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Typo "acutal" to "actual" #258

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2 changes: 1 addition & 1 deletion docs/src/manual.md
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Expand Up @@ -104,6 +104,6 @@ In the light of above, DiffOpt differentiates program variables ``x``, ``s``, ``
- OptNet: Differentiable Optimization as a Layer in Neural Networks

### Backward Pass vector
One possible point of confusion in finding Jacobians is the role of the backward pass vector - above eqn (7), *OptNet: Differentiable Optimization as a Layer in Neural Networks*. While differentiating convex programs, it is often the case that we don't want to find the acutal derivatives, rather we might be interested in computing the product of Jacobians with a *backward pass vector*, often used in backprop in machine learning/automatic differentiation. This is what happens in scheme 1 of `DiffOpt` backend.
One possible point of confusion in finding Jacobians is the role of the backward pass vector - above eqn (7), *OptNet: Differentiable Optimization as a Layer in Neural Networks*. While differentiating convex programs, it is often the case that we don't want to find the actual derivatives, rather we might be interested in computing the product of Jacobians with a *backward pass vector*, often used in backprop in machine learning/automatic differentiation. This is what happens in scheme 1 of `DiffOpt` backend.

But, for the conic system (scheme 2), we provide perturbations in conic data (`dA`, `db`, `dc`) to compute pertubations (`dx`, `dy`, `dz`) in input variables. Unlike the quadratic case, these perturbations are actual derivatives, not the product with a backward pass vector. This is an important distinction between the two schemes of differential optimization.
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