torch_openreml.covariance.HadamardProduct

class torch_openreml.covariance.HadamardProduct(*args, **kwargs)

Bases: Operator

Hadamard (element-wise) product of two covariance matrices.

\[\symbf{V} = \symbf{A} \odot \symbf{B}\]

Both operands must have the same shape. Either or both may be trainable Matrix instances or fixed torch.Tensor values.

Initialize a Hadamard product operator from exactly two operands.

Parameters:

• *args – Exactly two operands as positional arguments or a single dict. The first is \(\symbf{A}\), the second \(\symbf{B}\).

• **kwargs – Exactly two operands as keyword arguments.

Raises:

ValueError – If the number of operands is not exactly two.

Example:

import torch
from torch_openreml.covariance import EquicorrelationMatrix, HadamardProduct

n = 4
op = HadamardProduct(a=EquicorrelationMatrix(n), b=torch.tensor([5.0]))
free_params = torch.tensor([1.0])
op(free_params)

tensor([[5.0000, 3.2071, 3.2071, 3.2071],
        [3.2071, 5.0000, 3.2071, 3.2071],
        [3.2071, 3.2071, 5.0000, 3.2071],
        [3.2071, 3.2071, 3.2071, 5.0000]])

Methods

__call__([free_params])	Construct the matrix from a flat parameter tensor.
auto_grad([free_params])	Compute the Jacobian of build() with respect to free parameters using automatic differentiation.
build_operands([free_params])	Evaluate each operand at the current free parameters.
build_params([free_params, include_fixed, ...])	Construct the full parameter tensor by delegating to each operand.
disable_cache()	Disable intermediate caching on this operator and its operands.
enable_cache()	Enable intermediate caching on this operator and its operands.
get_default_dtype_device()	Get the dtype and the device of the parameter defaults.
get_intermediates(params)	Retrieve cached intermediate computation results if still valid.
grad([free_params])	Compute the Jacobian of __call__() with respect to trainable parameters.
grad_tree([free_params])	Compute the gradient of this operator and of every nested operand, returning each keyed by its path.
inverse([free_params])	Construct the matrix and return its inverse.
manual_grad([free_params])	Compute the Jacobian of __call__() with respect to trainable parameters using a closed-form analytic expression.
operands_grad([free_params])	Compute the Jacobian of each operand with respect to its parameters.
operands_inverse([free_params])	Compute the inverse of each operand at the current free parameters.
reset_intermediates()	Clear the intermediate caches of this operator and its operands.
resolve_dim(n)	Resolve a matrix dimension from an integer or a vector of levels.
set_intermediates(params, intermediates)	Cache intermediate computation results keyed by the parameter values.
set_param_specs(key, *[, fixed, default, trans])	Update the fields of one or more parameter specifications in place.
trans_grad([free_params])	Compute the element-wise derivative of the free parameter transforms.
tree([free_params])	Evaluate this operator and every nested operand, returning each result keyed by its path.

Attributes

fixed_param_defaults	Fixed parameter defaults.
fixed_param_index	Index of fixed parameters.
fixed_param_names	Fixed parameter names.
fixed_param_trans	Transforms for fixed parameters.
free_param_defaults	Free parameter defaults.
free_param_index	Index of free parameters.
free_param_names	Free parameter names.
free_param_trans	Transforms for free parameters.
num_fixed_params	Total number of fixed parameters.
num_free_params	Total number of free parameters.
num_params	Total number of parameters.
operands	Mapping from operand names to operand matrices or tensors.
param_defaults	Parameter defaults.
param_names	Parameter names.
param_specs	Parameter specifications, returned as stored rather than copied.
param_trans	Parameter transforms.
repr_dict	Key-value pairs used to build the string representation.
shape	Output matrix shape.
grad_mode	Gradient computation mode.
jacobian_method	Jacobian method used by auto_grad(), one of "jacrev", "jacfwd", or "jacobian".
jacobian_chunk_size	Number of outputs held per batch when auto_grad() differentiates with "jacrev", or None to compute the Jacobian in a single batch.
cache	Whether intermediate computation results are cached, toggled by enable_cache() and disable_cache().

__call__(free_params=None)

Construct the matrix from a flat parameter tensor.

Must be implemented by subclasses. Implementations should convert free_params via build_params() to validate, include fixed parameters, and apply transforms before any computation.

Parameters:

free_params (torch.Tensor or dict) – Flat 1D parameter tensor or parameter dictionary. If omitted, default values are used. Default: None.

Returns:

Constructed matrix of shape shape.

Return type:

torch.Tensor

manual_grad(free_params=None)

Compute the Jacobian of __call__() with respect to trainable parameters using a closed-form analytic expression.

Applies the product rule: if \(\symbf{V} = \symbf{A} \odot \symbf{B}\) then the gradient with respect to \(\theta_{\symbf{A}}\) is \(\frac{\partial \symbf{A}}{\partial \theta_{\symbf{A}}} \odot \symbf{B}\), and similarly for \(\theta_{\symbf{B}}\). Per-operand Jacobians from operands_grad() are multiplied element-wise by the other operand’s value.

Parameters:

free_params (torch.Tensor or dict) – Flat 1D parameter tensor or parameter dictionary. If omitted, default values are used. Default: None.

Returns:

(grad, grad_names), where grad is a 3D tensor of shape (num_free_params, *shape) and grad_names is a list of the corresponding parameter names. Returns (None, []) if all parameters are fixed.

Return type:

tuple

Raises:

• TypeError – If free_params is not a Torch tensor.

• ValueError – If free_params is not a 1D tensor or has the wrong length, or if free_params is a dict with missing or unexpected keys.

Example:

import torch
from torch_openreml.covariance import EquicorrelationMatrix, HadamardProduct

op = HadamardProduct(
    a=EquicorrelationMatrix(4),
    b=torch.tensor([5.0])
)
free_params = torch.tensor([1.0])
grad, grad_names = op.manual_grad(free_params)
grad

tensor([[[0.0000, 1.3107, 1.3107, 1.3107],
         [1.3107, 0.0000, 1.3107, 1.3107],
         [1.3107, 1.3107, 0.0000, 1.3107],
         [1.3107, 1.3107, 1.3107, 0.0000]]])

grad_names

['a/rho']