Three 2025-2026 papers fix a gene network's known topology inside an ODE or fixed-point solver, and fit only the continuous kinetic parameters by gradient descent.
lane: substrate · FLeCS — arXiv:2503.20027 (Bertin, Viviano, Tejada-Lapuerta, Wang, Bauer, Theis, Bengio; submitted 2025-03-25); CLAMP — ICML 2026, "Steady-State ODE Inference of Gene Regulatory Networks from Single-Cell Perturbations" (Gallagher-Syed, Wenteler, Martinez, Slabaugh; OpenReview id C0DTxoMuYO, no arXiv id found); MechPert — arXiv:2602.13791 (Boubnovski Martell et al., submitted 2026-02-14, ICLR 2026); anchors: scVelo (Bergen et al., Nature Biotechnology 38(12):1408-1414, 2020); Dynamo (Qiu et al., Cell 185(4):690-711, 2022 — Cell, not Nature Methods as the task brief states); P-NET (Elmarakeby et al., Nature 598(7880):348-352, 2021)
Gives. Known pathway or network topology inside the forward pass; only kinetic rates and edge weights move.
Needs. A topology you already trust; few samples.
Breaks. Edge fades with data: MechPert loses to plain consensus at N=500; nothing proposes structure.
All three papers put a biologically literal object directly inside the forward pass as fixed or semi-fixed structure: a GRN's edges, or a cell's pathway hierarchy. They restrict gradient descent to the small set of continuous numbers the mechanism leaves open, such as kinetic rates or edge weights. This is the opposite move from LLM-SR or FunSearch. Nothing here searches over program shape. The shape is biology, asserted once from prior knowledge (FANTOM5, Reactome, scATAC) or jointly fit as one shared adjacency, leaving only numeric fitting for the optimizer. No LLM proposes, edits, or receives a residual in any of the three papers — the "LLM in the loop" branch is empty here, and that absence is itself the finding.
FLeCS and CLAMP fit continuous kinetic or edge parameters by gradient descent, while topology is either a fixed prior or a single jointly-fit matrix. The biological parameterization sets that matrix's existence, not combinatorial search, and no LLM or evolutionary search appears in either paper. P-NET pushes furthest: topology is fixed at construction and never touched by the optimizer. The optimizer gradient-fits only weight magnitudes on existing edges. MechPert has no gradient boundary at all for its headline method; everything is discrete LLM text plus a training-free weighted average.
These methods win when the mechanism is known well enough to hand-fix most structure, leaving a tractable low-dimensional fit. P-NET's structured sparsity beats a dense network of matched parameter count specifically at small sample sizes, significant at ≤500 samples, for example p=0.003 at n=155, the typical size of a clinical cohort. The cost: results inherit the prior's errors. P-NET's Discussion says pathway encoding is hardcoded and depends on annotation quality, needing re-tuning per clinical context. CLAMP's joint-fit design is a scaling move: without it, k-gene combinations would need combinatorial training data. MechPert's "no retraining" design is cheapest, but its own ablation shows literature-driven hypotheses losing to random gene sampling in two of four cell lines, HepG2 and Jurkat.
P-NET: AUC 0.93, AUPRC 0.88, accuracy 0.83 on held-out test (1,013 prostate cancers: 333 CRPC, 680 primary; Fig. 1b-c/S3/S4), beating SVM, logistic regression, decision tree, random forest, AdaBoost, and a matched-size dense net at small n (Fig. 2a/S5). External validation, 225 samples across two cohorts, correctly classified approximately 73% primary and 76% CRPC (Fig. 2b-c); misclassified-as-aggressive cases linked to biochemical recurrence (p=8×10⁻⁵). FLeCS: per a secondary summary, not verified against primary PDF, functional insights on K562 knockdowns aligned with known biology in 11 of 12 cases versus near-chance differential expression, and matched or exceeded OT-CFM/scTour on A549 trajectories, though no numbers are given. CLAMP: reported, at abstract-level only, to predict non-additive combinatorial effects and align structurally with ChIP-seq and lineage data. No numeric table is retrievable; OpenReview is blocked. MechPert Table 1: few-shot N=50 correlation, LangPert 0.528 to Binary Consensus 0.553 to confidence-weighted 0.583 (+10.4%, abstract rounds to "+10.5%"). Table 3 Jurkat N=50: 0.405 to 0.448 binary to 0.468 confidence-weighted. Table 2 K562 anchor-selection: MechPert 0.536 versus PPI 0.230, though body text separately cites K562 MechPert as 0.336 with a "+46% over PPI" claim matching 0.336, not 0.536. Both values appear in the source; this is unresolved here.
1. MechPert: in HepG2 and Jurkat, LLM-sourced hypotheses underperform random sampling for anchor selection. The authors attribute this to literature bias for less-studied lines. 2. MechPert's gain reverses with more data: at N=500, Binary Consensus (0.606) beats confidence-weighted MechPert (0.589). The advantage is a low-data-only edge. 3. MechPert's own memorization confound: the paper notes that Replogle et al. 2022 is likely in the LLM's pretraining corpus. 4. P-NET's hardcoded Reactome structure: this bounds every result by that annotation's completeness, and hyperparameters need re-tuning per context. 5. FLeCS's modeling assumptions: FLeCS assumes linear, non-additive-logic-free, production, is fully deterministic, and fits multi-target drugs worse than single-gene knockouts (secondary-source, UNVERIFIED against primary PDF). 6. No identifiability analysis found: for FLeCS's or CLAMP's fitted adjacency, in any page opened. Neither paper discusses whether fit parameters are uniquely determined, versus one of many equally-fitting solutions.
A WebSearch, extended, for "LLM proposes GRN structure, gradient fit, residual fed back to LLM" found no matching paper. The closest hits were PHOENIX, prior adjacency with a neural-net derivative and no LLM, and PerturbODE, learned latent GRN modules with no LLM. The loop the task asked about was not found closed anywhere. MechPert is the closest LLM-adjacent paper, and it explicitly has no gradient-fit mechanistic step.
P-NET, 2021, is the ancestor pattern: encode a known hierarchy as a sparsity mask, and let backprop fit only surviving weights. FLeCS and CLAMP extend it from static classifier to dynamical system. FLeCS adds time, coupled ODEs with adjoint fitting; CLAMP adds the implicit-gradient fixed-point trick for combinatorial predictions without combinatorial data. scVelo and Dynamo form the separate RNA-velocity lineage: scVelo generalized the steady-state assumption into a fitted dynamical model, and Dynamo built a continuous vector field on top. MechPert positions itself against GEARS and TxPert, GNN and GO-graph methods, and against LangPert, LLM similarity retrieval, proposing consensus-filtered LLM hypotheses as the next step past both.
Verified: WebFetch on arxiv.org/abs/2503.20027 (abstract only — full PDF exceeded WebFetch's 10MB limit, no HTML render exists, ar5iv redirected back to abstract); WebFetch on arxiv.org/html/2602.13791 (full text); WebFetch on icml.cc/virtual/2026/70834 (CLAMP abstract page); WebFetch on openreview.net for CLAMP blocked by a verification wall, not opened; WebFetch on biorxiv.org/content/10.1101/2020.12.08.416446v1.full (P-NET preprint, chars 0-100000 of 116160); WebSearch cross-checks for FLeCS mechanism (lacuna.tiptreesystems.com, mcml.ai — secondary, flagged) and scVelo/Dynamo bibliographic facts. · code: FLeCS none found; CLAMP "code upon acceptance" per a related NeurIPS 2026 listing; MechPert none found; P-NET github.com/marakeby/pnet_prostate_paper (named in secondary sources, not opened)