Task Ecologies and the Evolution of World-Tracking Representations in Large Language Models

Giulio Valentino Dalla Riva

stat.MEApr 7, 2026

Task Ecologies and the Evolution of World-Tracking Representations in Large Language Models

Authors: Giulio Valentino Dalla Riva

Organizations: Baffelan OÜ

Abstract

We study language models as evolving model organisms and ask when autoregressive next-token learning selects for world-tracking representations. For any encoding of latent world states, the Bayes-optimal next-token cross-entropy decomposes into the irreducible conditional entropy plus a Jensen--Shannon excess term. That excess vanishes if and only if the encoding preserves the training ecology's equivalence classes. This yields a precise notion of ecological veridicality for language models and identifies the minimum-complexity zero-excess solution as the quotient partition by training equivalence. We then determine when this fixed-encoding analysis applies to transformer families: frozen dense and frozen Mixture-of-Experts transformers satisfy it, in-context learning does not enlarge the model's separation set, and per-task adaptation breaks the premise. The framework predicts two characteristic failure modes: simplicity pressure preferentially removes low-gain distinctions, and training-optimal models can still incur positive excess on deployment ecologies that refine the training ecology. A conditional dynamic extension shows how inter-model selection and post-training can recover such gap distinctions under explicit heredity, variation, and selection assumptions. Exact finite-ecology checks and controlled microgpt experiments validate the static decomposition, split-merge threshold, off-ecology failure pattern, and two-ecology rescue mechanism in a regime where the relevant quantities are directly observable. The goal is not to model frontier systems at scale, but to use small language models as laboratory organisms for theory about representational selection.

Figures & tables

Figure 1: Exact finite-ecology calibration of Thm. 8 . Each point is a discrete ecology/partition pair from the synthetic sweep. The excess loss coincides exactly with the Jensen–Shannon excess term, giving the diagonal identity predicted by the theorem.

Figure 2: Empirical-corpus corroboration of the static theory. Left: the exact empirical ecology built from held-out Alice and Manifesto corpora has partition size

k_{\mathrm{exact}}=1,2,3,5

as the ecology expands. Right: on those same exact empirical ecologies, the measured excess loss coincides with the exact Jensen–Shannon excess term, as predicted by Thm. 8 .

Ecological-veridicality framework	LLM ecosystem
Organism	A trained model (full weights, frozen at deployment)
Population	The set of extant models and variants
Encoding $p$	Induced world-state encoding $p_{\theta,D}$
Fitness $\mathcal{F}(p)$	Multi-task benchmark performance
Reproduction	Fine-tuning, distillation, next-generation training
Mutation	Architecture changes, data mix, RLHF

Table 3

Figure 3: Selection-stage diagnostics in the microgpt Wright–Fisher experiment. Left: cumulative selection-stage change in mean risk across generations. The downward trend shows a weak but persistent net selection pressure toward lower risk. Right: histogram of standardized residuals

z:=(\Delta\bar{R}_{\mathrm{sel}}-\mathbb{E}[\Delta\bar{R}_{\mathrm{sel}}\mid\text{risk, fitness}])/\mathrm{sd}(\Delta\bar{R}_{\mathrm{sel}}\mid\text{risk, fitness})

. The residuals are centered and mostly fall inside

\pm 2

, with rms

z=1.05

and exact 95%-band coverage

0.96

, consistent with the Wright–Fisher conditional sampling law.

Figure 4: Neural validation of the two-ecology mechanism on bracket balance in Lisp source code. Left: static sweep showing the fraction of maximum evaluation signal captured as a function of the recipe trait

\alpha

. Both tasks start at zero signal when

\alpha=0

. Balance checking (direct supervision via summary token) saturates quickly; code validation (no balance labels, held-out NLL discrimination only) rises more steadily, confirming that the transfer is indirect. Right: population selection drives

\bar{\alpha}

upward in both tasks, concentrating the recipe distribution on bracket-rich training.

Figure 5: Exact finite-ecology calibration of Thm. 55 . The plotted quantity is the objective difference

J_{D,\beta}(p_{\mathrm{merge}})-J_{D,\beta}(p_{\mathrm{split}})

for an illustrative local split. The crossing occurs at the theorem’s threshold

\beta^{\ast}

: below it the split is preferred, above it the merge is preferred.

Figure 6: Exact corpus-induced test of Thm. 55 . Left: the exact global optimum path under

J_{D,\beta}

for the Commedia and Manifesto ecologies as

\beta

increases. Right: the realized global transitions are compared step-by-step to the theorem’s local split-threshold prediction. The alignment is exact on Commedia and has a single nonlocal deviation on Manifesto .

Figure 7: Off-ecology failure in the microgpt model organism. Left: per-model cross-entropy rises from the training ecology (English, French, German) to related unseen languages (Italian, Finnish) and rises again on Voynich. Right: pairwise inter-model Jensen–Shannon disagreement shows the same ordering. This is the empirical signature predicted by the decomposition theorem: off-ecology probes incur larger excess and leave more room for divergent model behaviour.

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