arxiv: 2604.06896 · v1 · submitted 2026-04-08 · 💻 cs.LG · cs.SE· physics.bio-ph

Recognition: no theorem link

VertAX: a differentiable vertex model for learning epithelial tissue mechanics

Alessandro Pasqui , Jim Martin Catacora Ocana , Anshuman Sinha , Matthieu Perez , Fabrice Delbary , Giorgio Gosti , Mattia Miotto , Domenico Caudo

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Maxence Ernoult Herv\'e Turlier

Authors on Pith no claims yet

Pith reviewed 2026-05-10 18:20 UTC · model grok-4.3

classification 💻 cs.LG cs.SEphysics.bio-ph

keywords vertex modelsepithelial tissuesdifferentiable programmingparameter inferenceinverse designtissue mechanicsautomatic differentiationbilevel optimization

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The pith

A differentiable JAX framework turns vertex models into tools for inferring mechanical parameters and designing epithelial tissue behaviors.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Vertex models capture how epithelial tissues reshape through local cell mechanics but involve many tunable parameters that complicate inference and design. The paper presents VertAX as a JAX-based implementation that makes these models differentiable, enabling automatic gradient computation, GPU acceleration, and end-to-end bilevel optimization. Users write arbitrary energy and cost functions in plain Python and connect them directly to machine-learning pipelines for forward simulation, parameter recovery, and inverse design. The work demonstrates the approach on morphogenesis modeling, mechanical inference, and behavior design while comparing automatic differentiation, implicit differentiation, and equilibrium propagation as gradient strategies.

Core claim

VertAX is a differentiable JAX-based framework for vertex-modeling of confluent epithelia that supplies automatic differentiation, GPU acceleration, and end-to-end bilevel optimization for forward simulation, parameter inference, and inverse mechanical design, with users defining arbitrary energy and cost functions in pure Python.

What carries the argument

VertAX framework, which renders standard vertex-model energy functions differentiable inside JAX to support bilevel optimization and seamless machine-learning integration.

If this is right

Forward simulation of tissue morphogenesis gains efficiency from GPU acceleration and automatic differentiation.
Mechanical parameters of real tissues can be inferred by optimizing energy functions against observed cell geometries.
Tissue-scale behaviors can be inversely designed by minimizing user-defined cost functions through bilevel optimization.
Equilibrium propagation supplies gradient estimates using only repeated forward simulations, enabling extension to non-differentiable vertex simulators.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The approach could be combined with neural networks to learn energy functions directly from data rather than hand-specifying them.
Applications might include predicting how genetic or pharmacological perturbations alter tissue mechanics in developmental or disease contexts.
Validation on live-cell imaging datasets would test whether the inferred parameters generalize beyond the simulation environments used in the benchmarks.

Load-bearing premise

Standard vertex-model energy functions remain faithful representations of real epithelial mechanics once rendered differentiable and optimized inside the JAX pipeline.

What would settle it

If parameters recovered by VertAX from observed tissue shapes produce forward simulations that deviate systematically from independent experimental measurements of cell forces or tissue geometry, the framework's practical value would be refuted.

read the original abstract

Epithelial tissues dynamically reshape through local mechanical interactions among cells, a process well captured by vertex models. Yet their many tunable parameters make inference and optimization challenging, motivating computational frameworks that flexibly model and learn tissue mechanics. We introduce VertAX, a differentiable JAX-based framework for vertex-modeling of confluent epithelia. VertAX provides automatic differentiation, GPU acceleration, and end-to-end bilevel optimization for forward simulation, parameter inference, and inverse mechanical design. Users can define arbitrary energy and cost functions in pure Python, enabling seamless integration with machine-learning pipelines. We demonstrate VertAX on three representative tasks: (i) forward modeling of tissue morphogenesis, (ii) mechanical parameter inference, and (iii) inverse design of tissue-scale behaviors. We benchmark three differentiation strategies-automatic differentiation, implicit differentiation, and equilibrium propagation-showing that the latter can approximate gradients using repeated forward, adjoint-free simulations alone, offering a simple route for extending inverse biophysical problems to non-differentiable simulators with limited additional engineering effort.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

VertAX is a practical JAX implementation of vertex models with three gradient options for bilevel tasks, but the lack of any error numbers on the approximations undercuts the inference and design claims.

read the letter

The paper ships a JAX-based vertex model engine called VertAX that supports automatic differentiation, implicit differentiation, and equilibrium propagation for forward simulation, parameter fitting, and inverse design. Users write energy and cost functions in plain Python, and the code runs on GPU. That setup is the main deliverable, and it directly addresses the pain of tuning many parameters in tissue mechanics models by letting people run end-to-end optimization inside standard ML pipelines. The three-task demonstration (morphogenesis, inference, design) and the explicit comparison of the three differentiation routes are useful engineering steps that were not previously packaged this way for vertex models. Equilibrium propagation gets highlighted as an adjoint-free option that only needs repeated forward runs, which could matter for extending the approach to simulators that are not easily differentiated. The framework itself looks cleanly implemented and ready for reuse. The soft spot is the missing quantitative check on gradient quality. The abstract says equilibrium propagation “can approximate gradients” and that the three strategies were benchmarked, yet no relative error figures, no ablation on recovered parameters, and no stability tests appear when the inner energy minimization is inexact. Without those numbers it is hard to know whether the approximate routes actually produce usable results for the claimed inference and design tasks or whether they only work in narrow regimes. The central engineering claim still stands—the code and the basic examples are there—but the evidence for reliable bilevel optimization is thinner than the title suggests. This is for computational biophysicists who already run vertex models and want to add learning or optimization without writing their own adjoints. A reader who needs a drop-in differentiable engine will find concrete value in the implementation and the examples. The work is coherent on its own terms and shows clear thinking about the practical bottlenecks, so it deserves a serious referee. Referees will probably press for the gradient error analysis, but the framework contribution is real enough to review rather than desk-reject.

