template syntax

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Discrete convolutions in 1D

$(f * g)(x) \triangleq \sum_{i=-\infty}^{\infty} f(i) \cdot g(x-i) \tag{1}$

Fundamental Theorem of Calculus

$\begin{gathered} \int_a^b f^{\prime}(x) d x=f(b)-f(a) \\ \frac{d}{d x} \int_a^x f(t) d t=f(x) \end{gathered} \tag{2}$

a array

$f=[10,9,10,9,10,1,10,9,10,8] \tag{2}$

a function

$f={(0,10),(1,9),(2,10),(3,9),(4,10),(5,1),(6,10),(7,9),(8,10),(9,8)} \tag{3}$

Below is a graph block:

Here is a plot of the signal:

Below is how to do multiple equstion numbering: $\begin{aligned} \mathcal{P}\left(\left\{x_i, x_j\right\} \subseteq X\right) & =\left|\begin{array}{ll} K_{i i} & K_{i j} \\ K_{j i} & K_{j j} \end{array}\right| \\ & =K_{i i} K_{j j}-K_{i j} K_{j i} \\ & =\mathcal{P}\left(\left\{x_i\right\} \subseteq X\right) \mathcal{P}\left(\left\{x_j\right\} \subseteq X\right)-K_{i j}^2 \tag{4} \end{aligned}$

from tinygrad.tensor import Tensor
import tinygrad.nn.optim as optim

class TinyBobNet:
  def __init__(self):
    self.l1 = Tensor.uniform(784, 128)
    self.l2 = Tensor.uniform(128, 10)

  def forward(self, x):
    return x.dot(self.l1).relu().dot(self.l2).log_softmax()

model = TinyBobNet()
optim = optim.SGD([model.l1, model.l2], lr=0.001)

# ... complete data loader here

out = model.forward(x)
loss = out.mul(y).mean()
optim.zero_grad()
loss.backward()
optim.step()

$f=\left[\begin{array}{ccccc} 1 & 2 & 3 & 4 & 5 \\ 6 & 7 & 8 & 9 & 10 \\ 11 & 12 & 13 & 14 & 15 \\ 16 & 17 & 18 & 19 & 20 \end{array}\right] \quad g=\left[\begin{array}{ccc} a & b & c \\ d & e & f \\ g & h & i \end{array}\right]$