Type of Conditions handled by Condition Interface

[dario-coscia]

Interfaces

Name Condition	Input	Input N. Argument	Description
InputTargetCondition	,	2	Supervised condition
InputEquationCondition	,	2	PI condition

Must Have

Name Condition	Input	Input N. Argument	Description
TensorInputTensorTargetCondition	(Label)Tensor, (Label)Tensor	2	Supervised condition. The loss is y - model(X)
GraphInputGraphTargetCondition	Graph/iter[Graph]	1	Supervised condition. The loss is graph.y - model(graph.X, ...)
GraphInputTensorTargetCondition	Graph, (Label)Tensor	2	Supervised condition. The loss is y - model(graph.X, ...)
TensorEquationCondition	(Label)Tensor, Equation	2	PI condition. The loss is residual(model(x), equation)
GraphEquationCondition	Graph/iter[Graph], Equation	2	PI condition. The loss is residual(model(graph.x), equation)

Optional desiderata

Name Condition	Input	Input N. Argument	Description
EqualityDomainCondition	Domain, Domain	2	The model should return the same value in 2 different domain. The loss is model(X1) - model(X2), where X1 and X2 are the samples of the two domain

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Somehow related to #302. In the 0.2 version, the Condition class is viewing a huge refactoring to be more versatile and customizable by the user. However, before adding new conditions, I would like to suggest a standard interface for the majority of the problems in DL (of course there is always the possibility to add multiple conditions). Below, I summarize the API:

** Supervised Problems **
In supervised problems, we always have an input and a target thus, the condition must reflect this, so I propose something as
Condition(input=..., target=...), where the following combinations are available:

1. instance(input) == Graph/iter[Graph], instance(output) == Graph/iter[Graph], if iterable same len
2. instance(input) == Tensor/LabelTensor, instance(output) == Tensor/LabelTensor
3. instance(input) == Graph/iter[Graph], instance(output) == Tensor/LabelTensor, if iterable the output.shape[0] == graph len
   These three scenarios should cover the majority of Supervised Learning strategies. To construct the three, we use:
4. GraphInputOutputCondition => maybe renaming GraphInputGraphTargetCondition
5. InputOutputCondition => maybe renaming TensorInputTensorTargetCondition
6. GraphInputTensorOutputCondition => maybe renaming GraphInputTensorTargetCondition
   I suggest to factor everything into an InputTargetCondition, so that it will be useful for user to define a new solver i/o without needing to import all the conditions.

** Physics Informed Problems**
In physics-informed problems, we always have an input and an equation; where the equation computes specific differential operations on the processed input, thus I propose
Condition(input=..., equation=...), where the following combinations are available:

1. instance(input) == LabelTensor, instance(output) == LabelTensor
2. instance(input) == LabelGraph, instance(output) == LabelTensor
   where LabelGraph is simply a graph object with at least one attribute labetensor. To construct the two, we use:
3. InputEquationCondition => renaming TensorEquationCondition
4. GraphtEquationCondition=> renaming GraphEquationCondition
   I suggest to factor everything into an InputEquationCondition, so that it will be useful for the user to define a new solver i/eq without needing to import all the conditions.

** Unsupervised Problems**
In unsupervised problems, we always have a data and (possibly) a conditional_variable, thus I propose
Condition(data=..., conditional_variable=None), where the following combinations are available:

1. instance(data) == LabelTensor/Graph/iter[Graph]
2. instance(conditional_variable) == Tensor/LabelTensor (conditioning on graph is also possible but I would avoid at the moment).
   To construct the two, we use:
3. DataCondition which depending on the input returns one of the already built in above with the modified __slots__. For example DataCondition(Tensor, Tensor) would use TensorInputTensorTargetCondition.

[ndem0]

I didn't understand the final goal of the discussion: do you want to discuss the Condition interface or which type of condition should be available?

[dario-coscia]

The type of conditions, handled by condition interface. Modifying the title

[ndem0]

Ok nice, we need that! The proposed ones are fine, but I have some doubts with:

• instance(input) == LabelTensor, instance(output) == LabelTensor

Why should the target be a Tensor here? Isn't that a simple equation?

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• instance(input) == LabelGraph, instance(output) == LabelTensor

As before

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• Conditional variables in DataCondition: are not just a new alias for the TensorInputTensorTarget one?

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Very important: I would create intermediate interfaces like SupervisedConditionInterface, such that all the supervised condition can inherit from them (same for Unsupervised and Physical)

[dario-coscia]

Hi @ndem0

Very important: I would create intermediate interfaces like SupervisedConditionInterface, such that all the supervised condition can inherit from them (same for Unsupervised and Physical)

Completely agree. We call them a bit differently, though: InputTargetCondition for supervised, InputEquationCondition for physics-informed and DataCondition for unsupervised. Do you agree?

instance(input) == LabelTensor, instance(output) == LabelTensor
Why should the target be a Tensor here? Isn't that a simple equation?
instance(input) == LabelGraph, instance(output) == LabelTensor
As before

Yes, this is TensorInputTensorTargetCondition and it is used when passing data into PINN solvers. I just put it for completeness no more classes are created for that.

Conditional variables in DataCondition: are not just a new alias for the TensorInputTensorTarget one?

Yes, exactly

[ndem0]

No problem for the names, probably I would just change DataCondition, it can be quite misleading IMHO. Maybe just unsupervised...?
And probably remove the conditional_variable, I guess it's too redundant (too many ways to do the same thing).

[ndem0]

I edited the initial message adding two tables to list the needed and dreamed conditions. Please populate it!