activations

Deeper understanding of activations in MLP

Motivations

• We want to move to more complex neural networks like RNN, GRU, LSTM and transformers
• Before doing that better to gain deeper understanding of activations and back propogation and their historical context.
• While RNN very expressive - universal function approximator algorithms; they are not very easily optimizable from the first order techniques available to us and that we use all the time.
• Key to understanding why they don’t optimize easily ; is to understand activations and gradient and how they behave during training. Lot of variance in NN architectures that we see are owing to this fact and innovations are around how they have tried to rectify these situation.

words = open("../data/names.txt", 'r').read().split(); words[:5]
words[:8], len(words)

(['emma', 'olivia', 'ava', 'isabella', 'sophia', 'charlotte', 'mia', 'amelia'],
 32033)

s2i = stoi(words, start_str=".", end_str=".")
i2s = itos(s2i)
display(s2i)
display(i2s)

{'a': 1,
 'b': 2,
 'c': 3,
 'd': 4,
 'e': 5,
 'f': 6,
 'g': 7,
 'h': 8,
 'i': 9,
 'j': 10,
 'k': 11,
 'l': 12,
 'm': 13,
 'n': 14,
 'o': 15,
 'p': 16,
 'q': 17,
 'r': 18,
 's': 19,
 't': 20,
 'u': 21,
 'v': 22,
 'w': 23,
 'x': 24,
 'y': 25,
 'z': 26,
 '.': 0}

{1: 'a',
 2: 'b',
 3: 'c',
 4: 'd',
 5: 'e',
 6: 'f',
 7: 'g',
 8: 'h',
 9: 'i',
 10: 'j',
 11: 'k',
 12: 'l',
 13: 'm',
 14: 'n',
 15: 'o',
 16: 'p',
 17: 'q',
 18: 'r',
 19: 's',
 20: 't',
 21: 'u',
 22: 'v',
 23: 'w',
 24: 'x',
 25: 'y',
 26: 'z',
 0: '.'}

X, Y = build_XY(words, s2i, block_size=3, verbose=False)
display(X.shape, Y.shape)

n1 = int(0.8*len(X))
n2 = int(0.9*len(X))

Xtr, Ytr = X[:n1], Y[:n1]
Xdev, Ydev = X[n1:n2], Y[n1:n2]
Xte, Yte = X[n2:], Y[n2:]


display(Xtr.shape, Xdev.shape, Xte.shape)

torch.Size([228146, 3])

torch.Size([228146])

torch.Size([182516, 3])

torch.Size([22815, 3])

torch.Size([22815, 3])

vocab_sz = len(i2s); vocab_sz
model = Model(vocab_sz, emb_sz=10, hidden_units=200)
plot_embeddings(model, s2i, emb_model = TSNE(random_state=0, n_iter=1000, perplexity=26), cluster_model=KMeans(n_clusters=4) ); F.cross_entropy(model(X), Y) , model.num_params(), model.hidden_units

/opt/homebrew/Caskroom/miniforge/base/envs/aiking/lib/python3.9/site-packages/sklearn/cluster/_kmeans.py:1412: FutureWarning: The default value of `n_init` will change from 10 to 'auto' in 1.4. Set the value of `n_init` explicitly to suppress the warning
  super()._check_params_vs_input(X, default_n_init=10)

def weight_decay_scheduler(lrs=[0.1, 0.01], epochs=5):
    for i in range(epochs):
        if i <= epochs/2:
            yield torch.tensor(lrs[0])
        else:
            yield torch.tensor(lrs[1])

epochs = 200000
# epochs/2

for lr in weight_decay_scheduler():
    print(lr)

tensor(0.1000)
tensor(0.1000)
tensor(0.1000)
tensor(0.0100)
tensor(0.0100)

tracker = {'lr':[], 'batch_sz':[], 'loss':[], 'block_sz':[], 'emb_sz':[], 'hidden_units':[] }

train?

Signature:
train(
    model,
    X,
    Y,
    lr=0.1,
    epochs=1000,
    verbose=False,
    batch_sz=None,
    loss_fn=<function cross_entropy at 0x13f12d310>,
    tracker=None,
)
Docstring: <no docstring>
File:      ~/rahuketu/programming/minion/minion/makemore/mlp.py
Type:      function

train(model, Xtr, Ytr, lr = weight_decay_scheduler(epochs=200000),epochs=200000, batch_sz=32, tracker=tracker, verbose=True)

