boundlab.expr.LpEpsilon#

class boundlab.expr.LpEpsilon[source]#

Bases: Expr

A noise symbol bounded by the \(\ell_p\)-norm constraint.

Represents a perturbation variable \(\boldsymbol{\epsilon}\) satisfying:

\[\|\boldsymbol{\epsilon}\|_p \leq 1\]

During backward propagation with direction "<=" or ">=", the contribution is \(\pm\|\mathbf{w}\|_q\) where \(\mathbf{w}\) is the materialized weight tensor and \(q\) is the dual norm of \(p\) defined by \(\frac{1}{p} + \frac{1}{q} = 1\).

Only EinsumOp weights are supported.

Methods

`__init__`
`backward`	Compute the dual-norm bound contribution.
`bound_width`	Compute the width of the bounds for this expression.
`center`	Compute the center of the bounds for this expression.
`diag`
`expand`
`flatten`
`flip`
`gather`
`get_const`	Return the concrete tensor if self is a pure constant expression, else None.
`jacobian_ops_`	Recursively compute Jacobian ops for affine expressions.
`lb`	Compute a lower bound for this expression.
`narrow`
`permute`
`repeat`
`reshape`
`roll`
`scatter`
`squeeze`
`tile`
`to_string`	Return string representation with child strings substituted.
`transpose`
`ub`	Compute an upper bound for this expression.
`ublb`	Compute both an upper bound and a lower bound for this expression.
`unflatten`
`unsqueeze`
`with_children`	Return a new expression with the same type and flags but new children.
`zeros_set`

__init__(*shape, name=None, p='inf')[source]#

property shape: torch.Size#: The shape of the output(s) produced by this expression.

with_children()[source]#

Return a new expression with the same type and flags but new children.

property children: tuple[()]#: The child expressions that serve as inputs to this expression.

backward(weights, direction)[source]#

Compute the dual-norm bound contribution.

Parameters:

weights (LinearOp) – A EinsumOp accumulated weight. Must be a EinsumOp instance.
direction (Literal['>=', '<=', '==']) – "<=" returns \(+\|\mathbf{w}\|_q\); ">=" returns \(-\|\mathbf{w}\|_q\); "==" returns None.

Returns:

(±norm, []) or None for "==".

Return type:

tuple[torch.Tensor, list] | None

property T: Expr#: Convenience for transpose of the last two dimensions.

__add__(other)#

__mul__(other)#: Element-wise multiplication (no broadcast).

bound_width()#

Compute the width of the bounds for this expression.

center()#

Compute the center of the bounds for this expression.

diag(diagonal=0)#

expand(*sizes)#

flatten(start_dim=0, end_dim=-1)#

flip(dims)#

gather(indices)#

get_const()#

Return the concrete tensor if self is a pure constant expression, else None.

Works for ConstVal and any AffineSum that has no symbolic children.

jacobian_ops_()#: Recursively compute Jacobian ops for affine expressions.

lb()#

Compute a lower bound for this expression.

narrow(dim, start, length)#

permute(*dims)#

repeat(*sizes)#

reshape(*shape)#

roll(shifts, dims)#

scatter(indices, output_shape)#

squeeze(dim=None)#

tile(*sizes)#

to_string()[source]#

Return string representation with child strings substituted.

transpose(dim0, dim1)#

ub()#

Compute an upper bound for this expression.

ublb()#

Compute both an upper bound and a lower bound for this expression.

unflatten(dim, sizes)#

unsqueeze(dim)#

zeros_set(output_shape)#

id: int#: Unique identifier for the expression, used for topological sorting.

flags: ExprFlags#: Flags indicating expression properties for optimization.