boundlab.prop.lb#

boundlab.prop.lb(e)[source]#

Compute a lower bound via backward bound propagation.

This function propagates linear weights backward through the expression DAG in direction ">=" and accumulates resulting bias terms.

Parameters:: e (Expr) – The expression to bound.
Returns:: A tensor \(l\) such that \(x \ge l\) for all concrete values represented by e.
Return type:: torch.Tensor

Notes

Results are memoized in _LB_CACHE keyed by expression id.

Examples

>>> import torch
>>> import boundlab.expr as expr
>>> x = expr.ConstVal(torch.tensor([0.0])) + expr.LpEpsilon([1])
>>> lb(x).shape
torch.Size([1])