0 tensor(23.1901, grad_fn=<NllLossBackward0>)
100 tensor(9.0815, grad_fn=<NllLossBackward0>)
200 tensor(5.8802, grad_fn=<NllLossBackward0>)
300 tensor(5.1096, grad_fn=<NllLossBackward0>)
400 tensor(7.2417, grad_fn=<NllLossBackward0>)
500 tensor(4.6860, grad_fn=<NllLossBackward0>)
600 tensor(7.2835, grad_fn=<NllLossBackward0>)
700 tensor(5.3226, grad_fn=<NllLossBackward0>)
800 tensor(3.7588, grad_fn=<NllLossBackward0>)
900 tensor(3.3159, grad_fn=<NllLossBackward0>)
1000 tensor(3.9826, grad_fn=<NllLossBackward0>)
1100 tensor(4.1025, grad_fn=<NllLossBackward0>)
1200 tensor(3.7784, grad_fn=<NllLossBackward0>)
1300 tensor(2.9515, grad_fn=<NllLossBackward0>)
1400 tensor(3.4218, grad_fn=<NllLossBackward0>)
1500 tensor(3.2354, grad_fn=<NllLossBackward0>)
1600 tensor(3.3846, grad_fn=<NllLossBackward0>)
1700 tensor(3.7046, grad_fn=<NllLossBackward0>)
1800 tensor(3.9429, grad_fn=<NllLossBackward0>)
1900 tensor(2.6885, grad_fn=<NllLossBackward0>)
2000 tensor(2.7092, grad_fn=<NllLossBackward0>)
2100 tensor(4.4202, grad_fn=<NllLossBackward0>)
2200 tensor(3.2980, grad_fn=<NllLossBackward0>)
2300 tensor(4.0029, grad_fn=<NllLossBackward0>)
2400 tensor(3.3215, grad_fn=<NllLossBackward0>)
2500 tensor(2.5883, grad_fn=<NllLossBackward0>)
2600 tensor(3.1997, grad_fn=<NllLossBackward0>)
2700 tensor(2.9113, grad_fn=<NllLossBackward0>)
2800 tensor(3.0399, grad_fn=<NllLossBackward0>)
2900 tensor(2.6383, grad_fn=<NllLossBackward0>)
3000 tensor(3.0596, grad_fn=<NllLossBackward0>)
3100 tensor(3.0109, grad_fn=<NllLossBackward0>)
3200 tensor(3.0007, grad_fn=<NllLossBackward0>)
3300 tensor(3.7366, grad_fn=<NllLossBackward0>)
3400 tensor(3.7740, grad_fn=<NllLossBackward0>)
3500 tensor(2.8883, grad_fn=<NllLossBackward0>)
3600 tensor(2.9196, grad_fn=<NllLossBackward0>)
3700 tensor(2.6823, grad_fn=<NllLossBackward0>)
3800 tensor(2.6547, grad_fn=<NllLossBackward0>)
3900 tensor(2.7171, grad_fn=<NllLossBackward0>)
4000 tensor(2.8779, grad_fn=<NllLossBackward0>)
4100 tensor(2.5281, grad_fn=<NllLossBackward0>)
4200 tensor(3.0121, grad_fn=<NllLossBackward0>)
4300 tensor(2.7422, grad_fn=<NllLossBackward0>)
4400 tensor(2.6213, grad_fn=<NllLossBackward0>)
4500 tensor(2.7892, grad_fn=<NllLossBackward0>)
4600 tensor(2.2983, grad_fn=<NllLossBackward0>)
4700 tensor(2.1339, grad_fn=<NllLossBackward0>)
4800 tensor(2.2629, grad_fn=<NllLossBackward0>)
4900 tensor(2.3292, grad_fn=<NllLossBackward0>)
5000 tensor(3.2794, grad_fn=<NllLossBackward0>)
5100 tensor(2.5150, grad_fn=<NllLossBackward0>)
5200 tensor(2.9994, grad_fn=<NllLossBackward0>)
5300 tensor(2.5220, grad_fn=<NllLossBackward0>)
5400 tensor(2.4995, grad_fn=<NllLossBackward0>)
5500 tensor(2.4987, grad_fn=<NllLossBackward0>)
5600 tensor(2.5472, grad_fn=<NllLossBackward0>)
5700 tensor(3.1426, grad_fn=<NllLossBackward0>)
5800 tensor(3.1785, grad_fn=<NllLossBackward0>)
5900 tensor(2.3689, grad_fn=<NllLossBackward0>)
6000 tensor(3.5011, grad_fn=<NllLossBackward0>)
6100 tensor(3.2069, grad_fn=<NllLossBackward0>)
6200 tensor(2.9753, grad_fn=<NllLossBackward0>)
6300 tensor(2.2583, grad_fn=<NllLossBackward0>)
6400 tensor(2.5882, grad_fn=<NllLossBackward0>)
6500 tensor(2.4821, grad_fn=<NllLossBackward0>)
6600 tensor(2.2513, grad_fn=<NllLossBackward0>)
6700 tensor(2.8567, grad_fn=<NllLossBackward0>)
6800 tensor(2.3739, grad_fn=<NllLossBackward0>)
6900 tensor(2.3399, grad_fn=<NllLossBackward0>)
7000 tensor(2.2839, grad_fn=<NllLossBackward0>)
7100 tensor(2.3892, grad_fn=<NllLossBackward0>)
7200 tensor(2.3236, grad_fn=<NllLossBackward0>)
7300 tensor(2.5511, grad_fn=<NllLossBackward0>)
7400 tensor(2.7749, grad_fn=<NllLossBackward0>)
7500 tensor(2.9762, grad_fn=<NllLossBackward0>)
7600 tensor(2.9773, grad_fn=<NllLossBackward0>)
7700 tensor(2.7657, grad_fn=<NllLossBackward0>)
7800 tensor(3.0748, grad_fn=<NllLossBackward0>)
7900 tensor(2.8478, grad_fn=<NllLossBackward0>)
8000 tensor(2.2543, grad_fn=<NllLossBackward0>)
8100 tensor(2.2755, grad_fn=<NllLossBackward0>)
8200 tensor(2.7139, grad_fn=<NllLossBackward0>)
8300 tensor(1.9855, grad_fn=<NllLossBackward0>)
8400 tensor(2.3402, grad_fn=<NllLossBackward0>)
8500 tensor(3.8158, grad_fn=<NllLossBackward0>)
8600 tensor(2.3313, grad_fn=<NllLossBackward0>)
8700 tensor(2.6724, grad_fn=<NllLossBackward0>)
8800 tensor(2.3422, grad_fn=<NllLossBackward0>)
8900 tensor(3.0346, grad_fn=<NllLossBackward0>)
9000 tensor(2.4262, grad_fn=<NllLossBackward0>)
9100 tensor(2.6631, grad_fn=<NllLossBackward0>)
9200 tensor(2.3589, grad_fn=<NllLossBackward0>)
9300 tensor(2.3590, grad_fn=<NllLossBackward0>)
9400 tensor(2.7541, grad_fn=<NllLossBackward0>)
9500 tensor(2.2957, grad_fn=<NllLossBackward0>)
9600 tensor(2.3549, grad_fn=<NllLossBackward0>)
9700 tensor(2.8385, grad_fn=<NllLossBackward0>)
9800 tensor(2.2554, grad_fn=<NllLossBackward0>)
9900 tensor(2.6718, grad_fn=<NllLossBackward0>)
10000 tensor(2.2098, grad_fn=<NllLossBackward0>)
10100 tensor(2.5124, grad_fn=<NllLossBackward0>)
10200 tensor(2.4366, grad_fn=<NllLossBackward0>)
10300 tensor(3.0030, grad_fn=<NllLossBackward0>)
10400 tensor(2.7291, grad_fn=<NllLossBackward0>)
10500 tensor(1.9903, grad_fn=<NllLossBackward0>)
10600 tensor(2.9689, grad_fn=<NllLossBackward0>)
10700 tensor(2.4827, grad_fn=<NllLossBackward0>)
10800 tensor(2.9887, grad_fn=<NllLossBackward0>)
10900 tensor(2.6236, grad_fn=<NllLossBackward0>)
11000 tensor(3.1269, grad_fn=<NllLossBackward0>)
11100 tensor(2.0564, grad_fn=<NllLossBackward0>)
11200 tensor(2.3068, grad_fn=<NllLossBackward0>)
11300 tensor(2.5676, grad_fn=<NllLossBackward0>)
11400 tensor(2.3598, grad_fn=<NllLossBackward0>)
11500 tensor(3.0183, grad_fn=<NllLossBackward0>)
11600 tensor(2.6603, grad_fn=<NllLossBackward0>)
11700 tensor(2.6882, grad_fn=<NllLossBackward0>)
11800 tensor(3.3350, grad_fn=<NllLossBackward0>)
11900 tensor(2.3564, grad_fn=<NllLossBackward0>)
12000 tensor(2.6475, grad_fn=<NllLossBackward0>)
12100 tensor(2.4800, grad_fn=<NllLossBackward0>)
12200 tensor(2.3673, grad_fn=<NllLossBackward0>)
12300 tensor(2.0629, grad_fn=<NllLossBackward0>)
12400 tensor(2.3715, grad_fn=<NllLossBackward0>)
12500 tensor(2.3634, grad_fn=<NllLossBackward0>)
12600 tensor(2.7283, grad_fn=<NllLossBackward0>)
12700 tensor(2.5023, grad_fn=<NllLossBackward0>)
12800 tensor(3.4307, grad_fn=<NllLossBackward0>)
12900 tensor(2.7121, grad_fn=<NllLossBackward0>)
13000 tensor(2.6550, grad_fn=<NllLossBackward0>)
13100 tensor(2.8195, grad_fn=<NllLossBackward0>)
13200 tensor(2.2431, grad_fn=<NllLossBackward0>)
13300 tensor(3.2382, grad_fn=<NllLossBackward0>)
13400 tensor(2.6212, grad_fn=<NllLossBackward0>)
13500 tensor(3.2271, grad_fn=<NllLossBackward0>)
13600 tensor(2.4727, grad_fn=<NllLossBackward0>)
13700 tensor(2.4661, grad_fn=<NllLossBackward0>)
13800 tensor(2.3731, grad_fn=<NllLossBackward0>)
13900 tensor(2.3285, grad_fn=<NllLossBackward0>)
14000 tensor(2.4602, grad_fn=<NllLossBackward0>)
14100 tensor(2.2777, grad_fn=<NllLossBackward0>)
14200 tensor(2.5086, grad_fn=<NllLossBackward0>)
14300 tensor(2.1159, grad_fn=<NllLossBackward0>)
14400 tensor(2.6729, grad_fn=<NllLossBackward0>)
14500 tensor(2.4968, grad_fn=<NllLossBackward0>)
14600 tensor(2.4676, grad_fn=<NllLossBackward0>)
14700 tensor(3.0234, grad_fn=<NllLossBackward0>)
14800 tensor(2.3302, grad_fn=<NllLossBackward0>)
14900 tensor(3.1475, grad_fn=<NllLossBackward0>)
15000 tensor(2.4341, grad_fn=<NllLossBackward0>)
15100 tensor(2.5019, grad_fn=<NllLossBackward0>)
15200 tensor(2.7795, grad_fn=<NllLossBackward0>)
15300 tensor(2.7818, grad_fn=<NllLossBackward0>)
15400 tensor(2.5132, grad_fn=<NllLossBackward0>)
15500 tensor(2.4133, grad_fn=<NllLossBackward0>)
15600 tensor(2.5921, grad_fn=<NllLossBackward0>)
15700 tensor(2.4368, grad_fn=<NllLossBackward0>)
15800 tensor(2.3894, grad_fn=<NllLossBackward0>)
15900 tensor(2.2274, grad_fn=<NllLossBackward0>)
16000 tensor(2.4876, grad_fn=<NllLossBackward0>)
16100 tensor(2.5857, grad_fn=<NllLossBackward0>)
16200 tensor(2.0799, grad_fn=<NllLossBackward0>)
16300 tensor(2.5981, grad_fn=<NllLossBackward0>)
16400 tensor(2.0059, grad_fn=<NllLossBackward0>)
16500 tensor(2.3586, grad_fn=<NllLossBackward0>)
16600 tensor(2.4264, grad_fn=<NllLossBackward0>)
16700 tensor(2.4298, grad_fn=<NllLossBackward0>)
16800 tensor(2.4752, grad_fn=<NllLossBackward0>)
16900 tensor(2.0933, grad_fn=<NllLossBackward0>)
17000 tensor(2.3881, grad_fn=<NllLossBackward0>)
17100 tensor(2.4223, grad_fn=<NllLossBackward0>)
17200 tensor(2.7514, grad_fn=<NllLossBackward0>)
17300 tensor(2.8801, grad_fn=<NllLossBackward0>)
17400 tensor(3.0277, grad_fn=<NllLossBackward0>)
17500 tensor(2.4092, grad_fn=<NllLossBackward0>)
17600 tensor(2.2081, grad_fn=<NllLossBackward0>)
17700 tensor(2.2706, grad_fn=<NllLossBackward0>)
17800 tensor(2.3237, grad_fn=<NllLossBackward0>)
17900 tensor(2.4046, grad_fn=<NllLossBackward0>)
18000 tensor(2.4327, grad_fn=<NllLossBackward0>)
18100 tensor(2.6174, grad_fn=<NllLossBackward0>)
18200 tensor(2.1799, grad_fn=<NllLossBackward0>)
18300 tensor(1.9591, grad_fn=<NllLossBackward0>)
18400 tensor(2.4293, grad_fn=<NllLossBackward0>)
18500 tensor(2.4244, grad_fn=<NllLossBackward0>)
18600 tensor(2.1732, grad_fn=<NllLossBackward0>)
18700 tensor(2.3254, grad_fn=<NllLossBackward0>)
18800 tensor(2.3013, grad_fn=<NllLossBackward0>)
18900 tensor(2.5206, grad_fn=<NllLossBackward0>)
19000 tensor(2.1151, grad_fn=<NllLossBackward0>)
19100 tensor(2.9072, grad_fn=<NllLossBackward0>)
19200 tensor(2.6049, grad_fn=<NllLossBackward0>)
19300 tensor(2.4513, grad_fn=<NllLossBackward0>)
19400 tensor(2.4751, grad_fn=<NllLossBackward0>)
19500 tensor(2.1351, grad_fn=<NllLossBackward0>)
19600 tensor(2.3667, grad_fn=<NllLossBackward0>)
19700 tensor(2.2709, grad_fn=<NllLossBackward0>)
19800 tensor(2.9979, grad_fn=<NllLossBackward0>)
19900 tensor(2.1289, grad_fn=<NllLossBackward0>)
20000 tensor(2.3997, grad_fn=<NllLossBackward0>)
20100 tensor(2.0601, grad_fn=<NllLossBackward0>)
20200 tensor(2.4679, grad_fn=<NllLossBackward0>)
20300 tensor(2.9683, grad_fn=<NllLossBackward0>)
20400 tensor(2.3419, grad_fn=<NllLossBackward0>)
20500 tensor(2.3366, grad_fn=<NllLossBackward0>)
20600 tensor(2.7139, grad_fn=<NllLossBackward0>)
20700 tensor(2.4330, grad_fn=<NllLossBackward0>)
20800 tensor(2.4361, grad_fn=<NllLossBackward0>)
20900 tensor(2.7027, grad_fn=<NllLossBackward0>)
21000 tensor(2.7307, grad_fn=<NllLossBackward0>)
21100 tensor(2.8911, grad_fn=<NllLossBackward0>)
21200 tensor(2.3785, grad_fn=<NllLossBackward0>)
21300 tensor(1.9881, grad_fn=<NllLossBackward0>)
21400 tensor(2.3612, grad_fn=<NllLossBackward0>)
21500 tensor(2.1223, grad_fn=<NllLossBackward0>)
21600 tensor(3.0199, grad_fn=<NllLossBackward0>)
21700 tensor(2.4705, grad_fn=<NllLossBackward0>)
21800 tensor(2.3127, grad_fn=<NllLossBackward0>)
21900 tensor(2.2454, grad_fn=<NllLossBackward0>)
22000 tensor(2.3710, grad_fn=<NllLossBackward0>)
22100 tensor(2.2387, grad_fn=<NllLossBackward0>)
22200 tensor(2.4684, grad_fn=<NllLossBackward0>)
22300 tensor(2.6871, grad_fn=<NllLossBackward0>)
22400 tensor(2.1750, grad_fn=<NllLossBackward0>)
22500 tensor(3.2196, grad_fn=<NllLossBackward0>)
22600 tensor(2.1873, grad_fn=<NllLossBackward0>)
22700 tensor(2.2551, grad_fn=<NllLossBackward0>)
22800 tensor(2.4936, grad_fn=<NllLossBackward0>)
22900 tensor(2.3907, grad_fn=<NllLossBackward0>)
23000 tensor(2.3026, grad_fn=<NllLossBackward0>)
23100 tensor(2.1204, grad_fn=<NllLossBackward0>)
23200 tensor(2.8078, grad_fn=<NllLossBackward0>)
23300 tensor(2.0827, grad_fn=<NllLossBackward0>)
23400 tensor(2.2889, grad_fn=<NllLossBackward0>)
23500 tensor(2.3298, grad_fn=<NllLossBackward0>)
23600 tensor(2.4848, grad_fn=<NllLossBackward0>)
23700 tensor(2.5591, grad_fn=<NllLossBackward0>)
23800 tensor(1.8529, grad_fn=<NllLossBackward0>)
23900 tensor(2.3494, grad_fn=<NllLossBackward0>)
24000 tensor(2.0222, grad_fn=<NllLossBackward0>)
24100 tensor(2.0016, grad_fn=<NllLossBackward0>)
24200 tensor(2.1334, grad_fn=<NllLossBackward0>)
24300 tensor(2.0088, grad_fn=<NllLossBackward0>)
24400 tensor(2.3679, grad_fn=<NllLossBackward0>)
24500 tensor(2.5788, grad_fn=<NllLossBackward0>)
24600 tensor(2.0313, grad_fn=<NllLossBackward0>)
24700 tensor(2.8603, grad_fn=<NllLossBackward0>)
24800 tensor(2.1457, grad_fn=<NllLossBackward0>)
24900 tensor(1.8712, grad_fn=<NllLossBackward0>)
25000 tensor(2.7490, grad_fn=<NllLossBackward0>)
25100 tensor(2.1233, grad_fn=<NllLossBackward0>)
25200 tensor(2.3670, grad_fn=<NllLossBackward0>)
25300 tensor(2.6269, grad_fn=<NllLossBackward0>)
25400 tensor(2.4011, grad_fn=<NllLossBackward0>)
25500 tensor(3.1574, grad_fn=<NllLossBackward0>)
25600 tensor(2.4918, grad_fn=<NllLossBackward0>)
25700 tensor(2.0745, grad_fn=<NllLossBackward0>)
25800 tensor(2.0828, grad_fn=<NllLossBackward0>)
25900 tensor(2.5606, grad_fn=<NllLossBackward0>)
26000 tensor(2.5311, grad_fn=<NllLossBackward0>)
26100 tensor(2.8650, grad_fn=<NllLossBackward0>)
26200 tensor(2.1442, grad_fn=<NllLossBackward0>)
26300 tensor(2.1475, grad_fn=<NllLossBackward0>)
26400 tensor(2.0529, grad_fn=<NllLossBackward0>)
26500 tensor(2.1737, grad_fn=<NllLossBackward0>)
26600 tensor(2.1642, grad_fn=<NllLossBackward0>)
26700 tensor(2.7448, grad_fn=<NllLossBackward0>)
26800 tensor(2.6026, grad_fn=<NllLossBackward0>)
26900 tensor(2.5108, grad_fn=<NllLossBackward0>)
27000 tensor(2.0790, grad_fn=<NllLossBackward0>)
27100 tensor(2.5286, grad_fn=<NllLossBackward0>)
27200 tensor(2.2216, grad_fn=<NllLossBackward0>)
27300 tensor(2.1512, grad_fn=<NllLossBackward0>)
27400 tensor(2.4419, grad_fn=<NllLossBackward0>)
27500 tensor(2.1889, grad_fn=<NllLossBackward0>)
27600 tensor(2.7344, grad_fn=<NllLossBackward0>)
27700 tensor(2.3163, grad_fn=<NllLossBackward0>)
27800 tensor(2.3022, grad_fn=<NllLossBackward0>)
27900 tensor(1.9052, grad_fn=<NllLossBackward0>)
28000 tensor(2.3679, grad_fn=<NllLossBackward0>)
28100 tensor(1.6878, grad_fn=<NllLossBackward0>)
28200 tensor(2.5123, grad_fn=<NllLossBackward0>)
28300 tensor(1.9603, grad_fn=<NllLossBackward0>)
28400 tensor(2.2500, grad_fn=<NllLossBackward0>)
28500 tensor(2.1860, grad_fn=<NllLossBackward0>)
28600 tensor(1.6792, grad_fn=<NllLossBackward0>)
28700 tensor(2.4335, grad_fn=<NllLossBackward0>)
28800 tensor(2.5435, grad_fn=<NllLossBackward0>)
28900 tensor(2.5976, grad_fn=<NllLossBackward0>)
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197100 tensor(2.3751, grad_fn=<NllLossBackward0>)
197200 tensor(1.9968, grad_fn=<NllLossBackward0>)
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198000 tensor(1.8448, grad_fn=<NllLossBackward0>)
198100 tensor(2.2463, grad_fn=<NllLossBackward0>)
198200 tensor(2.1539, grad_fn=<NllLossBackward0>)
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198700 tensor(2.1581, grad_fn=<NllLossBackward0>)
198800 tensor(2.2775, grad_fn=<NllLossBackward0>)
198900 tensor(2.0384, grad_fn=<NllLossBackward0>)
199000 tensor(2.0218, grad_fn=<NllLossBackward0>)
199100 tensor(2.0317, grad_fn=<NllLossBackward0>)
199200 tensor(1.9592, grad_fn=<NllLossBackward0>)
199300 tensor(2.0689, grad_fn=<NllLossBackward0>)
199400 tensor(2.5553, grad_fn=<NllLossBackward0>)
199500 tensor(1.8968, grad_fn=<NllLossBackward0>)
199600 tensor(2.3238, grad_fn=<NllLossBackward0>)
199700 tensor(2.3708, grad_fn=<NllLossBackward0>)
199800 tensor(1.8701, grad_fn=<NllLossBackward0>)
199900 tensor(1.8181, grad_fn=<NllLossBackward0>)
199999 tensor(2.3143, grad_fn=<NllLossBackward0>)

<minion.makemore.mlp.Model at 0x29f1b5820>

train(model, Xtr, Ytr, lr = 0.01,epochs=2000, batch_sz=32, tracker=tracker, verbose=True)

0 tensor(1.7506, grad_fn=<NllLossBackward0>)
100 tensor(2.1854, grad_fn=<NllLossBackward0>)
200 tensor(2.0619, grad_fn=<NllLossBackward0>)
300 tensor(1.9894, grad_fn=<NllLossBackward0>)
400 tensor(2.4191, grad_fn=<NllLossBackward0>)
500 tensor(2.1392, grad_fn=<NllLossBackward0>)
600 tensor(1.7000, grad_fn=<NllLossBackward0>)
700 tensor(1.9909, grad_fn=<NllLossBackward0>)
800 tensor(1.7664, grad_fn=<NllLossBackward0>)
900 tensor(2.4764, grad_fn=<NllLossBackward0>)
1000 tensor(2.1658, grad_fn=<NllLossBackward0>)
1100 tensor(2.2411, grad_fn=<NllLossBackward0>)
1200 tensor(1.7980, grad_fn=<NllLossBackward0>)
1300 tensor(1.6242, grad_fn=<NllLossBackward0>)
1400 tensor(2.4609, grad_fn=<NllLossBackward0>)
1500 tensor(2.4231, grad_fn=<NllLossBackward0>)
1600 tensor(2.0172, grad_fn=<NllLossBackward0>)
1700 tensor(2.1574, grad_fn=<NllLossBackward0>)
1800 tensor(1.9371, grad_fn=<NllLossBackward0>)
1900 tensor(2.0047, grad_fn=<NllLossBackward0>)
1999 tensor(2.0442, grad_fn=<NllLossBackward0>)

<minion.makemore.mlp.Model at 0x29f1b5820>

@torch.no_grad()
def split_loss(split, model):
    x, y = {
        'train': (Xtr, Ytr),
        'val': (Xdev, Ydev),
        'test': (Xte, Yte)
    }[split]
    loss = F.cross_entropy(model(x), y)
    # print(x.shape, y.shape)
    print(split, loss.item())

split_loss('train', model)
split_loss('val', model)

gen_word_nn(model, i2s, n_samples=20,  g=torch.Generator().manual_seed(2147483647+10))

['carmah',
 'ambrileigh',
 'miliathtyn',
 'kanden',
 'jazonen',
 'amerynci',
 'geni',
 'nellara',
 'chaiiv',
 'kaleigh',
 'ham',
 'poru',
 'quinn',
 'suline',
 'livani',
 'wavero',
 'dearisi',
 'jaxeenissa',
 'mel',
 'edi']

Issues with the NN

• Error at initialization too high. We have a rough idea/ estimate of loss at the time of initialization for Neural Net ( almost always during training)
• 27 characters that can come next at the time of initialization. At initialization we have no more probability of one being more true than oth
• Probability at the time of starting should roughly be uniform distribution of character prediction at the time of initial assignment; assigning equal probability of prediction to all the characters

Initialization issues

## Expected loss
-torch.tensor(1/len(s2i)).log()

tensor(3.2958)

• Presently at the time of initialization, probability distribution are all messed up. Some characters are very confident and some are not confident at all -> Network is very confidently wrong that’s what makes it record high loss

vocab_sz = len(i2s); vocab_sz
model = Model(vocab_sz, emb_sz=10, hidden_units=200)
train(model, Xtr, Ytr, lr = 0.1,epochs=1, batch_sz=32, tracker=tracker, verbose=True)

0 tensor(29.8140, grad_fn=<NllLossBackward0>)
0 tensor(29.8140, grad_fn=<NllLossBackward0>)

<minion.makemore.mlp.Model at 0x29cd8d9a0>

logits = torch.tensor([0.0, 0.0, 0.0, 0.0]) # Assuming we only have 4 characters only - this is logits coming out of model

probs = torch.softmax(logits, dim=0)
loss = -probs[2].log()
probs, loss # Value of loss we expect in 4 characters with uniform distribution [ And we get it wrong]

(tensor([0.2500, 0.2500, 0.2500, 0.2500]), tensor(1.3863))

logits = torch.tensor([0.0, 0.0, 5.0, 0.0]) # if we are lucky

probs = torch.softmax(logits, dim=0)
loss = -probs[2].log()
probs, loss #  Here we luck out and record very low loss - prediction 2 and logits for idx 2 is 5.0 --very high

(tensor([0.0066, 0.0066, 0.9802, 0.0066]), tensor(0.0200))

logits = torch.tensor([0.0,  5.0, 0.0,  0.0]) # more likely we have high loss elsewhere

probs = torch.softmax(logits, dim=0)
loss = -probs[2].log()
probs, loss # More likely we record very high numbers for some other character--> We end up having high loss.

