cohort and virtual reconstructed twins of end-stage knee OA subjects to assess the shape-related knee OA risk and to evaluate possible correlations between phenotype and location of cartilage loss. Methods: Out of an anonymized dataset provided by the Medacta company (Medacta International SA, Castel S. Pietro, CH), 798 end-stage knee OA cases were extracted. Cartilage wear patterns were observed by computing joint space width. The three-dimensional joint space width data was translated into a two-dimensional pixel image, which served as the input for a principal polynomial autoencoder developed for non-linear encoding of wear patterns. Virtual healthy twin reconstruction enabled the investigation of the morphology-related risk for OA requiring joint arthroplasty. Results: The polynomial autoencoder revealed 4 dominant, orthogonal components, accounting for 94% of variance in the latent feature space. This could be interpreted as medial (54.8%), bicompartmental (25.2%) and lateral (9.1%) wear. Medial wear was subdivided into anteromedial (11.3%) and posteromedial (10.4%) wear. Pre-diseased limb geometry had a positive predictive value of 0.80 in the prediction of OA incidence (r 0.58, p < 0.001). Conclusion: An innovative methodological workflow is presented to correlate cartilage wear patterns with knee joint phenotype and to assess the distinct knee OA risk based on pre-diseased lower limb morphology. Confirming previous research, both alignment and joint geometry are of importance in knee OA disease onset and progression.

AGNet: weighing black holes with deep learning

ABSTRACT Supermassive black holes (SMBHs) are commonly found at the centres of most massive galaxies. Measuring SMBH mass is crucial for understanding the origin and evolution of SMBHs. Traditional approaches, on the other hand, necessitate the collection of spectroscopic data, which is costly. We present an algorithm that weighs SMBHs using quasar light time series information, including colours, multiband magnitudes, and the variability of the light curves, circumventing the need for expensive spectra. We train, validate, and test neural networks that directly learn from the Sloan Digital Sky Survey (SDSS) Stripe 82 light curves for a sample of 38 939 spectroscopically confirmed quasars to map out the non-linear encoding between SMBH mass and multiband optical light curves. We find a 1σ scatter of 0.37 dex between the predicted SMBH mass and the fiducial virial mass estimate based on SDSS single-epoch spectra, which is comparable to the systematic uncertainty in the virial mass estimate. Our results have direct implications for more efficient applications with future observations from the Vera C. Rubin Observatory. Our code, AGNet, is publicly available at https://github.com/snehjp2/AGNet.

A Codesigned Integrated Photonic Electronic Neuron

In the modern era of artificial intelligence, increasingly sophisticated artificial neural networks (ANNs) are implemented, which pose challenges in terms of execution speed and power consumption. To tackle this problem, recent research on reduced-precision ANNs opened the possibility to exploit analog hardware for neuromorphic acceleration. In this scenario, photonic-electronic engines are emerging as a short-medium term solution to exploit the high speed and inherent parallelism of optics for linear computations needed in ANN, while resorting to electronic circuitry for signal conditioning and memory storage. In this paper we introduce a precision-scalable integrated Photonic-Electronic Multiply-Accumulate Neuron (PEMAN). The proposed device relies on (i) an analog photonic engine to perform reduced-precision multiplications at high speed and low power, and (ii) an electronic front-end for accumulation and application of the nonlinear activation function by means of a nonlinear encoding in the analog-to-digital converter (ADC). The device has been numerically validated through cosimulations to perform multiply-accumulate operations (MAC). Simulations are based on the iSiPP50G SOI process for the photonic engine and a commercial 28 nm CMOS process for the electronic front-end. The PEMAN exhibits a multiplication accuracy of 6.1 ENOB up to 10 GMAC/s, while it can perform computations up to 56 GMAC/s with a reduced accuracy down to 2.1 ENOB. The device can trade off speed and power consumption with resolution, significantly outperforming its analog electronics counterparts both in terms of speed and energy consumption. With respect to other photonic ANNs, the PEMAN has comparable speed and energy consumption with a higher resolution, while outperforming them by a hundredfold in the fan-in, which opens the possibility to accelerate more complex networks.