The code behind the picture

3 teaching cells · Python standard library · Read-only

1. 1. Prepare the labels, scores and reference

   Four labels in a fixed order and one hand-set logit per label (demonstration scores, not a trained recognizer). The reference label is supplied with the picture; it is not computed from the scores.

   In [ ]:

   import json
   import math
   
   labels = ["watermelon", "fried egg", "mug", "no target object"]
   reference = "watermelon"  # supplied with the picture
   score_sets = {
       "A": [2.1, 0.4, -0.6, 0.8],
       "B": [1.0, -0.4, 0.0, 0.9],
       "D": [1.1, -0.2, 0.3, 1.1],  # an exact tie
       "E": [0.3, 2.5, -0.4, 0.6],  # chosen to show a mistake
   }

2. 2. Softmax, argmax and the label

   A stable softmax gives the shares. Argmax compares full values with a strict >, so in a tie the first tied position wins (the declared tie rule). The position is then looked up in the label list, and only then compared with the reference. Shares are rounded to six decimals for the report only.

   In [ ]:

   def softmax(z):
       m = max(z)
       e = [math.exp(v - m) for v in z]
       return [v / sum(e) for v in e]
   
   def argmax(values):
       best = 0
       for k in range(1, len(values)):
           if values[k] > values[best]:
               best = k
       return best
   
   result = {}
   for name, z in score_sets.items():
       p = softmax(z)
       k = argmax(p)
       result[name] = {
           "index": k,
           "label": labels[k],
           "share": round(p[k], 6),
           "same_as_logit_argmax": argmax(z) == k,
           "correct": labels[k] == reference,
       }

3. 3. Inspect the result

   Print the result as JSON so both languages use the same output format. B wins below one half, D is settled by the tie rule, and E is confidently wrong.

   In [ ]:

   print(json.dumps(result))

{
  "A": {
    "index": 0,
    "label": "watermelon",
    "share": 0.656849,
    "same_as_logit_argmax": true,
    "correct": true
  },
  "B": {
    "index": 0,
    "label": "watermelon",
    "share": 0.396933,
    "same_as_logit_argmax": true,
    "correct": true
  },
  "D": {
    "index": 0,
    "label": "watermelon",
    "share": 0.367396,
    "same_as_logit_argmax": true,
    "correct": true
  },
  "E": {
    "index": 1,
    "label": "fried egg",
    "share": 0.760228,
    "same_as_logit_argmax": true,
    "correct": false
  }
}