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fix notation error
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yoyolicoris authored Feb 22, 2024
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Expand Up @@ -100,7 +100,7 @@ Moreover, we can get $B_{t + i, i}$ by setting $`A_{t,i} := A_{t+i,i}`$, implies
```math
\frac{\partial \mathcal{L}}{\partial x_t}
= \frac{\partial \mathcal{L}}{\partial y_t}
+ \sum_{i=1}^{T - t} \hat{A}_{t+i,i} \frac{\partial \mathcal{L}}{\partial x_{t+i}}.
+ \sum_{i=1}^{N} \hat{A}_{t+i,i} \frac{\partial \mathcal{L}}{\partial x_{t+i}}.
```

In summary, getting the gradients for the time-varying IIR filter inputs is easy as filtering the backpropagated gradients backwards with the coefficient matrix shifted column-wised.
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