An Introduction to Cognidynamics

TL;DR

The paper tackles online lifelong learning for cognitive agents operating in environments without data collections. It reframes learning as continuous-time optimization under Dynamic Programming and Hamiltonian dynamics, yielding Cognidynamics with spatiotemporal locality and energy dissipation. Key contributions include the Hamiltonian learning equations, co-state based stability via dissipation weights, an energy-balance interpretation, and a gravitational neural network view to mitigate forgetting. The framework supports collectionless edge AI, aligns with developmental and neuroscience perspectives, and points to discrete-time translations for practical implementations.

Abstract

This paper gives an introduction to \textit{Cognidynamics}, that is to the dynamics of cognitive systems driven by optimal objectives imposed over time when they interact either with a defined virtual or with a real-world environment. The proposed theory is developed in the general framework of dynamic programming which leads to think of computational laws dictated by classic Hamiltonian equations. Those equations lead to the formulation of a neural propagation scheme in cognitive agents modeled by dynamic neural networks which exhibits locality in both space and time, thus contributing the longstanding debate on biological plausibility of learning algorithms like Backpropagation. We interpret the learning process in terms of energy exchange with the environment and show the crucial role of energy dissipation and its links with focus of attention mechanisms and conscious behavior.

Figures (3)

• Figure 1: Neural model, Lagrangian, and the two coordinates of learning. First, the theory of Optimal Control drives the velocity $\nu_{ij}$ of the weights, thus resembling gradient-descent learning policies. Second, the dissipative weights $\zeta$ control the overall learning process by gating mechanisms which takes place on both the network and the Lagrangian..
• Figure 2: Overall architecture of NARNIAN agents. The response of the optimization module is properly enabled by the conscious module when it returns $c=1$. On the opposite, when $c=0$ the response is disabled. In addition a similar gating mechanism is carried out on the Lagrangian term which somehow inhibit the learning process. The conscious model also carry out self-conscious control by returing function $s$.
• Figure 3: The dynamics of neural propagation is driven by the interaction of receptive fields composed of neurons whose outputs represent their coordinates. The interaction is inspired by classical Newtonian gravitational dynamics which is spatially localized since it vanishes at large distances. Such a localization property leads to generate dynamical structures that under appropriate classic conditions are stable, thus providing the support for a sort of addressable memory, which attacks by design issues of catastrophic forgetting.

Theorems & Definitions (35)

• Remark 1
• Remark 2
• Remark 3
• Remark 4
• Lemma 1
• Proposition 1
• Definition 1
• Lemma 2
• proof
• Corollary 1