SKA Time-Invariance Explorer
Fix the characteristic time T = η · K = 0.5 and run 6 different (η, K) pairs automatically. All entropy and cosine curves collapse onto the same trajectory — revealing the intrinsic timescale of the architecture [256, 128, 64, 10] on MNIST.
Architecture (fixed): [256, 128, 64, 10]
Characteristic time (fixed): T = η · K = 0.5
The 6 configurations
| η | K |
|---|---|
| 0.0200 | 25 |
| 0.0100 | 50 |
| 0.0050 | 100 |
| 0.0033 | 150 |
| 0.0025 | 200 |
| 0.0010 | 500 |
Reference Paper
Abstract This paper aims to extend the Structured Knowledge Accumulation (SKA) framework recently proposed by mahi. We introduce two core concepts: the Tensor Net function and the characteristic time property of neural learning. First, we reinterpret the learning rate as a time step in a continuous system. This transforms neural learning from discrete optimization into continuous-time evolution. We show that learning dynamics remain consistent when the product of learning rate and iteration steps stays constant. This reveals a time-invariant behavior and identifies an intrinsic timescale of the network. Second, we define the Tensor Net function as a measure that captures the relationship between decision probabilities, entropy gradients, and knowledge change. Additionally, we define its zero-crossing as the equilibrium state between decision probabilities and entropy gradients. We show that the convergence of entropy and knowledge flow provides a natural stopping condition, replacing arbitrary thresholds with an information-theoretic criterion. We also establish that SKA dynamics satisfy a variational principle based on the Euler-Lagrange equation. These findings extend SKA into a continuous and self-organizing learning model. The framework links computational learning with physical systems that evolve by natural laws. By understanding learning as a time-based process, we open new directions for building efficient, robust, and biologically-inspired AI systems.
SKA Explorer Suite
About this App
Six (η, K) pairs all share the same characteristic time T = η · K = 0.5, the intrinsic timescale of the architecture [256, 128, 64, 10]. Each configuration is run independently and plotted as a function of the step index K. The trajectory shapes remain identical across all configurations while the amplitude scales with η — demonstrating that T is the true timescale of learning, not η or K individually. The characteristic time is the necessary time exposure of the sample to the learning system to complete. T = 0.5 is the characteristic time of the architecture [256, 128, 64, 10] on MNIST.