Control.Monad.Distribution

Reexports

Definitions

record Dist : AxisName -> Nat -> Type

  Convex combination of a finite set of types, a point in a simplex △^(i-1)
  i=2 -> △¹ -> line segment
  i=3 -> △² -> triangle
  ...
  Probabilities are represented as logits, represented as a rank 1 tensor.
  Because the tensor has a name, and `Dist` is a thin wrapper around it,
  the name is exposed at the type level, allowing named operations to be
  extended to distributions
  TODO, is Dist a quotient container?

Totality: total
Visibility: public export
Constructor: 

MkDist : Tensor [(name ~~> i)] Double -> Dist name i

Projection: 

.logits : Dist name i -> Tensor [(name ~~> i)] Double

  Probabilities are represented as logits

Hint: 

Show (Dist axisName i)

.logits : Dist name i -> Tensor [(name ~~> i)] Double

  Probabilities are represented as logits

Totality: total
Visibility: public export

logits : Dist name i -> Tensor [(name ~~> i)] Double

  Probabilities are represented as logits

Totality: total
Visibility: public export

uniform : IsSucc i => Dist name i

  Logit representation of the uniform distribution

Totality: total
Visibility: public export

diracDelta : IsSucc i => Fin i -> Dist name i

  Logit representation of dirac delta
  Note that `0` is the canonical choice, as softargmax subtracts the max

Totality: total
Visibility: public export

Dist : AxisName -> Nat -> Cont

  Container whose shape represents a distribution over `n` choices, and
  whose position represents the choice made.

Totality: total
Visibility: public export

Simplex : AxisName -> Nat -> AddCont

  Container whose shapes are distributions, positions their gradients.
  Both are represented as logits
  If we were treating this as non-logit distributions then we'd have a
  one less dimension: both for the simplex in the forward pass and the
  gradients in the backwards one
  That is, the effective dimension of this space is n-1 (we can add a
  constant to all logits without changing the answer), and there's a
  direction in the gradient logit space that does not affect output

Totality: total
Visibility: public export

ProbabilisticChoice : AxisName -> Vect n AddCont -> AddCont

  A distribution over `n` branches together with, contingent on a choice made
  by the environment, the chosen branch's content
  TODO do we think of distr. on the fw pass as being part of Simplex or Nap?

Totality: total
Visibility: public export

ChoiceMade : AxisName -> Vect n AddCont -> AddCont

  The choice made: a distribution over the branches and the chosen branch's content

Totality: total
Visibility: public export

resolveByLabel : (ProbabilisticChoice distName branches >*< ChoiceMade distName branches) =%+> (ChoiceMade distName branches >*< ChoiceMade distName branches)

  Resolve probabilistic choice through the ground truth label. The labelled 
  branch is selected, and its gradient goes back as a singleton bag
  TODO do we need the right component of the codomain?

Totality: total
Visibility: public export