(tensor([0.0066, 0.9802, 0.0066, 0.0066]), tensor(5.0200))

logits = torch.tensor([-3.0,  5.0, 0.0,  2.0]) # reality

probs = torch.softmax(logits, dim=0)
loss = -probs[2].log()
probs, loss # Logits take on extreme value and record very high loss

(tensor([3.1741e-04, 9.4620e-01, 6.3754e-03, 4.7108e-02]), tensor(5.0553))

logits = torch.randn(4)
probs = torch.softmax(logits, dim=0)
loss = -probs[2].log()
logits, probs, loss # Logits are near zero so loss is ok

(tensor([ 1.7157,  0.5247, -1.7278, -0.3324]),
 tensor([0.6827, 0.2075, 0.0218, 0.0880]),
 tensor(3.8252))

logits = torch.randn(4)*10 # if logits are large
probs = torch.softmax(logits, dim=0)
loss = -probs[2].log()
logits, probs, loss # loss is extremely high

(tensor([ -1.0294,  -7.6559, -16.4280,  -0.8028]),
 tensor([4.4334e-01, 5.8730e-04, 9.1027e-08, 5.5607e-01]),
 tensor(16.2121))

logits = torch.randn(4)*1000 # if logits are large
probs = torch.softmax(logits, dim=0)
loss = -probs[2].log()
logits, probs, loss # loss is extremely high

(tensor([-1094.7864,   207.8663, -1206.6086,  -563.6341]),
 tensor([0., 1., 0., 0.]),
 tensor(inf))

We want logits to be roughly zeroes / uniform or equal when they initialize.By symmetry we don’t want any positive or negative due to symmetry ,so zero is ok

vocab_sz = len(i2s); vocab_sz
model = Model(vocab_sz, emb_sz=10, hidden_units=200)
train(model, Xtr, Ytr, lr = 0.1,epochs=1, batch_sz=32, tracker=tracker, verbose=True)

0 tensor(32.3362, grad_fn=<NllLossBackward0>)
0 tensor(32.3362, grad_fn=<NllLossBackward0>)

<minion.makemore.mlp.Model at 0x29cd8d580>

model(Xtr)[0]

tensor([ -0.2556,   4.1349,  -3.1335,  -2.1826, -22.7851, -17.8256,  -4.1581,
         16.7866,   0.7429,  10.3350, -13.2072,   2.3202,  -3.6444, -29.4586,
         15.1039,  13.4258,  14.0936,  11.8342, -14.6517,  16.8556, -17.8857,
        -18.0688,  19.3895,  -3.5593,  -1.0698, -13.6522,  -0.7200],
       grad_fn=<SelectBackward0>)

Logits are very high value => They should be closer to zero

class ModelInit(object):
    def __init__(self, vocab_sz, blck_sz=3, emb_sz=2, hidden_units=100, g=torch.Generator().manual_seed(2147483647), mul_W2=1.0, mul_b2=1.0, mul_W1=1.0, mul_b1=1.0) -> None:
        self.C = torch.randn((vocab_sz,emb_sz), generator=g)
        self.W1 = torch.randn((blck_sz*emb_sz, hidden_units), generator=g)*mul_W1
        self.b1 = torch.randn(hidden_units, generator=g)*mul_b1
        self.W2 = torch.randn((hidden_units, vocab_sz), generator=g) * mul_W2
        self.b2 = torch.randn(vocab_sz, generator=g) * mul_b2
        self.blck_sz = blck_sz
        self.emb_sz = emb_sz
        self.hidden_units = hidden_units
        self.emb = None
        self.h = None
        self.hpreact = None
        self._init_grad()


    def _init_grad(self):
        for p in self.parameters(): p.requires_grad = True

    def __call__(self, X):
        self.emb = self.C[X]
        self.hpreact = self.emb.view(self.emb.shape[0], -1)@self.W1 + self.b1
        self.h = torch.tanh(self.hpreact)
        logits = self.h@self.W2 + self.b2 ## logits are calculated here so W2 and b2 must be close to zero
        return logits
    
    def parameters(self):
        return [self.C, self.W1, self.b1, self.W2, self.b2]

    def num_params(self):
        return sum(p.nelement() for p in self.parameters())
    
    def zero_grad(self):
        for p in self.parameters(): 
            # print(p.shape, p.data, p.grad)
            p.grad = None

vocab_sz = len(i2s); vocab_sz
model_init = ModelInit(vocab_sz, emb_sz=10, hidden_units=200, mul_W2=0.1, mul_b2=0.0)
train(model_init, Xtr, Ytr, lr = 0.1, epochs=1, batch_sz=32, tracker=tracker, verbose=True)
logits = model_init(Xtr);logits[0]

0 tensor(4.3019, grad_fn=<NllLossBackward0>)
0 tensor(4.3019, grad_fn=<NllLossBackward0>)

tensor([ 1.0323,  0.4644, -0.1029,  0.4121, -0.9996, -1.0876, -2.0720,  0.3077,
         1.1270, -0.8996, -0.3860,  1.7267,  0.1542, -0.9568,  0.0400,  0.4074,
        -1.3500,  1.0367,  1.2130, -0.9362, -0.8425, -0.2311, -0.3305, -0.4859,
        -1.1374, -0.5085,  0.0350], grad_fn=<SelectBackward0>)

vocab_sz = len(i2s); vocab_sz
model_init = ModelInit(vocab_sz, emb_sz=10, hidden_units=200, mul_W2=0.01, mul_b2=0.0)
train(model_init, Xtr, Ytr, lr = 0.1, epochs=1, batch_sz=32, tracker=tracker, verbose=True)
logits = model_init(Xtr);logits[0]

0 tensor(3.3281, grad_fn=<NllLossBackward0>)
0 tensor(3.3281, grad_fn=<NllLossBackward0>)

tensor([ 0.0419, -0.1708, -0.0358,  0.1095,  0.0694,  0.7315,  0.0889, -0.0692,
        -0.4671,  0.0263,  0.2888,  0.1993, -0.1479, -0.1943,  0.6545,  0.0877,
        -0.2587, -0.3141,  0.3298, -0.0591, -0.2870,  0.4297, -0.3069, -0.0893,
        -0.4319, -0.1038, -0.1493], grad_fn=<SelectBackward0>)

vocab_sz = len(i2s); vocab_sz
model_init = ModelInit(vocab_sz, emb_sz=10, hidden_units=200, mul_W2=0.0, mul_b2=0.0)
train(model_init, Xtr, Ytr, lr = 0.1, epochs=1, batch_sz=32, tracker=tracker, verbose=True)
logits = model_init(Xtr);logits[0]

0 tensor(3.2958, grad_fn=<NllLossBackward0>)
0 tensor(3.2958, grad_fn=<NllLossBackward0>)

tensor([-0.3130, -0.1491, -0.0689,  0.4233, -0.1206, -0.2052, -0.1206, -0.1206,
         0.4233, -0.0325, -0.1206,  0.4233, -0.1503, -0.1976, -0.4449,  0.0290,
        -0.1206,  0.4233, -0.0132,  1.3050, -0.1206, -0.1206, -0.1206, -0.1206,
        -0.1206, -0.1259, -0.1206], grad_fn=<SelectBackward0>)

We don’t want to be setting weights to be equal to zero. We want to ensure our loss has some entropy which can be used for symmetry breaking (May be for output it could be fine)

tracker = {'lr':[], 'batch_sz':[], 'loss':[], 'block_sz':[], 'emb_sz':[], 'hidden_units':[] }
vocab_sz = len(i2s); vocab_sz
model_init = ModelInit(vocab_sz, emb_sz=10, hidden_units=200, mul_W2=0.01, mul_b2=0.0)
train(model_init, Xtr, Ytr, lr = 0.1, epochs=100000, batch_sz=32, tracker=tracker, verbose=True)
logits = model_init(Xtr);logits[0]

