Learning Inference Concurrency in DynamicGate MLP Structural and Mathematical Justification

Dropout is a representative regularization technique that stochastically deactivates hidden units during training to mitigate overfitting. In contrast, standard inference executes the full network with dense computation, so its goal and mechanism differ from conditional computation, where the executed operations depend on the input. This paper organizes DynamicGate-MLP into a single framework that simultaneously satisfies both the regularization view and the conditional-computation view. Instead of a random mask, the proposed model learns gates that decide whether to use each unit (or block), suppressing unnecessary computation while implementing sample-dependent execution that concentrates computation on the parts needed for each input. To this end, we define continuous gate probabilities and, at inference time, generate a discrete execution mask from them to select an execution path. Training controls the compute budget via a penalty on expected gate usage and uses a Straight-Through Estimator (STE) to optimize the discrete mask. We evaluate DynamicGate-MLP on MNIST, CIFAR-10, Tiny-ImageNet, Speech Commands, and PBMC3k, and compare it with various MLP baselines and MoE-style variants. Compute efficiency is compared under a consistent criterion using gate activation ratios and a layerweighted relative MAC metric, rather than wall-clock latency that depends on hardware and backend kernels.

We define an atomic generation fact f=(u,tau,omega,z;rho), recording the origin, realized transformation, concrete occurrence, generated result and relation role. Compiled into a Generation-Fact Graph (GFG), these facts provide an AI-native, compilable scientific fact substrate preserving generation histories. We establish a GFG-based recursive scientific process in which analysis, intervention, replay and validation form facts for later cycles. Using nanoGPT, we establish unified training-learning dynamics. Training is the evolution of a parameter-optimizer system with state and memory: each actual training action enters the receiving state and produces a finite-amplitude nonlinear functional response conditioned by that state and target-specific update geometry. Learning is the persistent reorganization of distributed functional support by these responses; capability formation, maintenance, decline or recovery becomes observable when target-specific states are evaluated against their readout boundaries. Three primary coordinates - target-boundary state, target-specific update geometry and parameter-Adam receiving state - yield a second-order predictor operating before post-update outputs are read. On held-out runs, it achieved 91.43% accuracy and 91.49% macro-averaged recall across four transitions. We further establish inference as a frozen projection of training-learning dynamics. Component gating and rollback show causal recruitment and non-additive combination of query-conditioned support formed during training, deriving organizational conditions realized by Attention. Controlled feedback indicates possible double-edged reinforcement effects. ResNet/CIFAR-100 and diffusion/CIFAR-10 experiments confirm receiving-state-conditioned responses, persistent support reorganization and frozen inference projection beyond nanoGPT.

In neural network models, soft mixtures of fixed candidate components (e.g., logic gates and sub-networks) are often used during training for stable optimization, while hard selection is typically used at inference. This raises questions about training-inference mismatch. We analyze this gap by separating forward-pass computation (hard selection vs. soft mixture) from stochasticity (with vs. without Gumbel noise). Using logic gate networks as a testbed, we observe distinct behaviors across four methods: Hard-ST achieves zero selection gap by construction; Gumbel-ST achieves near-zero gap when training succeeds but suffers accuracy collapse at low temperatures; Soft-Mix achieves small gap only at low temperature via weight concentration; and Soft-Gumbel exhibits large gaps despite Gumbel noise, confirming that noise alone does not reduce the gap. We propose CAGE (Confidence-Adaptive Gradient Estimation) to maintain gradient flow while preserving forward alignment. On logic gate networks, Hard-ST with CAGE achieves over 98% accuracy on MNIST and over 58% on CIFAR-10, both with zero selection gap across all temperatures, while Gumbel-ST without CAGE suffers a 47-point accuracy collapse.