Notebook · September 2026
Take the wiring diagram of a real fly brain. Put a simple neuron at every cell and a synapse at every measured connection. Let it pick which alloy to compute next, tell it how good the answer was, and let each synapse adjust using only what it can see locally. Does it learn to pick well?
This page is the notebook of that experiment: what was built, what was run, what was seen. The results, the replayable runs and the fifteen-chapter book hold the detail.
MaleCNS v1.0 is an electron-microscopy reconstruction of an adult male Drosophila central nervous system, published under CC BY 4.0 by FlyEM at Janelia with Cambridge, the MRC LMB and Google Research. From it Forager takes the graph only: 163,972 neurons and 6,143,838 directed connections, each weighted by its synapse count. Nothing was removed by a size cap. A smaller run used the 16,384 best-connected neurons. The neurons' skeletons are downloaded separately for 128 cells so the run viewers can draw activity on real anatomy.
We do not simulate a fly. Neurotransmitters, morphology, timing and biophysics are all absent. What is kept is who connects to whom, and how strongly.
A candidate alloy is described by a 20-number vector \(x\) (composition, radii, valence electrons, and so on). Each neuron \(i\) settles for three steps,
where \(B\) is a fixed random matrix, \(b_i\) a bias and \(w_{ij}\) the weight of the measured connection from \(j\) to \(i\). The score of a candidate is the mean goodness \(\overline{h^2}\) over all neurons after settling. Scores go through a softmax at temperature 0.06, mixed with 15 % uniform exploration, and one candidate is sampled.
After the evaluator answers, the reward is compared with a running baseline. The best and worst evaluations seen so far are replayed as a positive and a negative phase, and each synapse moves by the local derivative of a per-neuron Forward-Forward loss,
with \(y=\pm1\) the phase, \(\theta = 0.18\), and \(r-b\) the reward minus baseline. No gradient passes from one neuron to another. Incoming weights are renormalised so their absolute sum stays below \(\rho = 0.85\). This is Hinton's Forward-Forward idea made recurrent and reward-modulated; it is not, by itself, a way of assigning credit, and Section 8 shows what that costs.
Sixty-four near-equiatomic alloys of Mo, Nb, Ta, W, V, Ti, Zr and Hf, three to five elements each, all on the bcc lattice: the refractory high-entropy alloys. Their figure of merit is the mixing enthalpy against the pure bcc elements,
in eV per atom, from the same evaluator at the same settings. Negative means the elements prefer to mix, on this lattice, in this cell.
These are single random occupancies of a 16-atom cell, not special quasirandom structures, without vibrations or competing phases. That is a screening quantity, not a property.
Service conditions enter in two places. The screen relaxes each cell and its atoms at pressure \(P\) and uses the enthalpy \(H = E + PV\) in place of the energy, for the alloy and for its elemental references alike. Temperature adds the ideal configurational entropy of mixing:
DFT then runs at the geometry the screen relaxed and records the pressure it finds there, so the two fidelities are compared on the same atoms. The entropy term is a model, not a measurement: it always favours more components.
MACE-MP-0 (medium, float64, no dispersion) is a machine-learned interatomic potential trained on Materials Project relaxations. It answers in a few hundredths of a second and is used for the forty screening evaluations of each run. Quantum ESPRESSO 7.5 does density-functional theory: PBE, PAW pseudopotentials from pslibrary 1.0.0, 50/400 Ry cutoffs, 3×3×3 k-points, Marzari–Vanderbilt smearing 0.02 Ry. It takes minutes per cell on six cores and is used for ten calculations on the best fourteen screened alloys. Model hashes, pseudopotential hashes, inputs and outputs are all recorded.
Three runs were made on Colab A100 machines on 11 September 2026: the 16k-neuron graph at 0 K; the whole brain at 0 K; the whole brain at 1500 K and 5 GPa. On the whole-brain graph a decision over the 64 candidates took about 13 s and a learning update about 2.6 s. All three completed with no failed evaluation and a passing acceptance report.
At 0 K four of the ten alloys that reached DFT have negative mixing enthalpy: MoNbTaW and MoTaVW at −58 meV/atom, MoTaV at −44, MoNbTaVW at −36. Everything containing Zr or Hf is positive, +62 to +91. That is the expected chemistry: group 5 and 6 refractory metals with similar radii mix nearly ideally on bcc; Zr and Hf are larger and not bcc at 0 K, and a rigid bcc cell with a compromise lattice parameter makes them pay for it.
At 1500 K and 5 GPa the quinary MoNbTiVW leads at −247 meV/atom, but the entropy term (140–210 meV/atom) is three to five times any enthalpy, so the ranking is by number of components first. Relaxation at pressure helped the size-mismatched alloys a great deal (MoNbWZr +91 → +51 meV/atom) and the well-matched ones hardly at all (MoNbTaW −58 → −54). Both are physically sensible.
On the twenty alloys both evaluators saw, MACE's Spearman rank correlation with DFT is 0.77 (unrelaxed) and 0.78 (relaxed at 5 GPa). Its mean absolute error is 70 and 114 meV/atom, its bias −60 and −97 meV/atom, and on relaxed cells it gets the sign of ΔH wrong for five alloys out of ten. A straight line through the relaxed points gives DFT ≈ 0.28·MACE + 28 meV: the model's dynamic range is three to four times too large here. Random multi-component bcc cells are far from the ordered compounds it was trained on. Good enough to shortlist; not good enough to be the reward.
The three runs used graphs ten times apart in size and received quite different reward streams. Their choice probabilities are the same curve to plotting precision, and that curve is \(1/(\text{alloys remaining})\), the shape of uniform sampling with a fixed seed. The first twelve alloys chosen were the same, in the same order, in all three runs.
Re-scoring all 64 candidates with the saved initial and final weights confirms it without reference to the seed: a candidate's score correlates with the norm of its feature vector at \(r = 1.000\); learning moved the weights by \(\lVert\Delta w\rVert_2 = 111\) on the ΔH run and moved every choice probability by at most 0.0015. The whole policy lives between 0.013 and 0.019 per alloy, where uniform is 0.0156.
In these three runs the fly brain did not choose the alloys. The seed did, with a slight lean toward Hf- and Zr-rich compositions because they have the largest feature norms. MACE and Quantum ESPRESSO did all of the physics, and the DFT rankings above are exactly as valid as they would be for forty alloys drawn at random, which is what they are.
The cause is mechanical, not statistical. The mean goodness over 164,000 neurons is a law-of-large-numbers quantity: it depends on the magnitude of the input drive and on almost nothing else. A bounded local update on synapses whose incoming weights are held to a fixed absolute sum can raise every neuron's goodness together (the ΔH run's scores all rose by 0.125) but cannot open a gap between two candidates that the input did not already separate. Section 2 said the rule does not assign credit; this is what that looks like when it is run.