0 tensor(3.3392, grad_fn=<NllLossBackward0>)
100 tensor(2.5719, grad_fn=<NllLossBackward0>)
200 tensor(2.3635, grad_fn=<NllLossBackward0>)
300 tensor(2.1725, grad_fn=<NllLossBackward0>)
400 tensor(2.4429, grad_fn=<NllLossBackward0>)
500 tensor(2.5962, grad_fn=<NllLossBackward0>)
600 tensor(2.5540, grad_fn=<NllLossBackward0>)
700 tensor(2.4494, grad_fn=<NllLossBackward0>)
800 tensor(2.4602, grad_fn=<NllLossBackward0>)
900 tensor(2.4799, grad_fn=<NllLossBackward0>)
1000 tensor(2.3920, grad_fn=<NllLossBackward0>)
1100 tensor(2.4739, grad_fn=<NllLossBackward0>)
1200 tensor(2.5492, grad_fn=<NllLossBackward0>)
1300 tensor(2.0424, grad_fn=<NllLossBackward0>)
1400 tensor(1.9356, grad_fn=<NllLossBackward0>)
1500 tensor(2.5525, grad_fn=<NllLossBackward0>)
1600 tensor(2.7594, grad_fn=<NllLossBackward0>)
1700 tensor(2.7485, grad_fn=<NllLossBackward0>)
1800 tensor(2.4242, grad_fn=<NllLossBackward0>)
1900 tensor(2.4117, grad_fn=<NllLossBackward0>)
2000 tensor(2.2288, grad_fn=<NllLossBackward0>)
2100 tensor(2.5129, grad_fn=<NllLossBackward0>)
2200 tensor(1.9398, grad_fn=<NllLossBackward0>)
2300 tensor(2.3327, grad_fn=<NllLossBackward0>)
2400 tensor(2.8983, grad_fn=<NllLossBackward0>)
2500 tensor(2.3193, grad_fn=<NllLossBackward0>)
2600 tensor(2.5891, grad_fn=<NllLossBackward0>)
2700 tensor(2.3658, grad_fn=<NllLossBackward0>)
2800 tensor(2.3779, grad_fn=<NllLossBackward0>)
2900 tensor(2.1937, grad_fn=<NllLossBackward0>)
3000 tensor(2.1216, grad_fn=<NllLossBackward0>)
3100 tensor(2.3479, grad_fn=<NllLossBackward0>)
3200 tensor(2.2643, grad_fn=<NllLossBackward0>)
3300 tensor(1.9470, grad_fn=<NllLossBackward0>)
3400 tensor(2.1242, grad_fn=<NllLossBackward0>)
3500 tensor(2.0403, grad_fn=<NllLossBackward0>)
3600 tensor(2.1733, grad_fn=<NllLossBackward0>)
3700 tensor(2.5749, grad_fn=<NllLossBackward0>)
3800 tensor(2.4332, grad_fn=<NllLossBackward0>)
3900 tensor(2.0637, grad_fn=<NllLossBackward0>)
4000 tensor(2.3236, grad_fn=<NllLossBackward0>)
4100 tensor(1.8758, grad_fn=<NllLossBackward0>)
4200 tensor(2.3925, grad_fn=<NllLossBackward0>)
4300 tensor(2.2138, grad_fn=<NllLossBackward0>)
4400 tensor(2.5038, grad_fn=<NllLossBackward0>)
4500 tensor(2.2143, grad_fn=<NllLossBackward0>)
4600 tensor(2.3239, grad_fn=<NllLossBackward0>)
4700 tensor(2.4918, grad_fn=<NllLossBackward0>)
4800 tensor(2.4394, grad_fn=<NllLossBackward0>)
4900 tensor(2.2660, grad_fn=<NllLossBackward0>)
5000 tensor(2.3581, grad_fn=<NllLossBackward0>)
5100 tensor(2.2227, grad_fn=<NllLossBackward0>)
5200 tensor(2.3936, grad_fn=<NllLossBackward0>)
5300 tensor(2.2093, grad_fn=<NllLossBackward0>)
5400 tensor(2.3135, grad_fn=<NllLossBackward0>)
5500 tensor(2.2450, grad_fn=<NllLossBackward0>)
5600 tensor(2.1560, grad_fn=<NllLossBackward0>)
5700 tensor(2.4237, grad_fn=<NllLossBackward0>)
5800 tensor(2.2841, grad_fn=<NllLossBackward0>)
5900 tensor(2.6779, grad_fn=<NllLossBackward0>)
6000 tensor(2.4333, grad_fn=<NllLossBackward0>)
6100 tensor(2.2779, grad_fn=<NllLossBackward0>)
6200 tensor(2.2052, grad_fn=<NllLossBackward0>)
6300 tensor(2.2780, grad_fn=<NllLossBackward0>)
6400 tensor(2.2331, grad_fn=<NllLossBackward0>)
6500 tensor(2.2438, grad_fn=<NllLossBackward0>)
6600 tensor(2.6192, grad_fn=<NllLossBackward0>)
6700 tensor(2.1827, grad_fn=<NllLossBackward0>)
6800 tensor(2.6761, grad_fn=<NllLossBackward0>)
6900 tensor(2.1244, grad_fn=<NllLossBackward0>)
7000 tensor(2.0956, grad_fn=<NllLossBackward0>)
7100 tensor(2.0540, grad_fn=<NllLossBackward0>)
7200 tensor(2.2638, grad_fn=<NllLossBackward0>)
7300 tensor(2.6180, grad_fn=<NllLossBackward0>)
7400 tensor(1.9982, grad_fn=<NllLossBackward0>)
7500 tensor(2.2053, grad_fn=<NllLossBackward0>)
7600 tensor(1.9182, grad_fn=<NllLossBackward0>)
7700 tensor(2.1410, grad_fn=<NllLossBackward0>)
7800 tensor(2.2030, grad_fn=<NllLossBackward0>)
7900 tensor(2.0046, grad_fn=<NllLossBackward0>)
8000 tensor(2.1555, grad_fn=<NllLossBackward0>)
8100 tensor(2.3874, grad_fn=<NllLossBackward0>)
8200 tensor(2.1539, grad_fn=<NllLossBackward0>)
8300 tensor(2.2835, grad_fn=<NllLossBackward0>)
8400 tensor(2.2281, grad_fn=<NllLossBackward0>)
8500 tensor(2.1199, grad_fn=<NllLossBackward0>)
8600 tensor(2.6832, grad_fn=<NllLossBackward0>)
8700 tensor(1.8948, grad_fn=<NllLossBackward0>)
8800 tensor(2.4768, grad_fn=<NllLossBackward0>)
8900 tensor(2.0640, grad_fn=<NllLossBackward0>)
9000 tensor(2.4954, grad_fn=<NllLossBackward0>)
9100 tensor(2.2835, grad_fn=<NllLossBackward0>)
9200 tensor(1.7948, grad_fn=<NllLossBackward0>)
9300 tensor(2.3181, grad_fn=<NllLossBackward0>)
9400 tensor(2.5303, grad_fn=<NllLossBackward0>)
9500 tensor(2.2306, grad_fn=<NllLossBackward0>)
9600 tensor(2.1589, grad_fn=<NllLossBackward0>)
9700 tensor(1.7772, grad_fn=<NllLossBackward0>)
9800 tensor(1.6249, grad_fn=<NllLossBackward0>)
9900 tensor(2.4129, grad_fn=<NllLossBackward0>)
10000 tensor(2.4292, grad_fn=<NllLossBackward0>)
10100 tensor(2.5065, grad_fn=<NllLossBackward0>)
10200 tensor(1.8286, grad_fn=<NllLossBackward0>)
10300 tensor(2.1329, grad_fn=<NllLossBackward0>)
10400 tensor(2.2423, grad_fn=<NllLossBackward0>)
10500 tensor(1.7996, grad_fn=<NllLossBackward0>)
10600 tensor(2.0805, grad_fn=<NllLossBackward0>)
10700 tensor(2.2521, grad_fn=<NllLossBackward0>)
10800 tensor(2.4060, grad_fn=<NllLossBackward0>)
10900 tensor(2.0360, grad_fn=<NllLossBackward0>)
11000 tensor(2.0421, grad_fn=<NllLossBackward0>)
11100 tensor(2.2374, grad_fn=<NllLossBackward0>)
11200 tensor(1.8421, grad_fn=<NllLossBackward0>)
11300 tensor(1.9651, grad_fn=<NllLossBackward0>)
11400 tensor(2.4355, grad_fn=<NllLossBackward0>)
11500 tensor(2.3202, grad_fn=<NllLossBackward0>)
11600 tensor(2.3250, grad_fn=<NllLossBackward0>)
11700 tensor(2.5688, grad_fn=<NllLossBackward0>)
11800 tensor(2.1068, grad_fn=<NllLossBackward0>)
11900 tensor(1.8761, grad_fn=<NllLossBackward0>)
12000 tensor(2.3926, grad_fn=<NllLossBackward0>)
12100 tensor(2.0755, grad_fn=<NllLossBackward0>)
12200 tensor(1.8327, grad_fn=<NllLossBackward0>)
12300 tensor(2.4248, grad_fn=<NllLossBackward0>)
12400 tensor(2.0713, grad_fn=<NllLossBackward0>)
12500 tensor(2.3076, grad_fn=<NllLossBackward0>)
12600 tensor(2.1807, grad_fn=<NllLossBackward0>)
12700 tensor(1.8958, grad_fn=<NllLossBackward0>)
12800 tensor(2.7295, grad_fn=<NllLossBackward0>)
12900 tensor(2.0402, grad_fn=<NllLossBackward0>)
13000 tensor(2.1136, grad_fn=<NllLossBackward0>)
13100 tensor(2.2924, grad_fn=<NllLossBackward0>)
13200 tensor(2.1961, grad_fn=<NllLossBackward0>)
13300 tensor(2.2069, grad_fn=<NllLossBackward0>)
13400 tensor(1.6098, grad_fn=<NllLossBackward0>)
13500 tensor(2.5662, grad_fn=<NllLossBackward0>)
13600 tensor(2.0709, grad_fn=<NllLossBackward0>)
13700 tensor(2.0570, grad_fn=<NllLossBackward0>)
13800 tensor(2.8467, grad_fn=<NllLossBackward0>)
13900 tensor(2.1467, grad_fn=<NllLossBackward0>)
14000 tensor(2.2408, grad_fn=<NllLossBackward0>)
14100 tensor(2.0880, grad_fn=<NllLossBackward0>)
14200 tensor(2.1278, grad_fn=<NllLossBackward0>)
14300 tensor(1.9405, grad_fn=<NllLossBackward0>)
14400 tensor(2.2355, grad_fn=<NllLossBackward0>)
14500 tensor(2.3983, grad_fn=<NllLossBackward0>)
14600 tensor(2.5697, grad_fn=<NllLossBackward0>)
14700 tensor(2.3201, grad_fn=<NllLossBackward0>)
14800 tensor(1.9976, grad_fn=<NllLossBackward0>)
14900 tensor(2.0194, grad_fn=<NllLossBackward0>)
15000 tensor(2.2697, grad_fn=<NllLossBackward0>)
15100 tensor(2.0597, grad_fn=<NllLossBackward0>)
15200 tensor(2.3851, grad_fn=<NllLossBackward0>)
15300 tensor(2.1410, grad_fn=<NllLossBackward0>)
15400 tensor(2.1777, grad_fn=<NllLossBackward0>)
15500 tensor(2.3825, grad_fn=<NllLossBackward0>)
15600 tensor(1.9468, grad_fn=<NllLossBackward0>)
15700 tensor(2.3871, grad_fn=<NllLossBackward0>)
15800 tensor(1.9997, grad_fn=<NllLossBackward0>)
15900 tensor(2.0276, grad_fn=<NllLossBackward0>)
16000 tensor(2.6456, grad_fn=<NllLossBackward0>)
16100 tensor(2.0861, grad_fn=<NllLossBackward0>)
16200 tensor(2.3325, grad_fn=<NllLossBackward0>)
16300 tensor(1.9785, grad_fn=<NllLossBackward0>)
16400 tensor(2.7049, grad_fn=<NllLossBackward0>)
16500 tensor(2.0964, grad_fn=<NllLossBackward0>)
16600 tensor(2.2964, grad_fn=<NllLossBackward0>)
16700 tensor(2.1351, grad_fn=<NllLossBackward0>)
16800 tensor(2.1836, grad_fn=<NllLossBackward0>)
16900 tensor(1.6118, grad_fn=<NllLossBackward0>)
17000 tensor(2.6817, grad_fn=<NllLossBackward0>)
17100 tensor(2.3233, grad_fn=<NllLossBackward0>)
17200 tensor(2.1082, grad_fn=<NllLossBackward0>)
17300 tensor(2.1330, grad_fn=<NllLossBackward0>)
17400 tensor(2.5566, grad_fn=<NllLossBackward0>)
17500 tensor(2.4864, grad_fn=<NllLossBackward0>)
17600 tensor(2.2627, grad_fn=<NllLossBackward0>)
17700 tensor(1.5921, grad_fn=<NllLossBackward0>)
17800 tensor(1.8259, grad_fn=<NllLossBackward0>)
17900 tensor(2.5666, grad_fn=<NllLossBackward0>)
18000 tensor(2.1448, grad_fn=<NllLossBackward0>)
18100 tensor(2.5980, grad_fn=<NllLossBackward0>)
18200 tensor(2.2424, grad_fn=<NllLossBackward0>)
18300 tensor(2.1809, grad_fn=<NllLossBackward0>)
18400 tensor(2.3054, grad_fn=<NllLossBackward0>)
18500 tensor(2.0541, grad_fn=<NllLossBackward0>)
18600 tensor(2.3629, grad_fn=<NllLossBackward0>)
18700 tensor(1.9529, grad_fn=<NllLossBackward0>)
18800 tensor(2.8488, grad_fn=<NllLossBackward0>)
18900 tensor(1.9921, grad_fn=<NllLossBackward0>)
19000 tensor(2.6042, grad_fn=<NllLossBackward0>)
19100 tensor(2.7085, grad_fn=<NllLossBackward0>)
19200 tensor(2.0013, grad_fn=<NllLossBackward0>)
19300 tensor(1.9792, grad_fn=<NllLossBackward0>)
19400 tensor(2.1911, grad_fn=<NllLossBackward0>)
19500 tensor(2.1363, grad_fn=<NllLossBackward0>)
19600 tensor(1.8770, grad_fn=<NllLossBackward0>)
19700 tensor(1.8264, grad_fn=<NllLossBackward0>)
19800 tensor(2.0773, grad_fn=<NllLossBackward0>)
19900 tensor(2.3034, grad_fn=<NllLossBackward0>)
20000 tensor(2.2581, grad_fn=<NllLossBackward0>)
20100 tensor(2.2427, grad_fn=<NllLossBackward0>)
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91000 tensor(2.0378, grad_fn=<NllLossBackward0>)
91100 tensor(2.4567, grad_fn=<NllLossBackward0>)
91200 tensor(2.7205, grad_fn=<NllLossBackward0>)
91300 tensor(2.3376, grad_fn=<NllLossBackward0>)
91400 tensor(1.8419, grad_fn=<NllLossBackward0>)
91500 tensor(2.1995, grad_fn=<NllLossBackward0>)
91600 tensor(2.2812, grad_fn=<NllLossBackward0>)
91700 tensor(2.1569, grad_fn=<NllLossBackward0>)
91800 tensor(2.0318, grad_fn=<NllLossBackward0>)
91900 tensor(2.4206, grad_fn=<NllLossBackward0>)
92000 tensor(1.5856, grad_fn=<NllLossBackward0>)
92100 tensor(2.1782, grad_fn=<NllLossBackward0>)
92200 tensor(2.2818, grad_fn=<NllLossBackward0>)
92300 tensor(2.6201, grad_fn=<NllLossBackward0>)
92400 tensor(2.4641, grad_fn=<NllLossBackward0>)
92500 tensor(2.0781, grad_fn=<NllLossBackward0>)
92600 tensor(2.5108, grad_fn=<NllLossBackward0>)
92700 tensor(1.9539, grad_fn=<NllLossBackward0>)
92800 tensor(2.0299, grad_fn=<NllLossBackward0>)
92900 tensor(2.2352, grad_fn=<NllLossBackward0>)
93000 tensor(2.5643, grad_fn=<NllLossBackward0>)
93100 tensor(2.3359, grad_fn=<NllLossBackward0>)
93200 tensor(1.8524, grad_fn=<NllLossBackward0>)
93300 tensor(2.3912, grad_fn=<NllLossBackward0>)
93400 tensor(2.0609, grad_fn=<NllLossBackward0>)
93500 tensor(1.9542, grad_fn=<NllLossBackward0>)
93600 tensor(2.4354, grad_fn=<NllLossBackward0>)
93700 tensor(2.0144, grad_fn=<NllLossBackward0>)
93800 tensor(2.1974, grad_fn=<NllLossBackward0>)
93900 tensor(1.8923, grad_fn=<NllLossBackward0>)
94000 tensor(2.0038, grad_fn=<NllLossBackward0>)
94100 tensor(2.1496, grad_fn=<NllLossBackward0>)
94200 tensor(1.9185, grad_fn=<NllLossBackward0>)
94300 tensor(1.8482, grad_fn=<NllLossBackward0>)
94400 tensor(2.0537, grad_fn=<NllLossBackward0>)
94500 tensor(1.8682, grad_fn=<NllLossBackward0>)
94600 tensor(2.2363, grad_fn=<NllLossBackward0>)
94700 tensor(2.2971, grad_fn=<NllLossBackward0>)
94800 tensor(1.7891, grad_fn=<NllLossBackward0>)
94900 tensor(2.1213, grad_fn=<NllLossBackward0>)
95000 tensor(2.3525, grad_fn=<NllLossBackward0>)
95100 tensor(2.0023, grad_fn=<NllLossBackward0>)
95200 tensor(2.3427, grad_fn=<NllLossBackward0>)
95300 tensor(2.1539, grad_fn=<NllLossBackward0>)
95400 tensor(2.1952, grad_fn=<NllLossBackward0>)
95500 tensor(2.1336, grad_fn=<NllLossBackward0>)
95600 tensor(1.8892, grad_fn=<NllLossBackward0>)
95700 tensor(2.3625, grad_fn=<NllLossBackward0>)
95800 tensor(2.2875, grad_fn=<NllLossBackward0>)
95900 tensor(1.6639, grad_fn=<NllLossBackward0>)
96000 tensor(2.1059, grad_fn=<NllLossBackward0>)
96100 tensor(1.9674, grad_fn=<NllLossBackward0>)
96200 tensor(1.8364, grad_fn=<NllLossBackward0>)
96300 tensor(1.7891, grad_fn=<NllLossBackward0>)
96400 tensor(2.0697, grad_fn=<NllLossBackward0>)
96500 tensor(2.1965, grad_fn=<NllLossBackward0>)
96600 tensor(2.4863, grad_fn=<NllLossBackward0>)
96700 tensor(1.8435, grad_fn=<NllLossBackward0>)
96800 tensor(1.8466, grad_fn=<NllLossBackward0>)
96900 tensor(2.2148, grad_fn=<NllLossBackward0>)
97000 tensor(2.0440, grad_fn=<NllLossBackward0>)
97100 tensor(2.7933, grad_fn=<NllLossBackward0>)
97200 tensor(2.3338, grad_fn=<NllLossBackward0>)
97300 tensor(2.1479, grad_fn=<NllLossBackward0>)
97400 tensor(1.9432, grad_fn=<NllLossBackward0>)
97500 tensor(1.4926, grad_fn=<NllLossBackward0>)
97600 tensor(2.4865, grad_fn=<NllLossBackward0>)
97700 tensor(2.2305, grad_fn=<NllLossBackward0>)
97800 tensor(1.7571, grad_fn=<NllLossBackward0>)
97900 tensor(2.4103, grad_fn=<NllLossBackward0>)
98000 tensor(2.4508, grad_fn=<NllLossBackward0>)
98100 tensor(2.4308, grad_fn=<NllLossBackward0>)
98200 tensor(1.9161, grad_fn=<NllLossBackward0>)
98300 tensor(1.9564, grad_fn=<NllLossBackward0>)
98400 tensor(2.2733, grad_fn=<NllLossBackward0>)
98500 tensor(2.4241, grad_fn=<NllLossBackward0>)
98600 tensor(2.2743, grad_fn=<NllLossBackward0>)
98700 tensor(2.4230, grad_fn=<NllLossBackward0>)
98800 tensor(2.0299, grad_fn=<NllLossBackward0>)
98900 tensor(2.4573, grad_fn=<NllLossBackward0>)
99000 tensor(2.0287, grad_fn=<NllLossBackward0>)
99100 tensor(2.0910, grad_fn=<NllLossBackward0>)
99200 tensor(2.5758, grad_fn=<NllLossBackward0>)
99300 tensor(2.0344, grad_fn=<NllLossBackward0>)
99400 tensor(1.8703, grad_fn=<NllLossBackward0>)
99500 tensor(2.2634, grad_fn=<NllLossBackward0>)
99600 tensor(2.3414, grad_fn=<NllLossBackward0>)
99700 tensor(2.1698, grad_fn=<NllLossBackward0>)
99800 tensor(2.1386, grad_fn=<NllLossBackward0>)
99900 tensor(2.0918, grad_fn=<NllLossBackward0>)
99999 tensor(2.1045, grad_fn=<NllLossBackward0>)

