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__`
`all_subnodes`	Return a list of all sub-expressions in the DAG rooted at this expression, in topological order.
`backward`	Compute the dual-norm bound contribution.
`bound_width`	Compute the width of the bounds for this expression.
`bound_width_reasons_breakdown`	Compute the breakdown of the bound width by reason.
`center`	Compute the center of the bounds for this expression.
`diag`
`expand`
`expand_on`
`flatten`
`flip`
`gather`
`get_const`	Return the concrete tensor if self is a pure constant expression, else None.
`is_symmetric_to_0`	Return True if this expression is symmetric about zero, else False.
`lb`	Compute a lower bound for this expression.
`max_bound_width`	Compute the maximum width across all output dimensions.
`mean`
`narrow`
`permute`
`repeat`
`replace_subnode_once`	Return a new expression with the same structure but sub-expressions replaced by replace_fn.
`reshape`
`roll`
`scatter`
`simplify_ops_`	Recursively compute simplified ops for affine expressions.
`split_const`	Decompose this LpEpsilon into a constant part and a zero-constant expression.
`squeeze`
`sum`
`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.
`uncertainty_reasons`	Compute the breakdown of the bound width by reason, aggregated to total contributions.
`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', reason=None)[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

to_string()[source]#

Return string representation with child strings substituted.

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

__add__(other)#

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

all_subnodes()#

Return a list of all sub-expressions in the DAG rooted at this expression, in topological order.

bound_width()#

Compute the width of the bounds for this expression.

bound_width_reasons_breakdown()#

Compute the breakdown of the bound width by reason.

center()#

Compute the center of the bounds for this expression.

diag(diagonal=0)#

expand(*sizes)#

expand_on(dim, size)#

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

flip(dims)#

gather(indices, dim=0)#

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.

is_symmetric_to_0()#

Return True if this expression is symmetric about zero, else False.

lb()#

Compute a lower bound for this expression.

max_bound_width()#

Compute the maximum width across all output dimensions.

mean(dim=None, keepdim=False)#

narrow(dim, start, length)#

permute(*dims)#

repeat(*sizes)#

replace_subnode_once(replace_fn)#

Return a new expression with the same structure but sub-expressions replaced by replace_fn.

reshape(*shape)#

roll(shifts, dims)#

scatter(indices, output_shape)#

simplify_ops_()#: Recursively compute simplified ops for affine expressions.

split_const()[source]#

Decompose this LpEpsilon into a constant part and a zero-constant expression.

squeeze(dim=None)#

sum(dim=None, keepdim=False)#

tile(*sizes)#

transpose(dim0, dim1)#

ub()#

Compute an upper bound for this expression.

ublb()#

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

uncertainty_reasons()#

Compute the breakdown of the bound width by reason, aggregated to total contributions.

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.