With the continuous increase in the size and complexity of machine learning models, the need for specialized hardware to efficiently run such models is rapidly growing. To address such a need, silicon-photonic-based neural network (SP-NN) accelerators have recently emerged as a promising alternative to electronic accelerators due to their lower latency and higher energy efficiency. Not only can SP-NNs alleviate the fan-in and fan-out problem with linear algebra processors, their operational bandwidth can match that of the photodetection rate (typically 100 GHz), which is at least over an order of magnitude faster than electronic counterparts that are restricted to a clock rate of a few GHz. Unfortunately, the underlying silicon photonic devices in SP-NNs suffer from inherent optical losses and crosstalk noise originating from fabrication imperfections and undesired optical couplings, the impact of which accumulates as the network scales up. Consequently, the inferencing accuracy in an SP-NN can be affected by such inefficiencies -- e.g., can drop to below 10% -- the impact of which is yet to be fully studied. In this paper, we comprehensively model the optical loss and crosstalk noise using a bottom-up approach, from the device to the system level, in coherent SP-NNs built using Mach-Zehnder interferometer (MZI) devices. The proposed models can be applied to any SP-NN architecture with different configurations to analyze the effect of loss and crosstalk. Such an analysis is important where there are inferencing accuracy and scalability requirements to meet when designing an SP-NN. Using the proposed analytical framework, we show a high power penalty and a catastrophic inferencing accuracy drop of up to 84% for SP-NNs of different scales with three known MZI mesh configurations (i.e., Reck, Clements, and Diamond) due to accumulated optical loss and crosstalk noise.

We show how an "Elman" network architecture, constructed from recurrently connected oscillatory associative memory network mod(cid:173) ules, can employ selective "attentional" control of synchronization to direct the flow of communication and computation within the architecture to solve a grammatical inference problem. Previously we have shown how the discrete time "Elman" network algorithm can be implemented in a network completely described by continuous ordinary differential equations. The time steps (ma(cid:173) chine cycles) of the system are implemented by rhythmic variation (clocking) of a bifurcation parameter. In this architecture, oscilla(cid:173) tion amplitude codes the information content or activity of a mod(cid:173) ule (unit), whereas phase and frequency are used to "softwire" the network. Only synchronized modules communicate by exchang(cid:173) ing amplitude information; the activity of non-resonating modules contributes incoherent crosstalk noise.

We show how an "Elman" network architecture, constructed from recurrently connected oscillatory associative memory network mod(cid:173) ules, can employ selective "attentional" control of synchronization to direct the flow of communication and computation within the architecture to solve a grammatical inference problem. Previously we have shown how the discrete time "Elman" network algorithm can be implemented in a network completely described by continuous ordinary differential equations. The time steps (ma(cid:173) chine cycles) of the system are implemented by rhythmic variation (clocking) of a bifurcation parameter. In this architecture, oscilla(cid:173) tion amplitude codes the information content or activity of a mod(cid:173) ule (unit), whereas phase and frequency are used to "softwire" the network. Only synchronized modules communicate by exchang(cid:173) ing amplitude information; the activity of non-resonating modules contributes incoherent crosstalk noise.

We show how an "Elman" network architecture, constructed from recurrently connected oscillatory associative memory network modules, can employ selective "attentional" control of synchronization to direct the flow of communication and computation within the architecture to solve a grammatical inference problem. Previously we have shown how the discrete time "Elman" network algorithm can be implemented in a network completely described by continuous ordinary differential equations. The time steps (machine cycles) of the system are implemented by rhythmic variation (clocking) of a bifurcation parameter. In this architecture, oscillation amplitude codes the information content or activity of a module (unit), whereas phase and frequency are used to "softwire" the network. Only synchronized modules communicate by exchanging amplitude information; the activity of non-resonating modules contributes incoherent crosstalk noise. Attentional control is modeled as a special subset of the hidden modules with ouputs which affect the resonant frequencies of other hidden modules. They control synchrony among the other modules and direct the flow of computation (attention) to effect transitions between two subgraphs of a thirteen state automaton which the system emulates to generate a Reber grammar. The internal crosstalk noise is used to drive the required random transitions of the automaton.

We show how an "Elman" network architecture, constructed from recurrently connected oscillatory associative memory network modules, can employ selective "attentional" control of synchronization to direct the flow of communication and computation within the architecture to solve a grammatical inference problem. Previously we have shown how the discrete time "Elman" network algorithm can be implemented in a network completely described by continuous ordinary differential equations. The time steps (machine cycles) of the system are implemented by rhythmic variation (clocking) of a bifurcation parameter. In this architecture, oscillation amplitude codes the information content or activity of a module (unit), whereas phase and frequency are used to "softwire" the network. Only synchronized modules communicate by exchanging amplitude information; the activity of non-resonating modules contributes incoherent crosstalk noise. Attentional control is modeled as a special subset of the hidden modules with ouputs which affect the resonant frequencies of other hidden modules. They control synchrony among the other modules and direct the flow of computation (attention) to effect transitions between two subgraphs of a thirteen state automaton which the system emulates to generate a Reber grammar. The internal crosstalk noise is used to drive the required random transitions of the automaton.

We show how an "Elman" network architecture, constructed from recurrently connected oscillatory associative memory network modules, canemploy selective "attentional" control of synchronization to direct the flow of communication and computation within the architecture to solve a grammatical inference problem. Previously we have shown how the discrete time "Elman" network algorithm can be implemented in a network completely described by continuous ordinary differential equations. The time steps (machine cycles)of the system are implemented by rhythmic variation (clocking) of a bifurcation parameter. In this architecture, oscillation amplitudecodes the information content or activity of a module (unit), whereas phase and frequency are used to "softwire" the network. Only synchronized modules communicate by exchanging amplitudeinformation; the activity of non-resonating modules contributes incoherent crosstalk noise. Attentional control is modeled as a special subset of the hidden modules with ouputs which affect the resonant frequencies of other hidden modules. They control synchrony among the other modules anddirect the flow of computation (attention) to effect transitions betweentwo subgraphs of a thirteen state automaton which the system emulates to generate a Reber grammar. The internal crosstalk noise is used to drive the required random transitions of the automaton.

We show how an "Elman" network architecture, constructed from recurrently connected oscillatory associative memory network modules, canemploy selective "attentional" control of synchronization to direct the flow of communication and computation within the architecture to solve a grammatical inference problem. Previously we have shown how the discrete time "Elman" network algorithm can be implemented in a network completely described by continuous ordinary differential equations. The time steps (machine cycles)of the system are implemented by rhythmic variation (clocking) of a bifurcation parameter. In this architecture, oscillation amplitudecodes the information content or activity of a module (unit), whereas phase and frequency are used to "softwire" the network. Only synchronized modules communicate by exchanging amplitudeinformation; the activity of non-resonating modules contributes incoherent crosstalk noise. Attentional control is modeled as a special subset of the hidden modules with ouputs which affect the resonant frequencies of other hidden modules. They control synchrony among the other modules anddirect the flow of computation (attention) to effect transitions betweentwo subgraphs of a thirteen state automaton which the system emulates to generate a Reber grammar. The internal crosstalk noise is used to drive the required random transitions of the automaton.