update readme

README.md

@@ -84,7 +84,7 @@ y_t = x_t - \sum_{i=1}^N a_i y_{t-i}, \mathbf{a} = A_{1,:}.
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 The gradients $`\frac{\partial \mathcal{L}}{\partial \mathbf{x}}`$ are filtering $`\frac{\partial \mathcal{L}}{\partial \mathbf{y}}`$ with $\mathbf{a}$ backwards in time, same as in the time-varying case.
-$\frac{\partial \mathcal{L}}{\partial \mathbf{a}}$ is simply summing the gradients for $a_i$ at all the time steps $\frac{\partial \mathcal{L}}{\partial a_i} = \sum_{t=1}^T \frac{\partial \mathcal{L}}{\partial x_t} y_{t-i}$, which can be done by vecotr-matrix multiplication.
+$\frac{\partial \mathcal{L}}{\partial \mathbf{a}}$ is simply summing the gradients for $a_i$ at all the time steps $`\frac{\partial \mathcal{L}}{\partial a_i} = \sum_{t=1}^T \frac{\partial \mathcal{L}}{\partial x_t} y_{t-i}`$, which can be done by vecotr-matrix multiplication.
 This algorithm is more efficient than [^2] because it only needs one pass of filtering to get the two gradients while the latter needs two.
 
 [^1]: [Differentiable All-pole Filters for Time-varying Audio Systems](https://arxiv.org/abs/2404.07970).