Can a fruit fly brain solve an olympiad problem?

The classic solution stores, for every value, the sorted positions where it appears in a. It then walks through b and binary-searches the earliest position after the previous match; if a number has none left, the answer is NIE. All queries together take O((m + total length of b) log m), and solution/tes.py passes all 25 official tests. Step through it:

1. Puzzlea = 1 5 4 5 7 8 6
   b = 5 7 8
2. Smellsone 50 ms smell per number
3. Receptorsrandom spikes in the matching smell neurons
4. Fly brain138,639 spiking neurons, FlyWire wiring
5. Spike countsper neuron, per 75 ms
6. Readoutlinear, the only trained part
7. TAK / NIE

1. Load the wiring

   FlyWire release 783 lists which neuron connects to which, through how many synapses, and whether the sender excites or inhibits (predicted from its neurotransmitter). I use the processed connectivity of Shiu et al. 2024 and FlyWire's cell annotations to find smell receptors, mushroom body cells and the neurons that drive the body.

   138,639neurons

   15,091,983connections

   53smell receptor types

   5,177Kenyon cells, the learning centre

2. Make every neuron a leaky integrate-and-fire unit

   The same equations and constants as the published whole-brain model. A neuron spikes when its voltage passes -45 mV, resets to -52 mV and rests for 2.2 ms. Each spike of neuron \(j\) adds \(w_{ij} = 0.275\,\text{mV} \times n_{ij} \times s_j\) to neuron \(i\) after 1.8 ms, for \(n_{ij}\) synapses with sign \(s_j = \pm 1\).

   \[ \tau_m \frac{dv}{dt} = v_0 - v + g, \qquad \tau_s \frac{dg}{dt} = -g, \qquad \tau_m = 20\text{ ms},\; \tau_s = 5\text{ ms} \]

   The linear part is integrated exactly over each 0.1 ms step, so there is no numerical drift:

   \[ u(t+\Delta t) = u(t)\,e^{-\Delta t/\tau_m} + g(t)\,\frac{\tau_s}{\tau_s - \tau_m}\left(e^{-\Delta t/\tau_s} - e^{-\Delta t/\tau_m}\right), \qquad u = v - v_0 \]

   Checked against the published model

   Its headline result is that sugar-sensing neurons drive MN9, the motor neuron that extends the proboscis to feed. This implementation reproduces it: MN9 fires at 71.5 Hz with sugar input and stays silent without.

3. Turn numbers into smells

   Each number drives one type of olfactory receptor neuron with random (Poisson) spikes for 50 ms, one number per 75 ms slot: first b, a pause, then a, then a silent slot.

   

4. Simulate only what can fire, and prove nothing changes

   A neuron that never spikes cannot influence anything. A pilot on the full brain finds every neuron that spikes or comes within 3 mV of threshold; the experiment runs on that subnetwork. Fresh trials on the full and trimmed brain, with identical random input, must give identical spikes. Trials run side by side as (neurons x trials) arrays, and every condition gets the same random seeds, so the brain and its controls smell exactly the same thing.

   

5. Read the answer out

   A linear classifier reads the log spike count of every neuron in every 75 ms slot, about 140,000 features, and says TAK or NIE. That is the most generous question you can ask: is the answer present in the activity at all? The response matrix had 450 million nonzero entries, so the classifier is fitted exactly on the trial-by-trial kernel instead:

   \[ \hat t(x) = k(x)^\top \left(K + \lambda I\right)^{-1} t, \qquad K_{ij} = x_i^\top x_j \;\;(3{,}180 \times 3{,}180) \]

6. Grade it without fooling yourself

   Generated puzzlesrandom TES instances, official queries excluded

   • train fits the readout
   • validation picks settings
   • test gives the reported number

   Official examthe 12 official test queries small enough to smell, never used for training

   • each played 15 times, since the brain is noisy
   • the majority vote is the answer

   • Always answer TAKno computation at all
   • Raw smells, no brainthe same readout on a perfect record of the smells
   • Randomly rewired brainsame neurons, connection counts and signs, wiring shuffled
   • Trained artificial networkan upper reference that is not a fly

1. Short-term memory

   Two textbook mechanisms real neurons have, added on top of the published model: spike-frequency adaptation (a neuron that fires a lot fires less for a while) and short-term synaptic depression (a synapse used a lot delivers less for a while).

   \[ \tau_m \frac{dv}{dt} = v_0 - v + g - a, \qquad \tau_a \frac{da}{dt} = -a, \qquad a \leftarrow a + b \;\text{ at every spike} \]

   \[ \text{a spike of } j \text{ delivers } w_{ij}\,x_j,\;\text{ then } x_j \leftarrow (1-U)\,x_j, \qquad \tau_{rec}\frac{dx_j}{dt} = 1 - x_j \]

   preset	adaptation b	τa	depression U	τrec
   mild	0.1 mV	200 ms	0.05	300 ms
   strong	0.5 mV	800 ms	0.2	1000 ms

2. Realistic smells at a calibrated strength

   Every number now activates a blend of three receptor types, like a real odor. The strength is chosen per memory setting by what every task needs first: naming the number being smelled right now, in the middle of a stream of smells.

   

   memory	strength	smells named	Kenyon cells active
   none	3 Hz	30%	38.5%
   mild	40 Hz	56%	14.1%
   strong	40 Hz	89%	3.0%

3. A ladder of tasks instead of one pass or fail

   Same or different? Was it in the list? Which came first? Then full TES, each with train, validation and test sets and 95% confidence intervals. A trained network learns the first three almost perfectly; simply adding up the smells cannot.

   

   Status

   Calibration, trimming for strong memory (identical spikes: 44,540 on both brains) and every baseline are done and committed. The full ladder under every condition is an unattended, resumable pipeline estimated at about 12 hours of CPU, and has not been run to completion.

• One simple neuron model everywhere. No gap junctions, neuromodulators, learning or graded (non-spiking) neurons, and transmitter signs are predictions. This is the fly's exact wiring running on generic neurons.
• The readout is external. It asks whether the answer is linearly present in the activity, not whether a fly would act on it.
• The encoding is a choice. One smell per number, 75 ms per smell; a real fly would first have to be trained to treat smells as symbols.
• Tiny inputs only. Of the 25 official tests, only 12 queries are small enough to smell; the rest hold up to 1,000,000 numbers, about 21 hours of continuous smelling each.
• Round 2 is unfinished. The fairer design is built, calibrated and tested, but its full ladder has not been run.

• FlyWire Consortium; Dorkenwald, S. et al. Neuronal wiring diagram of an adult brain. Nature 634 (2024).
• Schlegel, P. et al. Whole-brain annotation and multi-connectome cell typing of Drosophila. Nature 634 (2024).
• Shiu, P. K. et al. A Drosophila computational brain model reveals sensorimotor processing. Nature 634 (2024).
• Task TES, Test na inteligencję, XVII Polish Olympiad in Informatics, stage I (2009).