We introduce a use of the \(M\)-cover (or \(M\)-layer) transform for machine learning. The method replicates a model \(M\) times, but instead of coupling the copies through parameter averaging or an explicit attractive force, as in replicated SGD or Elastic SGD, it rewires the contexts in which local learning messages are computed. Each local loss is evaluated on a routed model whose parameters are drawn from different copies according to permutations sampled from a structured mixing kernel \(Q\). Training then uses the original local update rule, while the resulting learning messages are redistributed across the copies through these routed computational paths. Thus \(Q\) defines a topology for message transport and controls the long-loop structure of the lifted factor graph. We formulate this construction for perceptrons, committee machines, and multilayer perceptrons, showing that the same principle applies from discrete models to differentiable neural networks. The resulting framework provides a mechanism for improving generalization through structured message sharing rather than replica collapse or parameter-space coupling.

The ability of a brain or a neural network to efficiently learn depends crucially on both the task structure and the learning rule.Previous works have analyzed the dynamical equations describing learning in the relatively simplified context of the perceptron under assumptions of a student-teacher framework or a linearized output. While these assumptions have facilitated theoretical understanding, they have precluded a detailed understanding of the roles of the nonlinearity and input-data distribution in determining the learning dynamics, limiting the applicability of the theories to real biological or artificial neural networks.Here, we use a stochastic-process approach to derive flow equations describing learning, applying this framework to the case of a nonlinear perceptron performing binary classification. We characterize the effects of the learning rule (supervised or reinforcement learning, SL/RL) and input-data distribution on the perceptron's learning curve and the forgetting curve as subsequent tasks are learned.In particular, we find that the input-data noise differently affects the learning speed under SL vs. RL, as well as determines how quickly learning of a task is overwritten by subsequent learning. Additionally, we verify our approach with real data using the MNIST dataset.This approach points a way toward analyzing learning dynamics for more-complex circuit architectures.

Let's consider a student perceptron with M synaptic populations indexed by m, wm, such that each wmi satisfies its own distributions constraints wmi Qm(wm).

The ability of a brain or a neural network to efficiently learn depends crucially on both the task structure and the learning rule.

Weproposetorepresent shapesasthedeformation andcombination oflearnable elementary 3D structures, which are primitives resulting from training over a collection of shapes.

Then the phenomenon has been thought as inevitable. However, the phenomenon seldom occurs in the context of recent deep learning. There is a gap between theory and reality.

In this paper we use explainability queries to formally compare the interpretability of machinelearningmodels.