# tf.contrib.kfac.fisher_blocks.FullyConnectedDiagonalFB

## Class FullyConnectedDiagonalFB

Inherits From: FisherBlock

FisherBlock for fully-connected (dense) layers using a diagonal approx.

Estimates the Fisher Information matrix's diagonal entries for a fully connected layer. Unlike NaiveDiagonalFB this uses the low-variance "sum of squares" estimator.

Let 'params' be a vector parameterizing a model and 'i' an arbitrary index into it. We are interested in Fisher(params)[i, i]. This is,

$$Fisher(params)[i, i] = E[ v(x, y, params) v(x, y, params)^T ][i, i] = E[ v(x, y, params)[i] ^ 2 ]$$

Consider fully connected layer in this model with (unshared) weight matrix 'w'. For an example 'x' that produces layer inputs 'a' and output preactivations 's',

$$v(x, y, w) = vec( a (d loss / d s)^T )$$

This FisherBlock tracks Fisher(params)[i, i] for all indices 'i' corresponding to the layer's parameters 'w'.

## Methods

### __init__

__init__(
layer_collection,
has_bias=False
)


Creates a FullyConnectedDiagonalFB block.

#### Args:

• layer_collection: The collection of all layers in the K-FAC approximate Fisher information matrix to which this FisherBlock belongs.
• has_bias: Whether the component Kronecker factors have an additive bias. (Default: False)

### instantiate_factors

instantiate_factors(
damping
)


### multiply

multiply(vector)


Multiplies the vector by the (damped) block.

#### Args:

• vector: The vector (a Tensor or tuple of Tensors) to be multiplied.

#### Returns:

The vector left-multiplied by the (damped) block.

### multiply_inverse

multiply_inverse(vector)


Multiplies the vector by the (damped) inverse of the block.

#### Args:

• vector: The vector (a Tensor or tuple of Tensors) to be multiplied.

#### Returns:

The vector left-multiplied by the (damped) inverse of the block.

### multiply_matpower

multiply_matpower(
vector,
exp
)


Multiplies the vector by the (damped) matrix-power of the block.

#### Args:

• vector: Tensor or 2-tuple of Tensors. if self._has_bias, Tensor of shape [input_size, output_size] corresponding to layer's weights. If not, a 2-tuple of the former and a Tensor of shape [output_size] corresponding to the layer's bias.
• exp: A scalar representing the power to raise the block before multiplying it by the vector.

#### Returns:

The vector left-multiplied by the (damped) matrix-power of the block.

### register_additional_tower

register_additional_tower(
inputs,
outputs
)


### register_inverse

register_inverse()


Registers a matrix inverse to be computed by the block.

### register_matpower

register_matpower(exp)


### tensors_to_compute_grads

tensors_to_compute_grads()


Tensors to compute derivative of loss with respect to.