✗ Failed on benchmark 2026

Chemotactic Feature Transport Layer

Implementation & benchmark of arXiv:2608.03685 — Pattern formation: reactivity is not necessary for chemotaxis--driven instabilities

Usefulness7/10

Difficulty6/10

Novelty8/10

Architecture Accuracy Stability Cnn Training dynamics Dynamical systems Pde Spectral theory

Source paper: Pattern formation: reactivity is not necessary for chemotaxis--driven instabilities arXiv:2608.03685 ⓘ · analyzed Aug 31, 2026

AI-generated research hypothesis, automatically tested. Not peer-reviewed.

Idea description

Replace part of a CNN or continuous-depth feature block with two coupled feature fields. One field is transported up gradients of the other through a conservative cross-gradient flux, creating adaptive spatial organization that ordinary diffusion or symmetric convolution cannot produce. The coupling strength and dominant wavelength are controlled by a directly testable linear-instability boundary.

Formulas

$$\partial_t u=D_u\Delta u-\beta\nabla\cdot(u\nabla v)+f(u,v),\qquad \partial_t v=D_v\Delta v+g(u,v).$$

$$M(q)=\begin{pmatrix}f_u-D_uq&f_v+\beta\bar{u}q\\g_u&g_v-D_vq\end{pmatrix},\qquad q=|k|^2.$$

$$\lambda_{\pm}(q)=\frac{\operatorname{tr}M(q)\pm\sqrt{(\operatorname{tr}M(q))^2-4\det M(q)}}{2},\qquad \text{instability if }\max_q\operatorname{Re}\lambda_+(q)>0.$$

$$\beta_c(q)=\frac{(f_u-D_uq)(g_v-D_vq)-g_uf_v}{g_u\bar{u}q},\qquad \det M(q)<0\text{ for }\beta>\beta_c(q)\text{ when }g_u\bar{u}q>0.$$

Mathematical statement

The model uses two fields u and v, diffusivities D_u and D_v, chemotactic strength beta, and reaction functions f and g. Around a homogeneous state (u_bar, v_bar), let f_u, f_v, g_u, and g_v denote the four partial derivatives of the reaction functions at that state. For a Fourier mode with squared wave number q equal to |k|^2, the linearized matrix is M(q) = [[f_u - D_u q, f_v + beta u_bar q], [g_u, g_v - D_v q]]. The chemotactic term changes an off-diagonal entry by beta u_bar q, unlike diffusion. If the trace is negative, instability occurs when the determinant becomes negative. When g_u u_bar q is positive, the critical chemotactic strength is beta_c(q) = ((f_u - D_u q)(g_v - D_v q) - g_u f_v) / (g_u u_bar q).

Implementation notes

Integrate this as a residual feature block in a CNN, U-Net, or continuous-depth vision model. Split a feature tensor into two channel groups U and V, optionally applying softplus so that U is nonnegative. For a step size h, use U_new = U + h times [D_u Delta_h U - beta div_h(U times grad_h V) + F_theta(U,V)] and V_new = V + h times [D_v Delta_h V + G_theta(U,V)]. Compute the chemotactic flux on cell faces using a face-averaged U multiplied by the centered spatial gradient of V, then apply a discrete divergence. This conservative discretization reduces artificial mass creation. Estimate f_u, f_v, g_u, and g_v by automatic differentiation of the small reaction networks F_theta and G_theta at the minibatch mean feature state. For each FFT frequency, construct M(q) and record its largest real eigenvalue. The paper supplies the linearized matrix and instability criterion; feature Jacobians and operating states are estimated empirically. First test CIFAR-10 with a small ResNet, comparing a standard residual block, diffusion-only coupling, and chemotactic coupling at equal parameter count. The prediction is a sharp onset near the smallest measured beta_c(q), and the growth rate of a sinusoidal perturbation should agree with the predicted eigenvalue within 20 percent.

Verification

Failed on benchmark

Stage 1 · Toy mechanism gate: Passed ✓

Stage 2 · Mechanism transferred to benchmark: Not reproduced ✗

Stage 2 · Practical benchmark result: No measurable effect

Methodology: 8 paired seeds, permutation test (p<0.05) against a learning-rate-tuned baseline. How verification works

Stage 1 — Mechanism check agent confidence 9/10

Built a conservative periodic chemotactic transport module with the stated two-field linearization, RK4 perturbation integrator, beta-critical calculation, and finite-volume face flux/divergence. The predicted instability boundary was beta_c=0.5739 at mode q=9; the sweep first became positive at beta=0.6614 on its coarse grid and was exactly zero at beta_c. At beta=0.8239, measured log-amplitude growth was 0.3677804427677 versus predicted eigenvalue 0.3677804427682 (relative error 1.5e-12); mass error of the conservative transport discretization was 0. The mechanism manifested clearly, but this is not evidence of improved image accuracy.

Agent confidence: 9/10

Baseline: Diffusion-only localized perturbation: total u deviation 0.0 in the transport-only comparison; beta=0 growth at q=9 = -1.11414
Idea: Chemotactic beta=0.8 localized perturbation: total u deviation 1.78584; beta sweep growth increments at beta=[0.1,0.2,0.3,0.4] = [0.23930,0.45288,0.64759,0.82770]; small-beta slope 2.29010

Limitations: No CIFAR-10, CNN/ResNet training, learned reaction networks, equal-parameter accuracy comparison, GPU benchmark, or long-horizon nonlinear pattern-spectrum analysis was tested. The onset sweep used a coarse beta grid, so its observed threshold is reported as a bracketed grid observation rather than a refined estimate.

How to run: python3 chemotactic_transport.py

Stage 2 — Benchmark vs. tuned baseline (arXiv:2608.03685) Sep 2, 2026

No significant difference vs. the tuned baseline (+1.4%, p=0.2826, wins 2 / 8 paired seeds).

Benchmark: Vision (image classification)
Model: cnn_small
Paired seeds: 8
Baseline mean: 0.8031
Idea mean: 0.8144
Effect (Δ): 0.0112 (+1.4%; negative = idea better)
Wins: 2 / 8 paired seeds
p-value: 0.2826 (permutation test, 20 000 shuffles)
Smallest detectable effect: ±2.7%
Mechanism: Not confirmed ✗
Practical effect: No effect
Baseline tuning: swept over 3 configs

Limitations:

The run used 400 training examples, 200 test examples, and 12 epochs. The learned reaction Jacobian and neural-network-scale Fourier growth signature were not measured; mechanism confirmation is false.

How to run: python3 stage2_bench.py

Verdict computed by deterministic test code from paired-seed statistics — not by the language model.

Stage 2 — Benchmark Aug 31, 2026 latest Failed ✗

Agent confidence: 9/10

The chemotactic feature transport layer was evaluated on the structurally matched registered vision track with a matched CNN system. It was worse than baseline: mean error 0.814375 versus 0.803125, paired delta +0.01125, permutation p=0.28255; there was no significant win.

Baseline: vision/cnn_small, tuned lr=0.001: mean error 0.8031249791
Idea: vision/cnn_small with chemotactic beta=0.25, lr=0.001: mean error 0.8143749759

Benchmark result