Knowledge as Dynamics: The Paper

Veso R&D released 'Knowledge as Dynamics', a research paper demonstrating that a neural network's latent vector field can be copied, merged, and inherited without training data or teacher weights, achieving 84% basin agreement between teacher and student. The paper introduces five laws of field-based knowledge transfer and a teacher-only instrument that predicts transfer success in minutes, with all results reproducible on a laptop.

Knowledge as Dynamics: The Paper Veso R&D releases Knowledge as Dynamics: distilling, composing, and inheriting the latent vector fields of neural networks. Five laws, one teacher-only instrument, every number reproducible on a laptop. Veso R&D has released Knowledge as Dynamics , a research paper on treating a neural network’s latent vector field as the knowledge itself: something that can be copied without data, merged across models, passed down generations of students, and priced before any transfer runs. The paper, code, and every run record are public. A trained autoencoder moves every point of its latent space: iterating f = Enc Dec z displaces each point by V z = f z - z , and training carves attractors into that field. Prior work analyzed this field. This paper uses it as a transmission channel. Release facts | Item | Value | |---|---| | Title | Knowledge as Dynamics: Distilling, Composing, and Inheriting the Latent Vector Fields of Neural Networks | | Authors | Elias Helou Veso AI , Ivan Nemytchenko independent researcher | | Version | v1.4, July 15, 2026 | | Repository | | runs/ The object - An autoencoder induces a dynamical system on its own latent space: z t+1 = f z t with f = Enc Dec z . - The displacement field is V z = f z - z . Attractors and their basins summarize what the network learned. - A fresh student trained only to match V , with no training data and no teacher weights, inherits the teacher’s basins of attraction. - Standard distillation matches static snapshots outputs, features, relations, Jacobians . This channel matches the dynamics. Figure 1. The core effect. Left: the teacher’s latent field; black stars are the attractors training carved. Right: a student rebuilt from field queries alone, no data, no weights. Its attractors land on the teacher’s; 84% of test points reach the same basin in both networks 0.86 mean across seeds . Figure 2. The field as a channel. Four operations, all data-free: transfer, merging, lineage, and a pre-transfer audit. The five laws | Law | Statement | Key number | |---|---|---| | 1. Sufficiency | The field alone transfers the teacher’s basins; static channels do not | Field 0.86 vs output 0.53, features 0.15, scratch 0.00 ceiling 0.99 | | 2. Order | Transmission reliability changes discontinuously where the teacher’s field becomes fully convergent | Seed spread 0.09 to 0.75 below the transition; 0.690, 0.685, 0.685 at it | | 3. Resolution | Mean field error is the wrong observable; it anti-correlates with basin transfer | Lookup carrier: 7.6x worse NMSE, 3.5x better basin agreement | | 4. Composition | Two disjoint specialists union into one data-free student, but only in a designed frame | Joint 0.82 vs behavioral merging 0.13, grafted side 0.00 | | 5. Heredity with selection | Knowledge survives five generations of re-distillation; the selection lives in the lossy carrier, not the channel | Lineage 0.91 to 0.83 over 5 generations, attractor sets stable | Figure 3. Four ways to copy a network. Field-matched copies reproduce the terrain. A network retrained from scratch on the same data builds unrelated terrain agreement 0.00 . Output distillation recovers part; feature matching almost none. The alpha instrument The paper’s main practical result is a teacher-only measurement that prices a transfer before it runs. - Perturb probe points by radius epsilon; measure the fraction whose endpoint basin flips. Fit f epsilon proportional to epsilon^alpha . - Alpha is the uncertainty exponent of the teacher’s basin boundaries; boundary dimension is D b = d - alpha . - The measurement takes minutes and needs no student. | Validation | Result | |---|---| | Newton fractals attractors known analytically | Estimator matches box-counted boundary dimension; pricing law basin = 1 - f delta predicts all 12 students to 0.01 to 0.03 | | Magnetic pendulum physical roughness dial | Alpha tracks the damping dial; ordering holds at both query budgets | | MNIST autoencoder | Alpha = 0.45 predicts the 0.69 transfer ceiling 0.71 measured where convergence fraction 0.97 predicts nothing | | Across all systems | Alpha orders distillation quality at Spearman +1.0; reliability follows it too spread vs alpha, rho = -1 | Figure 4. The pre-transfer audit. Scope note from the paper: read the full flip-rate curve at the copy’s achievable error scale, never the bare exponent; quantitative prediction holds in contracting maps. One lineage result is worth stating on its own: down a five-generation chain, alpha climbs while fidelity falls. Copies of copies grow more definite and less faithful. Single copies can reproduce their teacher’s fractal boundary geometry exactly, because the geometry is generated by iterating the learned map, not stored in it. External validation - Within a day of v1.0, an independent researcher filed a from-scratch replication with a four-part re-diagnosis as a GitHub issue. - Every claim was re-tested inside the original harness. Two confirmed decisively, one confirmed with a stronger result, one did not replicate reported with a teacher-weights offer . - Two laws were restated as a result. The paper says which, and the v1.0 diagnosis it overturned remains in the lab log. - The issue’s author is a co-author from v1.2. | Issue claim | Outcome in our harness | |---|---| | 2D losses belong to the SGD carrier, not the channel | Confirmed: a lossless lattice carrier hits union 0.99 with flat lineage | | Mean NMSE anti-correlates with basin transfer | Confirmed: NMSE-selected models score 0.000 basin agreement every seed | | The high-dimension wall is budgetary, not fundamental | Confirmed and extended: two-hop distillation reaches 0.31 to 0.50 in half the seeds from 61x fewer queries | | GP carrier reaches 0.48 from 16k pairs | Not replicated 0.095 +/- 0.06 ; divergence is teacher-level, weights offered | Scope - Quantitative alpha prediction is demonstrated in contracting maps; high-dimensional parametric field matching remains open best MNIST parametric arm: 0.19 against a 0.71 ceiling . - Lineage chains are single-seed; the paper discloses this and the best-of-5 ancestor selection. - The laws table in the paper separates demonstrated from conjectured, per law. - Method kinship: this is the same validate-the-mechanism approach as our JEPA reproduction /blog/what-we-learned-validating-jepa/ , scaled up to a full paper. Reproduce git clone https://github.com/Veso-AI-Open-Source/knowledge-as-dynamics uv sync uv run python -m m5 fielddistill.validate Law 1, ~3.5 min uv run python -m m5 fielddistill.gi Laws 4 and 5, ~3 min uv run python -m m5 fielddistill.alpha the instrument, ~1 min @misc{helou2026knowledgedynamics, title = {Knowledge as Dynamics: Distilling, Composing, and Inheriting the Latent Vector Fields of Neural Networks}, author = {Helou, Elias and Nemytchenko, Ivan}, year = {2026}, url = {https://github.com/Veso-AI-Open-Source/knowledge-as-dynamics} } Veso AI runs its R&D in the open. Questions about the paper or the instruments? Get in touch.