tensor([-3.8623,  1.5053, -0.1822,  0.4767,  0.4117,  1.5927, -0.2226,  0.7383,
        -0.5590, -0.5663,  1.2633,  1.2010,  1.5149,  1.6253,  0.3927, -0.3492,
         0.0226, -2.3850,  0.6161,  2.3872,  0.4261, -2.4462, -0.8572,  0.4106,
        -2.0006, -0.8019, -0.5386], grad_fn=<SelectBackward0>)

split_loss('train', model_init)
split_loss('val', model_init)

train 2.145718574523926
val 2.49676775932312

plt.plot(tracker['loss'])

Loss doesn’t have the hockey stick behaviour anymore. We took away the unnecessary easy part of the loss function, where weights were just being shrunk down

Activation Issues (Manually Fixing saturated tanh)

tracker = {'lr':[], 'batch_sz':[], 'loss':[], 'block_sz':[], 'emb_sz':[], 'hidden_units':[] }
vocab_sz = len(i2s); vocab_sz
model_init = ModelInit(vocab_sz, emb_sz=10, hidden_units=200, mul_W2=0.01, mul_b2=0.0)
train(model_init, Xtr, Ytr, lr = 0.1, epochs=1, batch_sz=32, tracker=tracker, verbose=True)
# logits = model_init(Xtr);logits[0] # Can't run this line if only want to see impact on single minibatch. What should be improved design?

0 tensor(3.3293, grad_fn=<NllLossBackward0>)
0 tensor(3.3293, grad_fn=<NllLossBackward0>)

<__main__.ModelInit at 0x2f4896e20>

# plt.hist(model_init.h.data.detach().numpy())
model_init.h.shape

torch.Size([32, 200])

plt.imshow(model_init.h.data.abs() >=0.95, cmap='gray', interpolation='nearest')

plt.hist(model_init.h.view(-1).data, 50);

plt.hist(model_init.hpreact.view(-1).data, 50);

Tanh has lot of values at -1 and 1 because hpreact takes a distribution which is very very broad, taking -15 to 15. Tanh being the squashing function have losts of values around -1 and 1 for those extreme values. Why is this a problem?

• During back propogation gradients are flowing backwards. What happens in backward pass for tanh ?

  Based on equation 1-t^2 - gradient becomes zero. ( Intuitively, when we are in the tail of tanh changing values of t won’t change tanh a lot. So gradients are zero) => Weights and biases on / around the neuron do n’t impact the loss. Neuron stops learning . Gradient flow shuts off. Gradient vanishes

  Similarily if t=0 , gradient just passes through

  Amount of squishing of gradient due to tanh depends on how far u are from the flat tail

plt.imshow(model_init.h.data.abs() >=0.99, cmap='gray', interpolation='nearest') # All whites are true

• In all white cases backward gradient gets destroyed

• If for anyone of the 200 neurons (x-axis) the entire column is white than we have a dead neuron - we will be in lot of trouble . It means no single example ever activates this neuron in active part of tanh

• Here for all the neurons, we still have some examples which activates individual neuron in active part of tanh. Some gradient will flow through and neurons will learn

• Lot of other non-linearities / activation functions show similar behaviour ( squeezing/ squashinh neuron once below -sigmoid, tanh, relu, may be elu as well as it has flat parts)

• This problem can happen at

  • Initialization

  • Optimization - If you have too higher a learning rate, some of the neuron have too much gradient and they get knocked out of data manifold. From then on no example ever activates this neuron

    “It’s like a permanent brain damage in the mind of a network”

Solution to this problem is to have hpreact ( formed from embeddings, W1 and b1 ) closer to zero

tracker = {'lr':[], 'batch_sz':[], 'loss':[], 'block_sz':[], 'emb_sz':[], 'hidden_units':[] }
vocab_sz = len(i2s); vocab_sz
model_init = ModelInit(vocab_sz, emb_sz=10, hidden_units=200, mul_W2=0.01, mul_b2=0.0, mul_W1=0.1, mul_b1=0.01)
train(model_init, Xtr, Ytr, lr = 0.1, epochs=1, batch_sz=32, tracker=tracker, verbose=True)

0 tensor(3.3097, grad_fn=<NllLossBackward0>)
0 tensor(3.3097, grad_fn=<NllLossBackward0>)

<__main__.ModelInit at 0x41ce65820>

plt.hist(model_init.hpreact.view(-1).data, 50);

plt.hist(model_init.h.view(-1).data, 50);

plt.imshow(model_init.h.data.abs() >=0.99, cmap='gray', interpolation='nearest') # All whites are true

As we expected little to no white

tracker = {'lr':[], 'batch_sz':[], 'loss':[], 'block_sz':[], 'emb_sz':[], 'hidden_units':[] }
vocab_sz = len(i2s); vocab_sz
model_init = ModelInit(vocab_sz, emb_sz=10, hidden_units=200, mul_W2=0.01, mul_b2=0.0, mul_W1=0.2, mul_b1=0.01)
train(model_init, Xtr, Ytr, lr = 0.1, epochs=1, batch_sz=32, tracker=tracker, verbose=True)

0 tensor(3.2982, grad_fn=<NllLossBackward0>)
0 tensor(3.2982, grad_fn=<NllLossBackward0>)

<__main__.ModelInit at 0x2f483c7f0>

plt.hist(model_init.hpreact.view(-1).data, 50);

plt.hist(model_init.h.view(-1).data, 50);

plt.imshow(model_init.h.data.abs() >=0.99, cmap='gray', interpolation='nearest') # All whites are true

This is nice enough. May be our multiplying constant should be around this

tracker = {'lr':[], 'batch_sz':[], 'loss':[], 'block_sz':[], 'emb_sz':[], 'hidden_units':[] }
vocab_sz = len(i2s); vocab_sz
model_init = ModelInit(vocab_sz, emb_sz=10, hidden_units=200, mul_W2=0.01, mul_b2=0.0, mul_W1=0.2, mul_b1=0.01)
train(model_init, Xtr, Ytr, lr = 0.1, epochs=200000, batch_sz=32, tracker=tracker, verbose=True)