Referee Report

2 major / 1 minor

Summary. The paper introduces VertAX, a JAX-based differentiable framework for vertex modeling of confluent epithelia. It provides automatic differentiation, GPU acceleration, and end-to-end bilevel optimization for forward simulation, parameter inference, and inverse mechanical design, allowing users to define arbitrary energy and cost functions in Python. The work demonstrates the framework on three tasks—forward modeling of tissue morphogenesis, mechanical parameter inference, and inverse design of tissue-scale behaviors—and benchmarks three differentiation strategies (automatic differentiation, implicit differentiation, and equilibrium propagation), claiming that the latter approximates gradients via repeated forward, adjoint-free simulations.

Significance. If the gradients from implicit differentiation and equilibrium propagation prove sufficiently accurate and stable for driving outer-loop optimizations on typical confluent-epithelia regimes, VertAX would offer a practical, extensible tool for integrating vertex models with machine-learning pipelines. This could enable more routine parameter inference and inverse design in biophysical modeling without requiring custom adjoint derivations for each new energy function.

major comments (2)

[Abstract] Abstract: the claim that equilibrium propagation 'can approximate gradients using repeated forward, adjoint-free simulations alone' is load-bearing for the central utility argument, yet the manuscript supplies no quantitative metrics (e.g., relative gradient error versus automatic differentiation, or downstream effect on recovered parameters/loss) on the inference or design tasks.
[Demonstrations] Demonstrations section: the three representative tasks are presented without ablation studies, ground-truth comparisons, or statistical tests showing that inference/design outcomes remain statistically indistinguishable across the three differentiation strategies when the inner energy minimization is inexact or non-unique.

minor comments (1)

[Abstract] The abstract refers to 'three representative tasks' without enumerating their precise quantitative outcomes or the specific vertex-model energy functions employed.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We appreciate the referee's constructive comments on our manuscript. We address each major comment point by point below and indicate the revisions we will make to strengthen the presentation of our results.

read point-by-point responses

Referee: [Abstract] Abstract: the claim that equilibrium propagation 'can approximate gradients using repeated forward, adjoint-free simulations alone' is load-bearing for the central utility argument, yet the manuscript supplies no quantitative metrics (e.g., relative gradient error versus automatic differentiation, or downstream effect on recovered parameters/loss) on the inference or design tasks.

Authors: We agree that quantitative support would strengthen the central claim about equilibrium propagation. In the revised manuscript, we will add explicit metrics including relative gradient error norms versus automatic differentiation as well as quantitative assessments of downstream effects on recovered parameters and final loss values for the inference and design tasks. revision: yes
Referee: [Demonstrations] Demonstrations section: the three representative tasks are presented without ablation studies, ground-truth comparisons, or statistical tests showing that inference/design outcomes remain statistically indistinguishable across the three differentiation strategies when the inner energy minimization is inexact or non-unique.

Authors: The demonstrations were designed to illustrate core capabilities rather than exhaustive validation. To address this point, we will expand the section with ablation studies across differentiation strategies, ground-truth comparisons where feasible, and statistical tests (such as paired t-tests) to evaluate whether inference and design outcomes differ significantly when inner minimization is inexact or non-unique. revision: yes

Circularity Check

0 steps flagged

No circularity: VertAX is a software framework with no load-bearing derivations or predictions that reduce to inputs by construction

full rationale

The paper introduces a JAX-based computational framework for vertex models, providing automatic differentiation and bilevel optimization capabilities. It demonstrates usage on forward simulation, parameter inference, and inverse design tasks, and benchmarks three differentiation strategies. No mathematical derivation chain is presented that claims to predict results from first principles; the work consists of software implementation and empirical benchmarks. There are no self-definitional steps, fitted inputs renamed as predictions, or self-citation chains that justify central claims. The framework is self-contained, with users defining their own energy functions, and reported results do not reduce to tautological reuse of inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The paper contributes a software implementation rather than new physical axioms or fitted constants. The vertex model itself inherits standard assumptions from the existing literature (polygonal cells, area and perimeter energies, T1 transitions). No new free parameters or invented entities are introduced beyond the usual vertex-model hyperparameters.

axioms (2)

domain assumption Vertex models with area, perimeter, and line-tension energies accurately capture the dominant mechanics of confluent epithelia.
Invoked in the opening sentence of the abstract as the modeling foundation.
standard math Automatic differentiation through the vertex-model energy and force calculations yields correct gradients for optimization.
Implicit in the claim that the framework supports end-to-end bilevel optimization.

pith-pipeline@v0.9.0 · 5517 in / 1451 out tokens · 123504 ms · 2026-05-10T18:20:31.927939+00:00 · methodology

discussion (0)

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

Training cell stress patterns in 3D cellular packings
cond-mat.dis-nn 2026-04 unverdicted novelty 7.0

3D cellular packings can be trained to realize prescribed stress patterns by updating cell shape indices with a contrastive learning algorithm in a vertex model.

Reference graph

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