Alice and the Frog of Destiny (3/3)
A short story about Convolutional Neural Networks
On the near side of the room, hundreds of dials stretched out into the distance. As Alice’s eyes grew accustomed to the dim light, she could see that every dial was connected to every pedestal, via exactly one wire.
Being careful not to trip, she started to turn one of the dials away from zero. Immediately the three attached wires began to glow and the pedestals over the other side of the room also lit up, though not equally.
“Why are some pedestals brighter that others?” she asked. “I’ve set this dial to 0.7 and the tomato pedestal is a lot brighter than the other two.”
“That because the wires are different strengths” he replied. “See, the wire connecting this dial to the tomato pedestal is green and thick, so boosts the signal strongly. However, the wires to the other two pedestals are red, so make the signal negative. The pedestals light up brightly if they receive a strong positive signal and only dimly if they receive a negative signal.”
Alice still wasn’t convinced. “But each pedestal is connected to every dial. How does it deal with all of the incoming signals?”
“It just adds them up!” replied the wizard gleefully. “Simple! Now we must get started setting these dials…”
He took the top sheet of paper from pile and twisted the first dial until it matched the number in the top left corner of grid. He then made the second dial match the next number in the grid and so on, until the first 36 of the dials were set to a distinct value from the grid.
“Well that’s one done — only 49 to go!” declared the wizard.
Alice made a quick mental calculation. “But there’s 1800 dials — we’ll be here for days!”
“Being a wizard does have some benefits…”
Bacchus flicked his wand and the sheets of paper flew into the air and burst into flames. When the smoke had cleared, Alice saw that all the 1800 values from the sheets of paper had been transferred to the dials and every wire was glowing. The brightest light however, came from the back of the room. The tomato pedestal was radiating a brilliant white light, whilst the other two were hardly visible.
“It worked!” exclaimed Bacchus. “It’s correctly predicted that the island cave will contain tomatoes.”
Alice had to admit, she was impressed.
“But there’s one thing I don’t understand” she said, with a furrowed brow. “How do you know how to set the thicknesses of the wires and lenses, so that this process works? It seems to me that there must be an infinite number of possibilities!”
Bacchus Propagus sudden looked very proud.
“That has been my life’s work!” he exclaimed. In my teenage years, I initially set up all the wires and lenses randomly. Over many epochs, the pirates, Arr, Gee and Bee have been bringing me batches of maps from new islands along with report of what’s in the cave. Each time, I push the maps through the whole process and see how well the machine predicts what’s inside the cave.”
The wizard’s eyes were gleaming with excitement. “Every time I see that the machine isn’t performing as well as it could, I first check to see if tweaking each wire in this room would improve the prediction. If so, I make the adjustment, then go back to the kaleidoscopes to see if there are any adjustments that can be made to the lenses that would also improve the prediction.”
Alice was starting to understand. “So gradually, the machine started to improve and now, it can predict just about any new island correctly! How clever!”
The wizard looked very pleased with himself. “There’s a few things that help of course. Sometimes some of the wires and lenses randomly drop out, whilst I’m tweaking the machine — probably a loose connection or something. But rather than be a hindrance to the process, I’ve actually found it to be very beneficial as it forces some of the lazier wires and lenses to start pulling their weight!”
“They seem to have a mind of their own!”
“Yes, their memories are impeccable — they all seem to remember how I tweaked them from the previous batch, and carry a bit of that momentum forward into the next update. Again, I don’t mind as it seems to help.”
“So let me see if I understand what we need to do.” Alice was enjoying learning about the wizard’s invention, but she did still want to get home in time for tea. “You have a heap of maps from islands where you don’t know what’s inside the cave. If we input these into the machine, eventually, one of them should light up the frog pedestal and the sunglasses pedestal. If the machine hasn’t made a mistake, this must be the island with the Frog of Destiny?”
“Exactly!” the wizard was pleased at how quickly Alice had learnt about his invention. “Let’s get to work…”
After many hours of kaleidoscopes, washing machines and wires, they found what they were looking for — one set of maps had lit up the frog and sunglasses pedestal simultaneously, whilst the tomato pedestal remained in the dark. Alice was overjoyed.
“I can’t wait to meet the Frog of Destiny” she said, as she walked with the wizard to the edge of the shore. “But how should we get to the island?”
“I have a ship waiting for you” replied Bacchus.
When they arrived at the coast, Alice couldn’t believe her eyes. A giant rowing boat sat at the edge of the beach, with thousands of oars. Most bizarrely, each oarsman appeared to be a small oak tree.
“Does the boat have a name?” Alice enquired.
The wizard grinned. “Yes, it’s the famous XG Booster! Let me show you how it works…”
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