0 tensor(3.2803, grad_fn=<NllLossBackward0>)
100 tensor(2.7941, grad_fn=<NllLossBackward0>)
200 tensor(2.6765, grad_fn=<NllLossBackward0>)
300 tensor(2.6213, grad_fn=<NllLossBackward0>)
400 tensor(2.3688, grad_fn=<NllLossBackward0>)
500 tensor(2.6147, grad_fn=<NllLossBackward0>)
600 tensor(2.0819, grad_fn=<NllLossBackward0>)
700 tensor(2.2611, grad_fn=<NllLossBackward0>)
800 tensor(2.4223, grad_fn=<NllLossBackward0>)
900 tensor(2.2402, grad_fn=<NllLossBackward0>)
1000 tensor(2.4718, grad_fn=<NllLossBackward0>)
1100 tensor(2.1366, grad_fn=<NllLossBackward0>)
1200 tensor(2.2823, grad_fn=<NllLossBackward0>)
1300 tensor(2.0967, grad_fn=<NllLossBackward0>)
1400 tensor(2.9293, grad_fn=<NllLossBackward0>)
1500 tensor(2.4066, grad_fn=<NllLossBackward0>)
1600 tensor(2.3438, grad_fn=<NllLossBackward0>)
1700 tensor(2.2003, grad_fn=<NllLossBackward0>)
1800 tensor(2.5877, grad_fn=<NllLossBackward0>)
1900 tensor(2.1141, grad_fn=<NllLossBackward0>)
2000 tensor(2.6357, grad_fn=<NllLossBackward0>)
2100 tensor(2.2092, grad_fn=<NllLossBackward0>)
2200 tensor(2.6538, grad_fn=<NllLossBackward0>)
2300 tensor(2.1671, grad_fn=<NllLossBackward0>)
2400 tensor(2.3611, grad_fn=<NllLossBackward0>)
2500 tensor(2.2665, grad_fn=<NllLossBackward0>)
2600 tensor(1.8435, grad_fn=<NllLossBackward0>)
2700 tensor(2.4587, grad_fn=<NllLossBackward0>)
2800 tensor(2.6229, grad_fn=<NllLossBackward0>)
2900 tensor(2.0546, grad_fn=<NllLossBackward0>)
3000 tensor(2.6319, grad_fn=<NllLossBackward0>)
3100 tensor(1.9751, grad_fn=<NllLossBackward0>)
3200 tensor(2.7360, grad_fn=<NllLossBackward0>)
3300 tensor(2.4259, grad_fn=<NllLossBackward0>)
3400 tensor(2.4851, grad_fn=<NllLossBackward0>)
3500 tensor(2.1138, grad_fn=<NllLossBackward0>)
3600 tensor(2.0695, grad_fn=<NllLossBackward0>)
3700 tensor(2.4176, grad_fn=<NllLossBackward0>)
3800 tensor(2.3413, grad_fn=<NllLossBackward0>)
3900 tensor(2.2575, grad_fn=<NllLossBackward0>)
4000 tensor(2.2378, grad_fn=<NllLossBackward0>)
4100 tensor(1.7880, grad_fn=<NllLossBackward0>)
4200 tensor(2.1536, grad_fn=<NllLossBackward0>)
4300 tensor(2.3044, grad_fn=<NllLossBackward0>)
4400 tensor(2.2202, grad_fn=<NllLossBackward0>)
4500 tensor(1.7085, grad_fn=<NllLossBackward0>)
4600 tensor(2.0200, grad_fn=<NllLossBackward0>)
4700 tensor(2.4845, grad_fn=<NllLossBackward0>)
4800 tensor(2.4862, grad_fn=<NllLossBackward0>)
4900 tensor(2.1216, grad_fn=<NllLossBackward0>)
5000 tensor(2.2712, grad_fn=<NllLossBackward0>)
5100 tensor(2.6266, grad_fn=<NllLossBackward0>)
5200 tensor(1.7879, grad_fn=<NllLossBackward0>)
5300 tensor(1.9230, grad_fn=<NllLossBackward0>)
5400 tensor(2.3293, grad_fn=<NllLossBackward0>)
5500 tensor(2.3293, grad_fn=<NllLossBackward0>)
5600 tensor(2.3695, grad_fn=<NllLossBackward0>)
5700 tensor(2.6635, grad_fn=<NllLossBackward0>)
5800 tensor(2.2351, grad_fn=<NllLossBackward0>)
5900 tensor(2.6890, grad_fn=<NllLossBackward0>)
6000 tensor(2.4018, grad_fn=<NllLossBackward0>)
6100 tensor(2.2363, grad_fn=<NllLossBackward0>)
6200 tensor(2.1809, grad_fn=<NllLossBackward0>)
6300 tensor(2.3698, grad_fn=<NllLossBackward0>)
6400 tensor(2.2732, grad_fn=<NllLossBackward0>)
6500 tensor(2.4666, grad_fn=<NllLossBackward0>)
6600 tensor(2.2249, grad_fn=<NllLossBackward0>)
6700 tensor(2.0666, grad_fn=<NllLossBackward0>)
6800 tensor(2.4735, grad_fn=<NllLossBackward0>)
6900 tensor(2.1548, grad_fn=<NllLossBackward0>)
7000 tensor(2.0232, grad_fn=<NllLossBackward0>)
7100 tensor(1.9084, grad_fn=<NllLossBackward0>)
7200 tensor(1.8595, grad_fn=<NllLossBackward0>)
7300 tensor(1.9834, grad_fn=<NllLossBackward0>)
7400 tensor(2.2591, grad_fn=<NllLossBackward0>)
7500 tensor(2.1362, grad_fn=<NllLossBackward0>)
7600 tensor(2.4154, grad_fn=<NllLossBackward0>)
7700 tensor(2.4733, grad_fn=<NllLossBackward0>)
7800 tensor(2.3087, grad_fn=<NllLossBackward0>)
7900 tensor(2.5345, grad_fn=<NllLossBackward0>)
8000 tensor(1.9391, grad_fn=<NllLossBackward0>)
8100 tensor(2.4298, grad_fn=<NllLossBackward0>)
8200 tensor(2.2577, grad_fn=<NllLossBackward0>)
8300 tensor(2.0041, grad_fn=<NllLossBackward0>)
8400 tensor(2.0446, grad_fn=<NllLossBackward0>)
8500 tensor(1.9885, grad_fn=<NllLossBackward0>)
8600 tensor(2.4969, grad_fn=<NllLossBackward0>)
8700 tensor(2.0724, grad_fn=<NllLossBackward0>)
8800 tensor(2.2655, grad_fn=<NllLossBackward0>)
8900 tensor(2.4193, grad_fn=<NllLossBackward0>)
9000 tensor(2.6621, grad_fn=<NllLossBackward0>)
9100 tensor(2.2878, grad_fn=<NllLossBackward0>)
9200 tensor(2.0962, grad_fn=<NllLossBackward0>)
9300 tensor(1.9752, grad_fn=<NllLossBackward0>)
9400 tensor(1.9483, grad_fn=<NllLossBackward0>)
9500 tensor(2.1111, grad_fn=<NllLossBackward0>)
9600 tensor(2.2073, grad_fn=<NllLossBackward0>)
9700 tensor(2.5375, grad_fn=<NllLossBackward0>)
9800 tensor(2.2454, grad_fn=<NllLossBackward0>)
9900 tensor(1.9175, grad_fn=<NllLossBackward0>)
10000 tensor(2.0750, grad_fn=<NllLossBackward0>)
10100 tensor(2.8791, grad_fn=<NllLossBackward0>)
10200 tensor(2.2528, grad_fn=<NllLossBackward0>)
10300 tensor(2.8798, grad_fn=<NllLossBackward0>)
10400 tensor(1.8976, grad_fn=<NllLossBackward0>)
10500 tensor(2.5134, grad_fn=<NllLossBackward0>)
10600 tensor(2.1347, grad_fn=<NllLossBackward0>)
10700 tensor(2.1273, grad_fn=<NllLossBackward0>)
10800 tensor(2.1905, grad_fn=<NllLossBackward0>)
10900 tensor(2.3644, grad_fn=<NllLossBackward0>)
11000 tensor(2.0511, grad_fn=<NllLossBackward0>)
11100 tensor(2.0473, grad_fn=<NllLossBackward0>)
11200 tensor(2.4269, grad_fn=<NllLossBackward0>)
11300 tensor(2.2948, grad_fn=<NllLossBackward0>)
11400 tensor(2.0932, grad_fn=<NllLossBackward0>)
11500 tensor(2.4583, grad_fn=<NllLossBackward0>)
11600 tensor(1.9513, grad_fn=<NllLossBackward0>)
11700 tensor(2.1994, grad_fn=<NllLossBackward0>)
11800 tensor(2.0017, grad_fn=<NllLossBackward0>)
11900 tensor(1.8935, grad_fn=<NllLossBackward0>)
12000 tensor(2.1267, grad_fn=<NllLossBackward0>)
12100 tensor(2.1863, grad_fn=<NllLossBackward0>)
12200 tensor(2.3730, grad_fn=<NllLossBackward0>)
12300 tensor(2.3468, grad_fn=<NllLossBackward0>)
12400 tensor(2.5496, grad_fn=<NllLossBackward0>)
12500 tensor(2.2037, grad_fn=<NllLossBackward0>)
12600 tensor(2.4290, grad_fn=<NllLossBackward0>)
12700 tensor(2.3112, grad_fn=<NllLossBackward0>)
12800 tensor(2.1721, grad_fn=<NllLossBackward0>)
12900 tensor(1.9410, grad_fn=<NllLossBackward0>)
13000 tensor(1.9993, grad_fn=<NllLossBackward0>)
13100 tensor(2.2865, grad_fn=<NllLossBackward0>)
13200 tensor(2.2167, grad_fn=<NllLossBackward0>)
13300 tensor(2.0493, grad_fn=<NllLossBackward0>)
13400 tensor(2.5603, grad_fn=<NllLossBackward0>)
13500 tensor(2.3624, grad_fn=<NllLossBackward0>)
13600 tensor(1.8678, grad_fn=<NllLossBackward0>)
13700 tensor(2.2196, grad_fn=<NllLossBackward0>)
13800 tensor(2.1038, grad_fn=<NllLossBackward0>)
13900 tensor(2.2645, grad_fn=<NllLossBackward0>)
14000 tensor(2.3547, grad_fn=<NllLossBackward0>)
14100 tensor(2.3206, grad_fn=<NllLossBackward0>)
14200 tensor(2.1660, grad_fn=<NllLossBackward0>)
14300 tensor(2.4161, grad_fn=<NllLossBackward0>)
14400 tensor(2.3662, grad_fn=<NllLossBackward0>)
14500 tensor(2.4619, grad_fn=<NllLossBackward0>)
14600 tensor(2.5559, grad_fn=<NllLossBackward0>)
14700 tensor(2.0974, grad_fn=<NllLossBackward0>)
14800 tensor(2.0122, grad_fn=<NllLossBackward0>)
14900 tensor(2.3922, grad_fn=<NllLossBackward0>)
15000 tensor(2.1694, grad_fn=<NllLossBackward0>)
15100 tensor(2.5740, grad_fn=<NllLossBackward0>)
15200 tensor(2.2482, grad_fn=<NllLossBackward0>)
15300 tensor(2.5417, grad_fn=<NllLossBackward0>)
15400 tensor(1.8742, grad_fn=<NllLossBackward0>)
15500 tensor(2.0387, grad_fn=<NllLossBackward0>)
15600 tensor(2.3556, grad_fn=<NllLossBackward0>)
15700 tensor(1.9310, grad_fn=<NllLossBackward0>)
15800 tensor(1.6042, grad_fn=<NllLossBackward0>)
15900 tensor(1.7335, grad_fn=<NllLossBackward0>)
16000 tensor(1.8339, grad_fn=<NllLossBackward0>)
16100 tensor(1.8170, grad_fn=<NllLossBackward0>)
16200 tensor(2.4062, grad_fn=<NllLossBackward0>)
16300 tensor(2.0214, grad_fn=<NllLossBackward0>)
16400 tensor(2.7507, grad_fn=<NllLossBackward0>)
16500 tensor(2.0841, grad_fn=<NllLossBackward0>)
16600 tensor(2.4012, grad_fn=<NllLossBackward0>)
16700 tensor(1.7762, grad_fn=<NllLossBackward0>)
16800 tensor(2.1446, grad_fn=<NllLossBackward0>)
16900 tensor(1.8770, grad_fn=<NllLossBackward0>)
17000 tensor(1.9831, grad_fn=<NllLossBackward0>)
17100 tensor(1.9943, grad_fn=<NllLossBackward0>)
17200 tensor(2.7800, grad_fn=<NllLossBackward0>)
17300 tensor(2.3091, grad_fn=<NllLossBackward0>)
17400 tensor(2.3990, grad_fn=<NllLossBackward0>)
17500 tensor(2.3377, grad_fn=<NllLossBackward0>)
17600 tensor(2.5766, grad_fn=<NllLossBackward0>)
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192000 tensor(1.7995, grad_fn=<NllLossBackward0>)
192100 tensor(1.8632, grad_fn=<NllLossBackward0>)
192200 tensor(2.1292, grad_fn=<NllLossBackward0>)
192300 tensor(1.9980, grad_fn=<NllLossBackward0>)
192400 tensor(2.4592, grad_fn=<NllLossBackward0>)
192500 tensor(2.3510, grad_fn=<NllLossBackward0>)
192600 tensor(2.2513, grad_fn=<NllLossBackward0>)
192700 tensor(1.9408, grad_fn=<NllLossBackward0>)
192800 tensor(2.0614, grad_fn=<NllLossBackward0>)
192900 tensor(2.1839, grad_fn=<NllLossBackward0>)
193000 tensor(2.4212, grad_fn=<NllLossBackward0>)
193100 tensor(1.9578, grad_fn=<NllLossBackward0>)
193200 tensor(2.3360, grad_fn=<NllLossBackward0>)
193300 tensor(2.4595, grad_fn=<NllLossBackward0>)
193400 tensor(1.8345, grad_fn=<NllLossBackward0>)
193500 tensor(1.9543, grad_fn=<NllLossBackward0>)
193600 tensor(2.1325, grad_fn=<NllLossBackward0>)
193700 tensor(2.3671, grad_fn=<NllLossBackward0>)
193800 tensor(1.8793, grad_fn=<NllLossBackward0>)
193900 tensor(2.1356, grad_fn=<NllLossBackward0>)
194000 tensor(2.0225, grad_fn=<NllLossBackward0>)
194100 tensor(2.0650, grad_fn=<NllLossBackward0>)
194200 tensor(2.0489, grad_fn=<NllLossBackward0>)
194300 tensor(2.1561, grad_fn=<NllLossBackward0>)
194400 tensor(1.9336, grad_fn=<NllLossBackward0>)
194500 tensor(2.2744, grad_fn=<NllLossBackward0>)
194600 tensor(2.1188, grad_fn=<NllLossBackward0>)
194700 tensor(2.0763, grad_fn=<NllLossBackward0>)
194800 tensor(2.4101, grad_fn=<NllLossBackward0>)
194900 tensor(2.2376, grad_fn=<NllLossBackward0>)
195000 tensor(1.9890, grad_fn=<NllLossBackward0>)
195100 tensor(2.1530, grad_fn=<NllLossBackward0>)
195200 tensor(2.1226, grad_fn=<NllLossBackward0>)
195300 tensor(2.0613, grad_fn=<NllLossBackward0>)
195400 tensor(1.8856, grad_fn=<NllLossBackward0>)
195500 tensor(1.8850, grad_fn=<NllLossBackward0>)
195600 tensor(1.9870, grad_fn=<NllLossBackward0>)
195700 tensor(2.3417, grad_fn=<NllLossBackward0>)
195800 tensor(2.1722, grad_fn=<NllLossBackward0>)
195900 tensor(2.1462, grad_fn=<NllLossBackward0>)
196000 tensor(2.0872, grad_fn=<NllLossBackward0>)
196100 tensor(2.2657, grad_fn=<NllLossBackward0>)
196200 tensor(2.3170, grad_fn=<NllLossBackward0>)
196300 tensor(2.0901, grad_fn=<NllLossBackward0>)
196400 tensor(1.9142, grad_fn=<NllLossBackward0>)
196500 tensor(2.1609, grad_fn=<NllLossBackward0>)
196600 tensor(1.7608, grad_fn=<NllLossBackward0>)
196700 tensor(2.3626, grad_fn=<NllLossBackward0>)
196800 tensor(2.1700, grad_fn=<NllLossBackward0>)
196900 tensor(1.9729, grad_fn=<NllLossBackward0>)
197000 tensor(1.8714, grad_fn=<NllLossBackward0>)
197100 tensor(1.8832, grad_fn=<NllLossBackward0>)
197200 tensor(2.1267, grad_fn=<NllLossBackward0>)
197300 tensor(1.7792, grad_fn=<NllLossBackward0>)
197400 tensor(1.7980, grad_fn=<NllLossBackward0>)
197500 tensor(2.1595, grad_fn=<NllLossBackward0>)
197600 tensor(2.2437, grad_fn=<NllLossBackward0>)
197700 tensor(2.6110, grad_fn=<NllLossBackward0>)
197800 tensor(1.9264, grad_fn=<NllLossBackward0>)
197900 tensor(1.9929, grad_fn=<NllLossBackward0>)
198000 tensor(2.1350, grad_fn=<NllLossBackward0>)
198100 tensor(2.2817, grad_fn=<NllLossBackward0>)
198200 tensor(2.4246, grad_fn=<NllLossBackward0>)
198300 tensor(2.3402, grad_fn=<NllLossBackward0>)
198400 tensor(2.0441, grad_fn=<NllLossBackward0>)
198500 tensor(1.5830, grad_fn=<NllLossBackward0>)
198600 tensor(1.6293, grad_fn=<NllLossBackward0>)
198700 tensor(2.1885, grad_fn=<NllLossBackward0>)
198800 tensor(2.2074, grad_fn=<NllLossBackward0>)
198900 tensor(2.0459, grad_fn=<NllLossBackward0>)
199000 tensor(2.2450, grad_fn=<NllLossBackward0>)
199100 tensor(2.2361, grad_fn=<NllLossBackward0>)
199200 tensor(1.6656, grad_fn=<NllLossBackward0>)
199300 tensor(1.8946, grad_fn=<NllLossBackward0>)
199400 tensor(2.3275, grad_fn=<NllLossBackward0>)
199500 tensor(2.2112, grad_fn=<NllLossBackward0>)
199600 tensor(2.2084, grad_fn=<NllLossBackward0>)
199700 tensor(2.0269, grad_fn=<NllLossBackward0>)
199800 tensor(2.2045, grad_fn=<NllLossBackward0>)
199900 tensor(1.7132, grad_fn=<NllLossBackward0>)
199999 tensor(2.0593, grad_fn=<NllLossBackward0>)

<__main__.ModelInit at 0x2f4b79c10>

split_loss('train', model_init)
split_loss('val', model_init)

train 2.072941780090332
val 2.4288761615753174

Activation issues (Automatically choosing initialization)

• Scaling above approach for a deeper and more complex network is challenging especially when you run into problems-diagnosing can be tedious

class ModelAutoInit(object):
    def __init__(self, vocab_sz, blck_sz=3, emb_sz=2, hidden_units=100, g=torch.Generator().manual_seed(2147483647), mul_W2=1.0, mul_b2=1.0, mul_W1='kaiming', mul_b1=1.0) -> None:
        if mul_W1 == 'kaiming':
            mul_W1 = (5/3)/((blck_sz*emb_sz)**0.5)
        self.C = torch.randn((vocab_sz,emb_sz), generator=g)
        self.W1 = torch.randn((blck_sz*emb_sz, hidden_units), generator=g)*mul_W1
        self.b1 = torch.randn(hidden_units, generator=g)*mul_b1
        self.W2 = torch.randn((hidden_units, vocab_sz), generator=g) * mul_W2
        self.b2 = torch.randn(vocab_sz, generator=g) * mul_b2
        self.blck_sz = blck_sz
        self.emb_sz = emb_sz
        self.hidden_units = hidden_units
        self.emb = None
        self.h = None
        self.hpreact = None
        self._init_grad()


    def _init_grad(self):
        for p in self.parameters(): p.requires_grad = True

    def __call__(self, X):
        self.emb = self.C[X]
        self.hpreact = self.emb.view(self.emb.shape[0], -1)@self.W1 + self.b1
        self.h = torch.tanh(self.hpreact)
        logits = self.h@self.W2 + self.b2 ## logits are calculated here so W2 and b2 must be close to zero
        return logits
    
    def parameters(self):
        return [self.C, self.W1, self.b1, self.W2, self.b2]

    def num_params(self):
        return sum(p.nelement() for p in self.parameters())
    
    def zero_grad(self):
        for p in self.parameters(): 
            # print(p.shape, p.data, p.grad)
            p.grad = None

x = torch.randn(1000, 10)
w = torch.randn(10, 200)
y = x@w; y
display((x.mean(), x.std()))
display((y.mean(), y.std()))
plt.figure(figsize=(20, 5))
plt.subplot(121)
plt.hist(x.view(-1).data, 50, density=True);
plt.subplot(122)
plt.hist(y.view(-1).data, 50, density=True);

(tensor(-0.0117), tensor(0.9867))

(tensor(0.0060), tensor(3.0606))

• Random input x drawn from gaussian, similarily random weights w again drawn from gaussian.
• When we look at y mean stays largely 0 but standard deviations expands from 1 to 3.
• We want roughly unit gaussian through out the neural net

x = torch.randn(1000, 10)
w = torch.randn(10, 200) *0.2
y = x@w; y
display((x.mean(), x.std()))
display((y.mean(), y.std()))
plt.figure(figsize=(20, 5))
plt.subplot(121)
plt.hist(x.view(-1).data, 50, density=True);
plt.subplot(122)
plt.hist(y.view(-1).data, 50, density=True);

(tensor(0.0075), tensor(0.9892))

(tensor(0.0014), tensor(0.6193))

• If we multiply the weights by 5 standard deviation grows and grows. If we multiply by 0.2 std. dev shrinks. What do we multiply weights by to preserve the standard deviation
• Mathematical answer - Divide the weights by sqrt of fann_in. fann_in ; here is w.shape[0]=10. Actual formulae is $$

x = torch.randn(1000, 10)
w = torch.randn(10, 200)/ 10**0.5
y = x@w; y
display((x.mean(), x.std()))
display((y.mean(), y.std()))
plt.figure(figsize=(20, 5))
plt.subplot(121)
plt.hist(x.view(-1).data, 50, density=True);
plt.subplot(122)
plt.hist(y.view(-1).data, 50, density=True);

(tensor(-0.0158), tensor(0.9957))

(tensor(-0.0014), tensor(1.0008))

• We need activations to be well behaved and gradients to be well behaved => they don’t go to infinity or shrink to zero in forward pass. Similarily backward pass also needs to be well behaved.

