The evolution of DNA sequences can be viewed as stochastic dynamics on a high-dimensional discrete space, but it is unclear when empirical transition biases reduce to an effective energy landscape versus retain irreducible non-equilibrium circulation. Human context-dependent mutation probabilities offer a direct test: every single-nucleotide substitution in a local context has a reverse substitution, so the logarithm of the forward-to-reverse probability ratio defines an antisymmetric field-the human mutation field. We show this field has a dominant gradient component and a smaller but reproducible curl component. Using seven-base human germline substitution probabilities, we infer an effective mutational landscape with a Siamese neural network constrained to predict only energy differences. This model predicts forward-to-reverse log-ratios for held-out mutations with a correlation of about 0.93, close to both an unconstrained predictive reference (0.948) and the empirical reversible ceiling from Hodge projection (about 0.96). Although trained only on mutation probabilities, the inferred landscape largely recovers short-word genomic composition and Chargaff reverse-complement symmetry for sequences up to length four. Deviations from equilibrium structure reveal a small but detectable nonequilibrium component: a residual irreversible circulation violating the Kolmogorov cycle condition for detailed balance, reproducible across African, Asian, and European populations, and strongest in CpG-linked cycles and CpG-transition edges, consistent with methylcytosine deamination. These results give a thermodynamic decomposition of the human mutation field: most mutation bias is organized by a local equilibrium-like energy landscape aligned with genome composition, while the residual circulation points to specific directional mutational mechanisms.
We decompose an evolutionary mixture-of-LoRA system on a from-scratch ~150M-parameter widened-D substrate (D=1536, V=32000; D/V approx 0.048; the "widened-1536" substrate) into three factors -- a router rewrite (parallel sigmoid gate with learnable per-adapter floor and bounded temperature anneal, fed post-stack hidden states rather than token-embedding means), a per-domain leave-one-out evaluation scope, and a lifecycle of death plus alpha-blend inheritance plus SVD mutation plus slot reallocation -- and report a 5-of-8 partial 2^3 factorial run at n=3 seeds and 25000 adaptation steps per cell. The attribution chain is sharp on this substrate: the router rewrite carries the entire +0.0426 nat balanced log-PPL improvement (Delta = log PPL_ref - log PPL_test, positive = improvement; t=12.86, p=0.006) attributed to "the full evolutionary system vs the static B3 baseline"; the headline full-system-vs-B3 balanced contrast itself is +0.015 nats, t=1.94, p=0.19 at n=3 and does not clear alpha=0.05. The per-domain evaluation scope is null at seed-resolution, and the lifecycle is a net drag of approx -0.028 nats (t=-4.46,p=0.047 in the primary chain). An auxiliary alpha=0 inheritance counterfactual at n=3 seeds is sign-inconsistent at the headline metric and underpowered for either an equivalence or load-bearing conclusion (corrected from an earlier arithmetic-mean aggregator that erroneously cleared inheritance; see Appendix B.11). A base-perturbation probe directionally refutes a "genomic-context" reframe of the lifecycle role. A controllable synthetic sandbox locates a substrate-conditional regime boundary: evolutionary search on the routing channel is load-bearing only when adapters are pre-aligned to the task; in every other regime tested it underperforms, ties, or actively degrades the gradient solution.
When an LLM repeatedly mutates a program, does it explore new forms or circle back to the same ones? We study this question by analyzing LLM-driven mutation chains in the absence of selection pressure within a domain-specific language, varying prompt design, model family, and stochastic replication. We find that LLM-based mutation consistently converges toward restricted attractor regions in program space. Convergence is especially severe at the structural level: in 87% of chains, over 93% of mutations revisit a previously seen structural form, with most variation confined to terminal substitutions within recurring templates. Cycle analysis reveals short cycles and self-loops dominating the transition structure. The rate of convergence varies with prompt wording and model choice, but the phenomenon is robust across conditions. A classical GP subtree mutation operator does not exhibit comparable convergence, suggesting that the effect is intrinsic to the LLM mutation pipeline. These findings reveal a tension at the heart of LLM-driven program evolution: the same capabilities that enable semantics-aware program transformation also carry a systematic bias toward structural homogeneity that must be accounted for if such systems are to sustain open-ended exploration. Source code is available at https://github.com/can-gurkan/lmca.
The inverse Potts problem for estimating evolutionary single-site fields and pairwise couplings in homologous protein sequences from their single-site and pairwise amino acid frequencies observed in their multiple sequence alignment would be still one of useful methods in the studies of protein structure and evolution. Since the reproducibility of fields and couplings are the most important, the Boltzmann machine method is employed here, although it is computationally intensive. In order to reduce computational time required for the Boltzmann machine, parallel, persistent Markov chain Monte Carlo method is employed to estimate the single-site and pairwise marginal distributions in each learning step. Also, stochastic gradient descent methods are used to reduce computational time for each learning. Another problem is how to adjust the values of hyperparameters; there are two regularization parameters for evolutionary fields and couplings. The precision of contact residue pair prediction is often used to adjust the hyperparameters. However, it is not sensitive to these regularization parameters. Here, they are adjusted for the fields and couplings to satisfy a specific condition that is appropriate for protein conformations. This method has been applied to eight protein families.