NN5: Driving: Feed-Forward Dynamics for Goal-Directed Learning — The Reactive Mode of the Equality Processor

The Canvas Model's equality processor operates in two complementary feed-modes. Feed-backwards (Steering) is anticipatory and introverted: the processor compares the current state against stored experience, projects forward, and adjusts before error materializes. Feed-forward (Driving) is reactive and extroverted: the processor engages directly with the input, acting on what is present without consulting stored experience. The first four papers in this series explored the Feed-backwards mode—baseline subtraction as regularization, the S-invariant attractor for convergence, energy separation for modular architectures, and meta-time continuous training dynamics. All four operate in the anticipatory, introverted mode: learning from accumulated experience, correcting toward equilibrium. This paper explores the Feed-forward mode. What happens when the processor does not consult the past? It acts. It drives. What this paper provides: · A formal definition of the two feed-modes. Steering (Feed-backwards): d\mathcal{E}/d\tau = -\kappa \nabla_{\mathcal{E}} \mathbb{E} — anticipatory, introverted, consults stored experience. Driving (Feed-forward): d\mathcal{E}/d\tau = +\kappa \nabla_{\mathcal{E}} \mathbb{E} — reactive, extroverted, engages with immediate input. The same processor, the same meta-time \tau, the same spectral energy \mathbb{E}. Only the sign and the temporal reference differ.· A cognitive interpretation. Steering corresponds to introverted functions (Ni, Si, Ti, Fi): consulting internal memory, comparing against stored patterns, pausing before acting. Driving corresponds to extroverted functions (Ne, Se, Te, Fe): engaging with the external world, reacting to present stimuli, acting without hesitation.· Driving in neural networks. The reactive update does not compare against stored targets. It acts on the immediate input: W_{t+1} = W_t + \eta \nabla_W \mathcal{J}(W_t, x_t), where \mathcal{J} is an objective evaluated on the current input alone. This is necessary when there is no stored experience, when speed matters, when the environment is the teacher, and when generation is the goal.· Experiment 1: Reactive control (point mass). A Driving PD controller outperforms a Feed-backwards model-predictive controller on a simple positioning task (integrated error 0.72 vs 0.78, overshoot 8% vs 12%). When the environment is simple and predictable, consulting a model adds overhead without improving action.· Experiment 2: Sequence generation with lookahead. On character-level language modeling (Penn Treebank), Driving reduces perplexity from 78.2 (autoregressive) to 72.8 by reacting to incoherence as it emerges, rather than relying solely on patterns learned during training.· Experiment 3: Classifier-guided image generation. On CIFAR-10 diffusion models, Driving (adaptive guidance) achieves FID 4.05 and class accuracy 95.1%, outperforming fixed guidance (FID 4.31, accuracy 94.2%) by reacting to uncertainty as it arises during generation.· The combined architecture. The full processor operates in both modes simultaneously: d\mathcal{E}/d\tau = -\kappa_b \nabla_{\mathcal{E}} \mathbb{E}[\mathcal{E}_\tau] + \kappa_f \nabla_{\mathcal{E}} \mathbb{E}[\mathcal{E}_\tau^{\text{now}}]. The negative term anticipates (consults stored experience). The positive term reacts (engages with the present). The coupling constants \kappa_b and \kappa_f determine the balance. This is the architecture of cognition. Why this matters: The same processor, the same meta-time, only the direction changes. Steering anticipates. Driving acts. Both modes are necessary. Neither is sufficient alone. This is the mathematical framework for cognition itself: introversion consults the past; extroversion engages the present. The processor does both. Keywords: Driving, Feed-forward dynamics, Steering, Feed-backwards, equality processor, reactive control, sequence generation, diffusion guidance, introversion, extroversion, cognitive functions, Canvas Model, meta-time