The code behind the picture

3 teaching cells · Python standard library · Read-only

1. 1. Start from the four logits

   These are the Logits lesson's raw class scores for the marked watermelon pixel, recomputed at full precision from its inputs and the hand-set weights (a teaching example, not learned).

   In [ ]:

   import json
   import math
   
   pixel = [27, 166, 85]  # the marked watermelon pixel: red, green, blue bytes
   x = [value / 255 for value in pixel]
   classes = ["flesh", "rind", "seed", "background"]
   W = [[2, -2, 0], [-1, 3, -1], [-1, -1, -1], [1, 1, 2]]
   b = [-0.5, -0.3, 1, -2.5]
   z = [sum(w * xi for w, xi in zip(row, x)) + bias for row, bias in zip(W, b)]

2. 2. Turn the scores into shares, safely

   Subtract the largest score, exponentiate, add the amounts into one total, and divide each amount by that total. Adding the same amount to every score (here 2) gives the same shares; raising seed's score by one changes every share. Only the reported result is rounded.

   In [ ]:

   def softmax(scores):
       m = max(scores)
       amounts = [math.exp(s - m) for s in scores]
       total = sum(amounts)
       return [a / total for a in amounts]
   
   round6 = lambda v: round(v, 6)
   p = softmax(z)
   result = {
       "shares": {name: round6(v) for name, v in zip(classes, p)},
       "sum": round6(sum(p)),
       "offset_unchanged": all(abs(a - c) < 1e-12 for a, c in zip(p, softmax([s + 2 for s in z]))),
       "seed_plus_one": {name: round6(v) for name, v in zip(classes, softmax([s + (k == 2) for k, s in enumerate(z)]))},
   }

3. 3. Inspect the result

   Print the result as JSON so both languages use the same output format.

   In [ ]:

   print(json.dumps(result))

{
  "shares": {
    "flesh": 0.042261,
    "rind": 0.697699,
    "seed": 0.189401,
    "background": 0.07064
  },
  "sum": 1,
  "offset_unchanged": true,
  "seed_plus_one": {
    "flesh": 0.031884,
    "rind": 0.526389,
    "seed": 0.388432,
    "background": 0.053295
  }
}