• Kaiming’s paper found properly initializing forward pass so that it’s well behaved also ensures that the backward pass is also well behaved upto a size of hidden neuron proportional to early and late layer.

• Mode in torch - Kaiming_normal_ –> Would you like to initialize the gaussian/ weights or would you like to initialize the gradients

• Why is initialization not a big problem anymore?

  • 7 years ago u had to be very careful with activations, ranges, values and histogram, precise settings of gain and scrutinizing of non- linearities used and so on. Everything was very finnicky, fragile and needed to be properly arranged for neural network to work esp. if neural network was very deep. However there are number of modern innovations which have made everything significantly more stable and more well behaved and it has become less important to initialize these networks exactly right

  • Residual connections

  • Use of number of normalization layers - Batch normalization, layer normalization, group normalization

  • Better optimizers => not just stochastic descent but also RMSProp and esp. Adam

tracker = {'lr':[], 'batch_sz':[], 'loss':[], 'block_sz':[], 'emb_sz':[], 'hidden_units':[] }
vocab_sz = len(i2s); vocab_sz
model_init = ModelAutoInit(vocab_sz, emb_sz=10, hidden_units=200, mul_W2=0.01, mul_b2=0.0, mul_W1='kaiming', mul_b1=0.01)
train(model_init, Xtr, Ytr, lr = weight_decay_scheduler(epochs=200000), epochs=200000, batch_sz=32, tracker=tracker, verbose=True)

0 tensor(3.3024, grad_fn=<NllLossBackward0>)
100 tensor(2.5187, grad_fn=<NllLossBackward0>)
200 tensor(2.8143, grad_fn=<NllLossBackward0>)
300 tensor(2.4132, grad_fn=<NllLossBackward0>)
400 tensor(2.3990, grad_fn=<NllLossBackward0>)
500 tensor(2.4342, grad_fn=<NllLossBackward0>)
600 tensor(2.4968, grad_fn=<NllLossBackward0>)
700 tensor(2.1909, grad_fn=<NllLossBackward0>)
800 tensor(2.2206, grad_fn=<NllLossBackward0>)
900 tensor(2.3197, grad_fn=<NllLossBackward0>)
1000 tensor(2.2844, grad_fn=<NllLossBackward0>)
1100 tensor(2.3681, grad_fn=<NllLossBackward0>)
1200 tensor(2.3035, grad_fn=<NllLossBackward0>)
1300 tensor(2.4185, grad_fn=<NllLossBackward0>)
1400 tensor(2.3158, grad_fn=<NllLossBackward0>)
1500 tensor(2.1326, grad_fn=<NllLossBackward0>)
1600 tensor(1.9019, grad_fn=<NllLossBackward0>)
1700 tensor(2.2801, grad_fn=<NllLossBackward0>)
1800 tensor(2.4545, grad_fn=<NllLossBackward0>)
1900 tensor(2.4646, grad_fn=<NllLossBackward0>)
2000 tensor(2.4106, grad_fn=<NllLossBackward0>)
2100 tensor(2.1249, grad_fn=<NllLossBackward0>)
2200 tensor(1.8426, grad_fn=<NllLossBackward0>)
2300 tensor(2.1682, grad_fn=<NllLossBackward0>)
2400 tensor(2.1720, grad_fn=<NllLossBackward0>)
2500 tensor(2.0681, grad_fn=<NllLossBackward0>)
2600 tensor(2.1518, grad_fn=<NllLossBackward0>)
2700 tensor(2.2253, grad_fn=<NllLossBackward0>)
2800 tensor(2.5040, grad_fn=<NllLossBackward0>)
2900 tensor(2.6968, grad_fn=<NllLossBackward0>)
3000 tensor(2.3221, grad_fn=<NllLossBackward0>)
3100 tensor(2.5816, grad_fn=<NllLossBackward0>)
3200 tensor(2.1321, grad_fn=<NllLossBackward0>)
3300 tensor(2.2914, grad_fn=<NllLossBackward0>)
3400 tensor(2.3778, grad_fn=<NllLossBackward0>)
3500 tensor(2.4706, grad_fn=<NllLossBackward0>)
3600 tensor(2.1554, grad_fn=<NllLossBackward0>)
3700 tensor(2.3014, grad_fn=<NllLossBackward0>)
3800 tensor(2.4513, grad_fn=<NllLossBackward0>)
3900 tensor(2.2788, grad_fn=<NllLossBackward0>)
4000 tensor(2.3476, grad_fn=<NllLossBackward0>)
4100 tensor(2.5861, grad_fn=<NllLossBackward0>)
4200 tensor(2.1059, grad_fn=<NllLossBackward0>)
4300 tensor(2.1608, grad_fn=<NllLossBackward0>)
4400 tensor(2.4324, grad_fn=<NllLossBackward0>)
4500 tensor(2.3549, grad_fn=<NllLossBackward0>)
4600 tensor(2.3525, grad_fn=<NllLossBackward0>)
4700 tensor(2.4479, grad_fn=<NllLossBackward0>)
4800 tensor(2.1099, grad_fn=<NllLossBackward0>)
4900 tensor(2.3958, grad_fn=<NllLossBackward0>)
5000 tensor(2.5440, grad_fn=<NllLossBackward0>)
5100 tensor(2.1042, grad_fn=<NllLossBackward0>)
5200 tensor(2.0994, grad_fn=<NllLossBackward0>)
5300 tensor(2.4417, grad_fn=<NllLossBackward0>)
5400 tensor(1.9345, grad_fn=<NllLossBackward0>)
5500 tensor(2.6847, grad_fn=<NllLossBackward0>)
5600 tensor(1.9880, grad_fn=<NllLossBackward0>)
5700 tensor(2.5920, grad_fn=<NllLossBackward0>)
5800 tensor(2.2307, grad_fn=<NllLossBackward0>)
5900 tensor(1.9437, grad_fn=<NllLossBackward0>)
6000 tensor(2.2293, grad_fn=<NllLossBackward0>)
6100 tensor(2.0395, grad_fn=<NllLossBackward0>)
6200 tensor(2.0969, grad_fn=<NllLossBackward0>)
6300 tensor(1.8588, grad_fn=<NllLossBackward0>)
6400 tensor(1.9116, grad_fn=<NllLossBackward0>)
6500 tensor(2.1867, grad_fn=<NllLossBackward0>)
6600 tensor(1.7954, grad_fn=<NllLossBackward0>)
6700 tensor(2.2135, grad_fn=<NllLossBackward0>)
6800 tensor(2.3484, grad_fn=<NllLossBackward0>)
6900 tensor(2.2514, grad_fn=<NllLossBackward0>)
7000 tensor(1.8359, grad_fn=<NllLossBackward0>)
7100 tensor(2.0980, grad_fn=<NllLossBackward0>)
7200 tensor(2.7872, grad_fn=<NllLossBackward0>)
7300 tensor(1.9570, grad_fn=<NllLossBackward0>)
7400 tensor(2.3076, grad_fn=<NllLossBackward0>)
7500 tensor(2.3079, grad_fn=<NllLossBackward0>)
7600 tensor(2.0740, grad_fn=<NllLossBackward0>)
7700 tensor(2.1045, grad_fn=<NllLossBackward0>)
7800 tensor(2.5564, grad_fn=<NllLossBackward0>)
7900 tensor(2.0937, grad_fn=<NllLossBackward0>)
8000 tensor(2.2355, grad_fn=<NllLossBackward0>)
8100 tensor(2.1011, grad_fn=<NllLossBackward0>)
8200 tensor(2.1976, grad_fn=<NllLossBackward0>)
8300 tensor(2.1861, grad_fn=<NllLossBackward0>)
8400 tensor(2.2358, grad_fn=<NllLossBackward0>)
8500 tensor(2.1160, grad_fn=<NllLossBackward0>)
8600 tensor(2.0229, grad_fn=<NllLossBackward0>)
8700 tensor(1.9191, grad_fn=<NllLossBackward0>)
8800 tensor(2.2953, grad_fn=<NllLossBackward0>)
8900 tensor(2.6642, grad_fn=<NllLossBackward0>)
9000 tensor(2.3211, grad_fn=<NllLossBackward0>)
9100 tensor(2.2186, grad_fn=<NllLossBackward0>)
9200 tensor(2.4424, grad_fn=<NllLossBackward0>)
9300 tensor(2.0324, grad_fn=<NllLossBackward0>)
9400 tensor(2.1641, grad_fn=<NllLossBackward0>)
9500 tensor(2.1027, grad_fn=<NllLossBackward0>)
9600 tensor(2.1114, grad_fn=<NllLossBackward0>)
9700 tensor(2.1602, grad_fn=<NllLossBackward0>)
9800 tensor(2.0442, grad_fn=<NllLossBackward0>)
9900 tensor(2.1754, grad_fn=<NllLossBackward0>)
10000 tensor(2.2290, grad_fn=<NllLossBackward0>)
10100 tensor(2.3932, grad_fn=<NllLossBackward0>)
10200 tensor(1.8372, grad_fn=<NllLossBackward0>)
10300 tensor(2.3016, grad_fn=<NllLossBackward0>)
10400 tensor(1.9999, grad_fn=<NllLossBackward0>)
10500 tensor(1.9767, grad_fn=<NllLossBackward0>)
10600 tensor(1.8608, grad_fn=<NllLossBackward0>)
10700 tensor(2.4016, grad_fn=<NllLossBackward0>)
10800 tensor(2.5590, grad_fn=<NllLossBackward0>)
10900 tensor(2.1239, grad_fn=<NllLossBackward0>)
11000 tensor(2.2071, grad_fn=<NllLossBackward0>)
11100 tensor(1.9146, grad_fn=<NllLossBackward0>)
11200 tensor(2.0678, grad_fn=<NllLossBackward0>)
11300 tensor(2.1992, grad_fn=<NllLossBackward0>)
11400 tensor(2.1654, grad_fn=<NllLossBackward0>)
11500 tensor(2.3882, grad_fn=<NllLossBackward0>)
11600 tensor(2.4267, grad_fn=<NllLossBackward0>)
11700 tensor(1.7729, grad_fn=<NllLossBackward0>)
11800 tensor(2.2109, grad_fn=<NllLossBackward0>)
11900 tensor(2.3636, grad_fn=<NllLossBackward0>)
12000 tensor(1.8122, grad_fn=<NllLossBackward0>)
12100 tensor(2.1600, grad_fn=<NllLossBackward0>)
12200 tensor(2.3730, grad_fn=<NllLossBackward0>)
12300 tensor(2.2463, grad_fn=<NllLossBackward0>)
12400 tensor(1.9094, grad_fn=<NllLossBackward0>)
12500 tensor(2.0218, grad_fn=<NllLossBackward0>)
12600 tensor(2.1935, grad_fn=<NllLossBackward0>)
12700 tensor(1.8155, grad_fn=<NllLossBackward0>)
12800 tensor(1.9653, grad_fn=<NllLossBackward0>)
12900 tensor(2.3374, grad_fn=<NllLossBackward0>)
13000 tensor(1.8118, grad_fn=<NllLossBackward0>)
13100 tensor(2.1455, grad_fn=<NllLossBackward0>)
13200 tensor(2.2703, grad_fn=<NllLossBackward0>)
13300 tensor(2.2141, grad_fn=<NllLossBackward0>)
13400 tensor(1.9321, grad_fn=<NllLossBackward0>)
13500 tensor(1.9607, grad_fn=<NllLossBackward0>)
13600 tensor(2.3464, grad_fn=<NllLossBackward0>)
13700 tensor(1.9005, grad_fn=<NllLossBackward0>)
13800 tensor(2.5999, grad_fn=<NllLossBackward0>)
13900 tensor(2.2074, grad_fn=<NllLossBackward0>)
14000 tensor(2.2912, grad_fn=<NllLossBackward0>)
14100 tensor(2.4711, grad_fn=<NllLossBackward0>)
14200 tensor(2.1533, grad_fn=<NllLossBackward0>)
14300 tensor(2.4508, grad_fn=<NllLossBackward0>)
14400 tensor(1.9902, grad_fn=<NllLossBackward0>)
14500 tensor(2.1709, grad_fn=<NllLossBackward0>)
14600 tensor(2.1116, grad_fn=<NllLossBackward0>)
14700 tensor(1.9090, grad_fn=<NllLossBackward0>)
14800 tensor(2.3655, grad_fn=<NllLossBackward0>)
14900 tensor(2.0735, grad_fn=<NllLossBackward0>)
15000 tensor(1.8843, grad_fn=<NllLossBackward0>)
15100 tensor(2.2024, grad_fn=<NllLossBackward0>)
15200 tensor(2.3541, grad_fn=<NllLossBackward0>)
15300 tensor(1.8007, grad_fn=<NllLossBackward0>)
15400 tensor(2.2836, grad_fn=<NllLossBackward0>)
15500 tensor(1.8757, grad_fn=<NllLossBackward0>)
15600 tensor(1.9034, grad_fn=<NllLossBackward0>)
15700 tensor(2.0957, grad_fn=<NllLossBackward0>)
15800 tensor(1.9618, grad_fn=<NllLossBackward0>)
15900 tensor(2.1426, grad_fn=<NllLossBackward0>)
16000 tensor(2.3608, grad_fn=<NllLossBackward0>)
16100 tensor(2.2540, grad_fn=<NllLossBackward0>)
16200 tensor(2.4097, grad_fn=<NllLossBackward0>)
16300 tensor(2.2516, grad_fn=<NllLossBackward0>)
16400 tensor(1.9201, grad_fn=<NllLossBackward0>)
16500 tensor(2.3689, grad_fn=<NllLossBackward0>)
16600 tensor(2.5231, grad_fn=<NllLossBackward0>)
16700 tensor(2.4255, grad_fn=<NllLossBackward0>)
16800 tensor(2.0016, grad_fn=<NllLossBackward0>)
16900 tensor(2.1740, grad_fn=<NllLossBackward0>)
17000 tensor(1.9832, grad_fn=<NllLossBackward0>)
17100 tensor(1.7704, grad_fn=<NllLossBackward0>)
17200 tensor(2.1598, grad_fn=<NllLossBackward0>)
17300 tensor(2.1801, grad_fn=<NllLossBackward0>)
17400 tensor(2.0147, grad_fn=<NllLossBackward0>)
17500 tensor(1.9384, grad_fn=<NllLossBackward0>)
17600 tensor(2.2247, grad_fn=<NllLossBackward0>)
17700 tensor(2.2819, grad_fn=<NllLossBackward0>)
17800 tensor(1.9162, grad_fn=<NllLossBackward0>)
17900 tensor(2.2029, grad_fn=<NllLossBackward0>)
18000 tensor(1.9941, grad_fn=<NllLossBackward0>)
18100 tensor(2.3869, grad_fn=<NllLossBackward0>)
18200 tensor(1.9997, grad_fn=<NllLossBackward0>)
18300 tensor(2.2280, grad_fn=<NllLossBackward0>)
18400 tensor(1.9760, grad_fn=<NllLossBackward0>)
18500 tensor(1.9908, grad_fn=<NllLossBackward0>)
18600 tensor(2.2988, grad_fn=<NllLossBackward0>)
18700 tensor(2.2086, grad_fn=<NllLossBackward0>)
18800 tensor(2.2566, grad_fn=<NllLossBackward0>)
18900 tensor(2.3471, grad_fn=<NllLossBackward0>)
19000 tensor(1.9032, grad_fn=<NllLossBackward0>)
19100 tensor(2.4466, grad_fn=<NllLossBackward0>)
19200 tensor(1.8904, grad_fn=<NllLossBackward0>)
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199000 tensor(2.0083, grad_fn=<NllLossBackward0>)
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199800 tensor(2.0920, grad_fn=<NllLossBackward0>)
199900 tensor(2.0772, grad_fn=<NllLossBackward0>)
199999 tensor(1.9277, grad_fn=<NllLossBackward0>)

