nDNA -- the Semantic Helix of Artificial Cognition

TL;DR

This work introduces Neural Genomics and the nDNA framework to diagnose the latent cognition of foundation models beyond surface outputs. It formalizes three per-layer latent-geometric measures—spectral curvature $\kappa_\ell$, thermodynamic length $\mathcal{L}_\ell$, and belief vector field $\mathbf{v}_\ell^{(c)}$—and combines them into a unified nDNA score that captures inheritance, drift, and adaptation across training histories. The Cartograph and its subsections lay out why trajectories, not weights, are fundamental, and present diagnostics (nHD, nGDI, nTEDS, nTDS, nKaryotyping, nDIV, nEPI, nCCL) to quantify heritable transformations, cultural priors, and corpus dependence. By framing latent cognition as a lineage with measurable geometry, the framework aims to enable safer governance, transparency, and auditing of AI systems as they evolve through pretraining, fine-tuning, alignment, distillation, and merging.

Abstract

As AI foundation models grow in capability, a deeper question emerges: What shapes their internal cognitive identity -- beyond fluency and output? Benchmarks measure behavior, but the soul of a model resides in its latent geometry. In this work, we propose Neural DNA (nDNA) as a semantic-genotypic representation that captures this latent identity through the intrinsic geometry of belief. At its core, nDNA is synthesized from three principled and indispensable dimensions of latent geometry: spectral curvature, which reveals the curvature of conceptual flow across layers; thermodynamic length, which quantifies the semantic effort required to traverse representational transitions through layers; and belief vector field, which delineates the semantic torsion fields that guide a model's belief directional orientations. Like biological DNA, it encodes ancestry, mutation, and semantic inheritance, found in finetuning and alignment scars, cultural imprints, and architectural drift. In naming it, we open a new field: Neural Genomics, where models are not just tools, but digital semantic organisms with traceable inner cognition. Modeling statement. We read AI foundation models as semantic fluid dynamics: meaning is transported through layers like fluid in a shaped conduit; nDNA is the physics-grade readout of that flow -- a geometry-first measure of how meaning is bent, paid for, and pushed -- yielding a stable, coordinate-free neural DNA fingerprint tied to on-input behavior; with this fingerprint we cross into biology: tracing lineages across pretraining, fine-tuning, alignment, pruning, distillation, and merges; measuring inheritance between checkpoints; detecting drift as traits shift under new data or objectives; and, ultimately, studying the evolution of artificial cognition to compare models, diagnose risks, and govern change over time.

Figures (11)

• Figure 1: Semantic hydrodynamics.Model. We read the forward pass as semantic hydrodynamics: a prompt injects semantic mass that is transported through depth like a fluid through a shaped channel. Why. Weight/attention coordinates can change without altering behavior; the on-input flow provides behavior-first, coordinate-free signals. Reading guide.Bend$\to$spectral curvature$\kappa$ (sharp reroutes vs. laminar refinement); Pay$\to$thermodynamic length$L$ (where the model expends effort; $\Delta L$ bursts mark bottlenecks); Push$\to$belief field$\mathbf{v}$ (direction/magnitude of local drive; eddies indicate recirculation). Benefit. The same metaphor specifies where to measure—bends, throats, and eddies—turning inner computation into actionable diagnostics and governance thresholds.
• Figure 2: LLM as an input$\to$output semantic channel.Model: we read the forward pass as semantic hydrodynamics—a prompt injects semantic mass that is transported through depth like a fluid through a shaped conduit. Bend (top row): curvature $\kappa$ distinguishes laminar refinement from sharp reroutes. Pay (bottom left): thermodynamic length $L$ localizes where effort concentrates via $\Delta L$ bursts (bottlenecks). Push (bottom right): the belief field $\mathbf{v}$ reveals whether a layer update directly advances belief (high alignment) or reorganizes information (low alignment); eddies signal local recirculation. Why this lens: weight--space and attention views are non--identifiable and unstable across checkpoints; nDNA instead reads the on--input trajectory and its information geometry, yielding coordinate--free, behavior--first measurements. Vision: treat inner computation as a measurable flow so that bends, effort, and push become quantifiable traits of cognition—comparable across inputs, layers, models, and training phases. Benefits:actionable diagnostics—$\kappa$ spikes flag brittle turns, $\Delta L$ bursts expose capacity bottlenecks, low $\cos\theta$ (between $\mathbf{v}$ and the tangent $\mathbf{T}$) indicates movement that does not immediately update belief; stable comparability—geometry--based fingerprints are robust to neuron permutations and head--role drift; governance hooks—set thresholds on $\kappa$ or $\Delta L$, track fingerprint drift after fine--tuning/pruning, and audit capacity before release.
• Figure 3: Spectral Curvature ($\boldsymbol{\kappa_\ell}$) quantifies second-order deviations in latent representations across transformer layers--computed via the discrete geometric operator $\boxed{\kappa_\ell := | h_{\ell+1} - 2 h_\ell + h_{\ell-1} |}$. High curvature signals semantic inflection points where internal geometry bends sharply--often in culturally dense, ideologically loaded, or epistemically volatile regions. Peaks in $\kappa_\ell$ typically emerge in upper decoder layers ($\ell \in [21,30]$), where the model accommodates sociolinguistic priors during alignment, multicultural or multilingual fusion. Within the nDNA framework, such curvature reflects latent inheritance dynamics, offering a fine-grained geometric fingerprint of representational restructuring.
• Figure 4: Thermodynamic Length$\boxed{\mathcal{L}_\ell := \sum_{x \in \mathcal{D}} | \nabla_\theta \log p_\ell(x) |^2}$ quantifies the epistemic work performed across transformer layers, calculated as the cumulative squared gradient norm of layerwise log-likelihoods. Higher values signal internal resistance--zones of significant restructuring, belief compression, or negotiation of conflicting priors. In culturally fine-tuned models, these peaks localize to upper decoder layers, indicating intense adaptation near output-generating blocks. Within the nDNA construct, $\mathcal{L}_\ell$ helps reveal latent epistemic effort that underlies surface-level behavior. This metric thus provides a nuanced window into where and how models internally allocate effort during learning and inference.
• Figure 5: Belief Vector Field Visualization: $\mathbf{v}_\ell^{(c)} = \mathbb{E}_{x \sim \mathcal{P}^{(c)}_{\mathrm{CIVIC}}} \left[ \nabla_{h_\ell} \log p(y \mid x) \right]$ represents the belief semantic steering force at layer $\ell$ toward concept $c$, conditioned on CIVIC cultural priors (cf. \ref{['sec:aether_benchmark']}). Large magnitudes (e.g., $\| \mathbf{v}_\ell^{(c)} \| \in [0.15, 0.50]$) indicate strong directional pressure--zones where cultural values actively reshape latent geometry. Color-coded arrows trace distinct conceptual trajectories (protest, peace, order, power, disobedience, justice), while numeric labels quantify local steering strength. Upper layers ($\ell \ge 20$) typically exhibit epistemic reorientation, where cultural priors most heavily influence belief encoding. Such visualizations reveal whether a model internalizes culturally contingent reasoning or merely mimics alignment at the output surface.