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Stream Neural Networks: Epoch-Free Learning with Persistent Temporal State

Amama Pathan

TL;DR

The execution principles introduced in this work define a minimal substrate for neural computation under irreversible streaming constraints, and establish three structural guarantees that ensure stable long-horizon execution.

Abstract

Most contemporary neural learning systems rely on epoch-based optimization and repeated access to historical data, implicitly assuming reversible computation. In contrast, real-world environments often present information as irreversible streams, where inputs cannot be replayed or revisited. Under such conditions, conventional architectures degrade into reactive filters lacking long-horizon coherence. This paper introduces Stream Neural Networks (StNN), an execution paradigm designed for irreversible input streams. StNN operates through a stream-native execution algorithm, the Stream Network Algorithm (SNA), whose fundamental unit is the stream neuron. Each stream neuron maintains a persistent temporal state that evolves continuously across inputs. We formally establish three structural guarantees: (1) stateless mappings collapse under irreversibility and cannot encode temporal dependencies; (2) persistent state dynamics remain bounded under mild activation constraints; and (3) the state transition operator is contractive for λ < 1, ensuring stable long-horizon execution. Empirical phase-space analysis and continuous tracking experiments validate these theoretical results. The execution principles introduced in this work define a minimal substrate for neural computation under irreversible streaming constraints.

Stream Neural Networks: Epoch-Free Learning with Persistent Temporal State

TL;DR

The execution principles introduced in this work define a minimal substrate for neural computation under irreversible streaming constraints, and establish three structural guarantees that ensure stable long-horizon execution.

Abstract

Most contemporary neural learning systems rely on epoch-based optimization and repeated access to historical data, implicitly assuming reversible computation. In contrast, real-world environments often present information as irreversible streams, where inputs cannot be replayed or revisited. Under such conditions, conventional architectures degrade into reactive filters lacking long-horizon coherence. This paper introduces Stream Neural Networks (StNN), an execution paradigm designed for irreversible input streams. StNN operates through a stream-native execution algorithm, the Stream Network Algorithm (SNA), whose fundamental unit is the stream neuron. Each stream neuron maintains a persistent temporal state that evolves continuously across inputs. We formally establish three structural guarantees: (1) stateless mappings collapse under irreversibility and cannot encode temporal dependencies; (2) persistent state dynamics remain bounded under mild activation constraints; and (3) the state transition operator is contractive for λ < 1, ensuring stable long-horizon execution. Empirical phase-space analysis and continuous tracking experiments validate these theoretical results. The execution principles introduced in this work define a minimal substrate for neural computation under irreversible streaming constraints.
Paper Structure (13 sections, 3 theorems, 14 equations, 4 figures)

This paper contains 13 sections, 3 theorems, 14 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Stream Neural Networks
  3. Definition of Stream Neural Networks
  4. Formal Definition of Irreversibility
  5. Relation to Spiking Neural Networks
  6. Stream Neuron Architecture
  7. Structural Necessity of Persistent State
  8. Boundedness of Persistent Dynamics
  9. Phase Space Dynamics of Stream Execution
  10. Temporal Retention Dynamics
  11. Continuous Tracking Under Irreversible Input
  12. Scope and Limitations
  13. Conclusion

Key Result

Theorem 1

Let a stateless model be defined as: where $\theta$ is time-invariant and does not encode past inputs. Under irreversible execution, the model cannot encode temporal dependencies beyond the current time step.

Figures (4)

  • Figure 1: High-detail stream neuron architecture. Each neuron integrates the current input with a persistent temporal state stored across time steps, enabling irreversible stream execution without replay.
  • Figure 2: Phase space analysis of stream execution. State-enabled dynamics converge to a stable limit cycle, while state-disabled execution collapses to a point attractor, indicating loss of temporal coherence.
  • Figure 3: Temporal state retention under different decay factors $\lambda$. Larger values maintain long-horizon influence, while smaller values favor rapid responsiveness.
  • Figure 4: Baseline continuous tracking under irreversible input streams. State-enabled execution sustains coherent temporal dynamics, while execution without persistent state fails to preserve temporal structure.

Theorems & Definitions (7)

  • Definition 1: Irreversible Input Stream
  • Theorem 1: Stateless Collapse Under Irreversibility
  • proof
  • Theorem 2: Bounded State Dynamics
  • proof
  • Lemma 1: Contraction Property
  • proof