<__main__.ModelAutoInit at 0x17b98a4f0>

split_loss('train', model_init)
split_loss('val', model_init)

train 1.991290807723999
val 2.3239383697509766

Batch Normalization

• Enabled to train very deep NN reliably

• It just works

• Motivations

  • We don’t want the pre-activation or model.hpreact layers to be too small because then the tanh is not doing anything

  • We don’t want them to be too large because then tanh is saturated.

  • We want them to be roughly gaussian - zero mean, 1 std. dev. atleast during initialization

  • Insight from BN paper is =>

    ” You want your hidden states to be roughly gaussian, then why not just take the hidden states and just normalize them to be gaussian”

  • We can standardize hidden states because - Standardization is a perfectly differentiable operation

  • We want model.hpreact to be roughly gaussian but only at initialization. We don’t want it to be gaussian always

  • We like the distribution of neuron at hpreact to move around to become sharp/ squeezed, trigger happy more or less. And we want back propogation to tell us how the distribution should move around. So inaddition to normalization of neuron we also have to introduce scale and shift weights in BN. We are basically looking at standardized gains and offseting them by some gain and adding some bias

  • With BN layer following a particular layer. We don’t need bias for those layers ( esp. conv and linear). Bias weights have no impact as they are removed during normalization. Our bias in bn layer can play the role of bias.

  • Since bngain and bnbias are initialized to 1 and 0 respectively. The hpreact_bn will get normalized gaussian. During backpropogation we can change bngain and bnbias so that network have full ability to do what it wants

  • With deeper networks, it becomes extremely finnicky to maintain and do proper weight initialization at different layers. Instead we can sprinkle many batch normalization at will.

  • It’s common to sprinkle batch normalization layers just after convolutions ( simply a multiplication with weight matrix but with a more structured format) and linear layers to control the state of activation at every point in the neural net.

    • Helps us control activations through out the NN
    • Doesn’t require us to do perfect mathematics and care about the activations distributions, for all different types of lego building blocks you might want to integrate with the NN.
    • Significantly stablizes the training

  • Cons of BN

    • Stability offered by BN layers comes at a terrible cost. Due to the way BN is normalizing , we are coupling examples mathematically in forward pass and backward pass. hpreact and logits are not just an example of it’s on inputs but also a function of other examples that just happen to come for a ride in that batch.
    • hpreact is going to change slightly depending on what other examples are there in the batch. Depending on how you sample hpreact is going to change subtley or jitter; same is the case for the logits. This may feel like a bug or undesirable -> but in practice turns out to be good for the training as a side effect. We can think of this as a kind of regularization. It’s padding out anyone of these stupid examples and is introducing a bit of entropy. Because of padding out, it’s actually a form of data augmentation. This makes is harder for the neural net to overfit.
    • Deceivingly as a second order effect, BN is a regularizer.
    • No one likes this property attempts to remove it - group normalization, instance normalization , layer normalization.

class ModelAutoInitBN(object):
    def __init__(self, vocab_sz, blck_sz=3, emb_sz=2, hidden_units=100, g=torch.Generator().manual_seed(2147483647), 
                 mul_W2='kaiming', mul_b2=1.0, mul_W1='kaiming', mul_b1=1.0, 
                 eps=10**-5, momentum = 0.01, training=True) -> None:
        
        if mul_W1 == 'kaiming': mul_W1 = (5/3)/((blck_sz*emb_sz)**0.5) ## For tanh
        if mul_W2 == 'kaiming': mul_W2 = 1/((hidden_units)**0.5) ## For linear layer
    
        self.C = torch.randn((vocab_sz,emb_sz), generator=g)
        self.W1 = torch.randn((blck_sz*emb_sz, hidden_units), generator=g)*mul_W1
        # self.b1 = torch.randn(hidden_units, generator=g)*mul_b1
        self.W2 = torch.randn((hidden_units, vocab_sz), generator=g) * mul_W2
        self.b2 = torch.randn(vocab_sz, generator=g) * mul_b2
        self.bngain = torch.ones((1, hidden_units))
        self.bnbias = torch.zeros((1, hidden_units))
        self.blck_sz = blck_sz
        self.emb_sz = emb_sz
        self.hidden_units = hidden_units
        self.emb = None
        self.h = None
        self.hpreact = None
        self.eps = eps
        self.momentum = momentum
        self.training = training
        self.hpreact_mean = None
        self.hpreact_var = None
        self._init_grad()


    def _init_grad(self):
        for p in self.parameters(): p.requires_grad = True

    def __call__(self, X):
        self.emb = self.C[X]
        self.hpreact = self.emb.view(self.emb.shape[0], -1)@self.W1  # + self.b1
        if self.training:
            self.hpreact_mean = self.hpreact.mean(dim=0, keepdim=True)
            self.hpreact_var = self.hpreact.var(dim=0, keepdim=True)
        self.hpreact_bn = self.bngain*((self.hpreact - self.hpreact_mean)/ (self.hpreact_var + self.eps)**0.5) + self.bnbias
        self.h = torch.tanh(self.hpreact_bn)
        logits = self.h@self.W2 + self.b2 ## logits are calculated here so W2 and b2 must be close to zero
        return logits
    
    def parameters(self):
        return [self.C, self.W1, self.W2, self.b2, self.bnbias, self.bngain] # remove  self.b1

    def num_params(self):
        return sum(p.nelement() for p in self.parameters())
    
    def zero_grad(self):
        for p in self.parameters(): 
            # print(p.shape, p.data, p.grad)
            p.grad = None

def train(model, X, Y, lr=0.1, epochs=1000, verbose=False, batch_sz=None, loss_fn=F.cross_entropy, tracker = None):
    

    for i in range(epochs):
    
        #minibatch construct
        inputs = X
        target = Y
        if batch_sz:
            ix = torch.randint(low=0, high=X.shape[0], size=(batch_sz,))
            inputs = X[ix]
            target = Y[ix]
        
        # Forward Pass
        logits = model(inputs); logits.shape 
        # loss = nll(logits, Y)
        loss = loss_fn(logits, target)
        # loss2 = nll(logits, Y)

        # Backward Pass
        model.zero_grad()
        loss.backward(); 
        if i%100 == 0 and verbose: print(i, loss)
        if i == epochs-1: print(i, loss)


        ## Update / Gradient
        lri = next(lr).item() if hasattr(lr, "__next__") else lr
        for p in model.parameters():
            p.data -=lri*p.grad

        if tracker is not None:
            tracker.get('lr', []).append(lri)
            tracker.get('loss', []).append(loss.item())
            tracker.get('batch_sz', []).append(batch_sz)
            tracker.get('block_sz', []).append(X.shape[1])
            tracker.get('emb_sz', []).append(model.C.shape[1])
            tracker.get('hidden_units', []).append(model.hidden_units)
    return model

tracker = {'lr':[], 'batch_sz':[], 'loss':[], 'block_sz':[], 'emb_sz':[], 'hidden_units':[] }
vocab_sz = len(i2s); vocab_sz
model_init = ModelAutoInitBN(vocab_sz, emb_sz=10, hidden_units=200, mul_W2='kaiming', mul_b2=0.0, mul_W1='kaiming', mul_b1=0.01)
train(model_init, Xtr, Ytr, lr = weight_decay_scheduler(epochs=100000), epochs=100000, batch_sz=32, tracker=tracker, verbose=True)

0 tensor(3.4678, grad_fn=<NllLossBackward0>)
100 tensor(2.7834, grad_fn=<NllLossBackward0>)
200 tensor(2.4547, grad_fn=<NllLossBackward0>)
300 tensor(2.7189, grad_fn=<NllLossBackward0>)
400 tensor(2.6705, grad_fn=<NllLossBackward0>)
500 tensor(2.3696, grad_fn=<NllLossBackward0>)
600 tensor(2.5320, grad_fn=<NllLossBackward0>)
700 tensor(2.4482, grad_fn=<NllLossBackward0>)
800 tensor(2.1285, grad_fn=<NllLossBackward0>)
900 tensor(2.1645, grad_fn=<NllLossBackward0>)
1000 tensor(2.2621, grad_fn=<NllLossBackward0>)
1100 tensor(2.3032, grad_fn=<NllLossBackward0>)
1200 tensor(2.3277, grad_fn=<NllLossBackward0>)
1300 tensor(2.0905, grad_fn=<NllLossBackward0>)
1400 tensor(1.9403, grad_fn=<NllLossBackward0>)
1500 tensor(2.2550, grad_fn=<NllLossBackward0>)
1600 tensor(2.6272, grad_fn=<NllLossBackward0>)
1700 tensor(2.3444, grad_fn=<NllLossBackward0>)
1800 tensor(2.2626, grad_fn=<NllLossBackward0>)
1900 tensor(2.6527, grad_fn=<NllLossBackward0>)
2000 tensor(2.5426, grad_fn=<NllLossBackward0>)
2100 tensor(2.3766, grad_fn=<NllLossBackward0>)
2200 tensor(2.1561, grad_fn=<NllLossBackward0>)
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2400 tensor(2.2592, grad_fn=<NllLossBackward0>)
2500 tensor(2.0387, grad_fn=<NllLossBackward0>)
2600 tensor(2.2179, grad_fn=<NllLossBackward0>)
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2800 tensor(1.9581, grad_fn=<NllLossBackward0>)
2900 tensor(2.7357, grad_fn=<NllLossBackward0>)
3000 tensor(2.4857, grad_fn=<NllLossBackward0>)
3100 tensor(2.7058, grad_fn=<NllLossBackward0>)
3200 tensor(2.2855, grad_fn=<NllLossBackward0>)
3300 tensor(2.3332, grad_fn=<NllLossBackward0>)
3400 tensor(2.1415, grad_fn=<NllLossBackward0>)
3500 tensor(2.1656, grad_fn=<NllLossBackward0>)
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5000 tensor(2.1935, grad_fn=<NllLossBackward0>)
5100 tensor(2.1842, grad_fn=<NllLossBackward0>)
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6000 tensor(2.4270, grad_fn=<NllLossBackward0>)
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18300 tensor(2.0225, grad_fn=<NllLossBackward0>)
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91500 tensor(1.5597, grad_fn=<NllLossBackward0>)
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92000 tensor(1.8649, grad_fn=<NllLossBackward0>)
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92400 tensor(1.9697, grad_fn=<NllLossBackward0>)
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93000 tensor(2.6488, grad_fn=<NllLossBackward0>)
93100 tensor(2.2150, grad_fn=<NllLossBackward0>)
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93700 tensor(2.1061, grad_fn=<NllLossBackward0>)
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94200 tensor(2.1342, grad_fn=<NllLossBackward0>)
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96700 tensor(2.0534, grad_fn=<NllLossBackward0>)
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97800 tensor(1.8705, grad_fn=<NllLossBackward0>)
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98000 tensor(2.0582, grad_fn=<NllLossBackward0>)
98100 tensor(1.6028, grad_fn=<NllLossBackward0>)
98200 tensor(1.9905, grad_fn=<NllLossBackward0>)
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98700 tensor(1.8734, grad_fn=<NllLossBackward0>)
98800 tensor(2.1964, grad_fn=<NllLossBackward0>)
98900 tensor(1.7820, grad_fn=<NllLossBackward0>)
99000 tensor(2.1029, grad_fn=<NllLossBackward0>)
99100 tensor(2.0634, grad_fn=<NllLossBackward0>)
99200 tensor(2.3714, grad_fn=<NllLossBackward0>)
99300 tensor(2.0227, grad_fn=<NllLossBackward0>)
99400 tensor(1.9423, grad_fn=<NllLossBackward0>)
99500 tensor(2.5336, grad_fn=<NllLossBackward0>)
99600 tensor(1.9480, grad_fn=<NllLossBackward0>)
99700 tensor(2.1292, grad_fn=<NllLossBackward0>)
99800 tensor(1.8056, grad_fn=<NllLossBackward0>)
99900 tensor(2.4923, grad_fn=<NllLossBackward0>)
99999 tensor(2.0945, grad_fn=<NllLossBackward0>)

<__main__.ModelAutoInitBN at 0x17fed56a0>

model_init.hpreact.mean(dim=0, keepdim=True).shape, model_init.hpreact.shape

(torch.Size([1, 200]), torch.Size([32, 200]))

split_loss('train', model_init)
split_loss('val', model_init)

train 2.050381660461426
val 2.344590187072754

Calibration of BN for inference

Proposal - Set mean and std. dev of BN layer single time over the training set before inference after the training

def calibrate_bn_inference(model, Xtr):
    model.training = False
    with torch.no_grad():
        emb = model.C[Xtr]
        hpreact = emb.view(emb.shape[0], -1)@model.W1  # + self.b1
        model.hpreact_mean = hpreact.mean(dim=0, keepdim=True)  # storing this variable in model helps us modify them 
        model.hpreact_var = hpreact.var(dim=0, keepdim=True)
    return model