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Determinism in the Undetermined: Deterministic Output in Charge-Conserving Continuous-Time Neuromorphic Systems with Temporal Stochasticity

arXiv:2603.15987v1 Announce Type: new Abstract: Achieving deterministic computation results in asynchronous neuromorphic systems remains a fundamental challenge due to the inherent temporal stochasticity of continuous-time hardware. To address this, we develop a unified continuous-time framework for spiking neural networks (SNNs) that couples the Law of Charge Conservation with minimal neuron-level constraints. This integration ensures that the terminal state depends solely on the aggregate input charge, providing a unique cumulated output invariant to temporal stochasticity. We prove that this mapping is strictly invariant to spike timing in acyclic networks, whereas recurrent connectivity can introduce temporal sensitivity. Furthermore, we establish an exact representational correspondence between these charge-conserving SNNs and quantized artificial neural networks, bridging the gap between static deep learning and event-driven dynamics without approximation errors. These results e

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Jing Yan, Kang You, Zhezhi He, Yaoyu Zhang · · 1 min read · 7 views
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arXiv:2603.15987v1 Announce Type: new Abstract: Achieving deterministic computation results in asynchronous neuromorphic systems remains a fundamental challenge due to the inherent temporal stochasticity of continuous-time hardware. To address this, we develop a unified continuous-time framework for spiking neural networks (SNNs) that couples the Law of Charge Conservation with minimal neuron-level constraints. This integration ensures that the terminal state depends solely on the aggregate input charge, providing a unique cumulated output invariant to temporal stochasticity. We prove that this mapping is strictly invariant to spike timing in acyclic networks, whereas recurrent connectivity can introduce temporal sensitivity. Furthermore, we establish an exact representational correspondence between these charge-conserving SNNs and quantized artificial neural networks, bridging the gap between static deep learning and event-driven dynamics without approximation errors. These results establish a rigorous theoretical basis for designing continuous-time neuromorphic systems that harness the efficiency of asynchronous processing while maintaining algorithmic determinism.

Executive Summary

This article presents a novel framework for spiking neural networks (SNNs) that integrates the Law of Charge Conservation with minimal neuron-level constraints, ensuring deterministic computation despite temporal stochasticity in continuous-time hardware. The proposed framework provides a unique cumulated output that is invariant to spike timing in acyclic networks and establishes a rigorous theoretical basis for designing continuous-time neuromorphic systems. The results bridge the gap between static deep learning and event-driven dynamics without approximation errors, opening up new possibilities for the development of efficient and deterministic neuromorphic systems. The study's findings have significant implications for the future of neuromorphic computing and artificial intelligence.

Key Points

  • ▸ Developed a unified continuous-time framework for SNNs that ensures deterministic computation despite temporal stochasticity
  • ▸ Integrated the Law of Charge Conservation with minimal neuron-level constraints to achieve cumulated output invariance
  • ▸ Established a rigorous theoretical basis for designing continuous-time neuromorphic systems

Merits

Strength in Theoretical Foundations

The study provides a comprehensive theoretical framework for understanding the behavior of continuous-time neuromorphic systems, which is a major advancement in the field.

Advancements in Neuromorphic Computing

The proposed framework has significant implications for the development of efficient and deterministic neuromorphic systems, which could lead to breakthroughs in artificial intelligence and machine learning.

Demerits

Limited Experimental Validation

The study primarily focuses on theoretical analysis and simulation results, and experimental validation is limited, which may raise concerns about the practical applicability of the proposed framework.

Complexity of the Proposed Framework

The integration of the Law of Charge Conservation with minimal neuron-level constraints may add complexity to the proposed framework, which could make it challenging to implement in practice.

Expert Commentary

The article presents a significant advancement in the field of neuromorphic computing by providing a rigorous theoretical framework for understanding the behavior of continuous-time neuromorphic systems. The proposed framework has the potential to bridge the gap between static deep learning and event-driven dynamics, which could lead to breakthroughs in artificial intelligence and machine learning. However, the study's limitations, such as limited experimental validation and complexity of the proposed framework, need to be addressed in future research. The findings of this study have significant implications for the future of neuromorphic computing and artificial intelligence, and it is essential to continue exploring the theoretical and practical aspects of the proposed framework.

Recommendations

  • ✓ Future research should focus on experimental validation of the proposed framework to ensure its practical applicability.
  • ✓ The complexity of the proposed framework should be addressed by developing simpler and more efficient implementation strategies.

Sources

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