Learning Without Weights: a Geometric Learner that Needs Less Data, Predicts Without Training, and Cannot Forget

What can a learner do with no trained parameters at all? This paper reports three measured capabilities of a distance-based learner with no trained parameters, each replicated on two unrelated real-data modalities (spoken digits and pen-motion handwriting). Data efficiency. Classifying by distance to class barycentres, with no training of any kind, reaches a matched neural network's 50-example-per-class accuracy using 5 examples on speech and 10 on handwriting. Forgetting. Taught classes in sequence, the construction shows forgetting of exactly 0.000 on every seed — not reduced forgetting. Building the store in reverse order yields byte-identical answers, so the end state provably cannot depend on presentation order: forgetting is impossible by construction rather than merely absent. A standard network under the identical protocol loses 50–80% of its first-task accuracy. Prediction. Continuing a process along its geodesic — a closed-form step with zero learned parameters — is second-order in the frame spacing where a matched trained network is first-order. Capacity did not buy that order over the range measured, and a learned model carrying the same step inside its architecture loses it, so the order belongs to the absence of learning rather than to the geometry as such. Training does not buy order. The boundary is stated as plainly as the results: this is not a general model and does not approach one. On character-level language modelling the same geodesic prediction costs about 16% perplexity against an ordinary recurrent network — the demarcation is the finding, not an embarrassment. Negative results and corrections are reported at equal weight with the wins. Part of the Vektorgeist Method. Research index: xfloukiex-lab.github.io/vektorgeist-researchEvery finding, including the negative and corrected ones: xfloukiex-lab.github.io/hodos-studyPreprint, not peer reviewed. No result here has been reproduced outside the project.