Formulas

Deferred computation for easier model building.

The key insight here is that we build up a stored comptuation graph composed of Layers and Arrays, and then we pass data to the stored computation graph and it knows what to do.

This means we have to define the set of operations we want to support for Layers and Arrays in advance.

Abstractly, at the end of the day we want an Array, so everything needs to be resolvable to arrays.

You can think of this in two parts, instance creation creates the deferred computation graph, and the call method accepts actual data and resolves the deferred computation to a real JAX Array.

So let’s focus on a specific thing

a(f.x1 + f.x2) * a(f.x1 | f.x2)

What’s going to happen here is we go from right to left so

``` Prod(

AdaptiveLayer(

Sum(

f.x1, f.x2

)

), AdaptiveLayer(

Concat(

f.x1, f.x2

)

)

```

deferred.__call__ –> now

class blayers.experimental.syntax.Deferred

Bases: ABC

class blayers.experimental.syntax.DeferredBinaryOp(left_deferred, right_deferred, op, symbol)

Bases: Deferred

Defers and then calls op(left_now, right_now)

__init__(left_deferred, right_deferred, op, symbol)

__call__(data=None)

Call self as a function.

pretty(indent=0)

class blayers.experimental.syntax.Sum(left, right)

Bases: DeferredBinaryOp

__init__(left, right)

class blayers.experimental.syntax.Prod(left, right)

Bases: DeferredBinaryOp

__init__(left, right)

class blayers.experimental.syntax.Concat(left, right)

Bases: DeferredBinaryOp

__init__(left, right)

class blayers.experimental.syntax.DeferredManyOp(op, symbol, *args)

Bases: Deferred

Defers and then calls op(left_now, right_now)

__init__(op, symbol, *args)

__call__(data=None)

Call self as a function.

class blayers.experimental.syntax.ConcatMany(*args)

Bases: DeferredManyOp

__init__(*args)

class blayers.experimental.syntax.Formula(lhs, rhs)

Bases: object

__init__(lhs, rhs)

__call__(data, pred_only=False)

Call self as a function.

class blayers.experimental.syntax.DeferredArray(name)

Bases: Deferred

__init__(name)

__call__(data)

Call self as a function.

class blayers.experimental.syntax.SymbolicLayer(layer_instance)

Bases: object

__init__(layer_instance)

abstractmethod __call__(*args, **kwargs)

Call self as a function.

class blayers.experimental.syntax.DeferredLayer(layer_instance, *args, **kwargs)

Bases: object

__init__(layer_instance, *args, **kwargs)

__call__(data=None)

Call self as a function.

class blayers.experimental.syntax.SymbolFactory

Bases: object

blayers.experimental.syntax.bl(formula, data, num_steps=20000)

Parameters:

• formula (Formula)

• data (dict[str, Array])

blayers.experimental.syntax.cat

alias of ConcatMany