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

TL;DR

This paper introduces Stream Neural Networks (StNN), a new paradigm for neural computation on irreversible data streams, emphasizing persistent temporal states and a stream-native execution algorithm to handle real-world streaming environments.

Contribution

The paper proposes the Stream Network Algorithm (SNA) and formalizes the concept of stream neurons with persistent states, establishing theoretical guarantees for stability and temporal dependency encoding.

Findings

Persistent state dynamics are bounded under mild activation constraints.

State transition operators are contractive for λ < 1, ensuring stability.

Empirical analysis confirms theoretical guarantees.

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 {\lambda} < 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.