A neural network with 80,608 parameters reads handwritten digits with 99.34% accuracy. Parameters are the numbers a network learns during training and then has to store somewhere, so the fewer there are, the less room the model takes. ResNet18, which has been one of the standard yardsticks of computer vision for years, has about 139 times as many parameters, and when trained from scratch on the same data it reaches 99.22%.
The design of the small network comes from the eye of the fruit fly. A group at Columbia University named it FlyVision and showed this month that the same design can be scaled up and used on natural photographs and medical images too.
So does the fly have a better recipe for a machine's eye? The short answer is yes, provided you know exactly what the fly economises on, because if you follow the numbers to the end you find that this low-parameter network, on large images, computes several times more per picture than ResNet18.
a map the size of a brain
Where did the design come from? From a map. In 2024 the FlyWire project published the complete wiring diagram, or connectome, of an adult female fruit fly's brain: a list of which neuron connects to which. It covers 139,255 neurons and roughly 50 million synapses, a synapse being the point where two neurons meet and a signal passes from one to the other.
The same year another group asked a simple question with a hard answer. If we know only who connects to whom, and nothing about how each neuron behaves, can we work out what the circuit does? To find out, they built a network of 45,669 neurons and about 1.5 million connections whose wiring was taken directly from 64 cell types in the fly eye's motion pathway. Only the properties nobody had measured, such as how quickly each neuron responds, were tuned with deep-learning methods so that the network could detect motion. Its predictions agreed with real measurements across 26 separate studies.
That was neuroscience, aimed at understanding the fly itself. The new Columbia paper turns the question around and asks whether what the fly's eye learned over evolution is useful to a machine's eye too.
three principles from a fly's eye
The Columbia network does not copy the map neuron by neuron. It takes three general principles from the fly's eye.
The first is that the image is split into two separate streams right at the start: one sensitive to places brighter than their surroundings, the other to places darker than their surroundings. The fly's eye has this split, and the 2024 network had predicted the same bright and dark streams from the wiring alone, without anyone telling it to.
The second is recurrence. In an ordinary network each layer works on the image once and passes its result on, but here some layers work on their own output twice in a row with the same weights, like someone looking at a photograph a second time to catch details they missed the first time.
The third is that the units of each layer are split into four groups that act on one another, and that influence can make another group more or less active, the way some neurons in the brain excite the next neuron and others inhibit it.
With these three principles the authors built the network in three sizes, from a small version for handwritten digits up to a medium and a large version for 224 by 224 pixel images, keeping the structure fixed each time and only widening the channels. Time to see how it stands against its rival.
put the numbers side by side
What happened? Look carefully here, because the Columbia network does not win everywhere.
On CIFAR-10, a collection of small photographs of ten kinds of object such as cats and aeroplanes, the small network with 81,000 parameters reached 78.03% and the standard model 83.44%, so here the bigger network is more than five points ahead. On ImageNet, whose photographs fall into a thousand categories, the large version with 3.7 million parameters reached 66.25% and the standard model with 11.7 million reached 69.25%.
Chest X-rays told a different story. There the network had to tell apart four conditions, healthy, COVID-19, lung opacity and viral pneumonia, and the medium version with 1.33 million parameters reached 92.60% while ResNet18 with 11.18 million reached 91.56%.
So the overall picture is that with three to eight times fewer parameters, depending on the task, the Columbia network lands a few points behind or slightly ahead. So far this is the familiar story of "smaller but nearly as good", but there is another table in the same paper that changes the story.
where the fly's thrift lies
Do fewer parameters necessarily mean a cheaper network? The paper's own numbers say otherwise. For every image a network has to perform a large number of multiplications and additions, and that count is what decides how long an answer takes and how much battery it drains.
Follow the numbers. On ImageNet the standard model performs about 3.6 billion operations per image. The medium Columbia network performs about 6.6 billion and the large one about 14.8 billion. Now divide: the large version has about three times fewer parameters than ResNet18, but does about four times as much computation per image.
The reason is the second principle. When a layer works on the image twice with the same weights, the weights are stored once but the computation happens twice. The authors say plainly that parameter efficiency and computational efficiency are distinct properties, and that recurrence and population interaction can raise computation without raising the parameter count in proportion.
Now go back to the fly. A brain that has to fit inside a fly's head has little room for each wire and each synapse, and the authors note that animal visual circuits were shaped under simultaneous pressure on wiring, energy, speed and robustness. So the fly is stingy with wiring and fills the gap by reusing the same circuit, and the network built from the fly has inherited that thrift as well: little memory, plenty of patience.
Another detail shows that this trade can be tuned. In the chest X-ray experiment the same network was run with fewer repetitions and the image was shrunk sooner, and there the medium version did about 1.3 billion operations per image against ResNet18's 3.6 billion. How many times the network is allowed to look again is what sets the cost of computation.
which shortage is yours
What does this trade mean in practice? It depends on what is scarce for you.
When a model runs on a smartwatch or a virtual-reality headset, you have two scarce resources. One is memory, the size the model has to fit into on the device or be downloaded at with every update; the other is the battery and time spent on each answer. Parameters eat into the first and computation into the second, and the two are rarely short by the same amount at the same time.
If what you lack is space and you have time, the fly's thrift is exactly what you want. A model that analyses medical images and has to fit on a hospital device with no internet connection can wait a few seconds but cannot be bulky. But if what you lack is time and battery, as with hand tracking in a headset where every fraction of a second of delay is felt, those repetitions become expensive.
In my view the main lesson of this paper is that "small" is not a single number. Whenever someone says their model is smaller, you should ask smaller in what sense: the space it takes on disk, or the work it does for each answer.
which principle did the work
One question is still open, and the paper does not hide it. Which of the three principles produced this result? Most of the credit may belong to recurrence, which has long been familiar in networks with no biology behind them, while the bright and dark split or the four groups may play a small part. The authors write that the next step is to change each principle separately while holding parameters and training budget fixed, so that each one's share becomes clear.
There is one more point from the 2024 work that is missing here. That study showed that predicting a circuit's function from its wiring works better when connections are sparse, meaning each neuron connects to only a few others, as it does in the brains of every animal. But as far as the paper's own description goes, the Columbia network's layers are built from ordinary three-by-three filters that connect each unit to all its neighbours, and the authors themselves list sparsity among the things still to be tested separately. The fly's most important lesson may not have reached the machine yet.
what you borrow from a fly
A design built by nature is an answer to nature's budget. A fly has a small brain and enough time to look twice, and the design of its eye was made for exactly that situation.
So when you borrow the fly's design you borrow its budget too, and the deal only works in your favour if your shortage is the fly's shortage. To my mind the real value of the Columbia work is that it turns the brain's wiring diagram from a scientific curiosity into a source of engineering hypotheses, ones that can be measured and then kept or set aside.