HRRTensor

class torchhd.HRRTensor[source]

Holographic Reduced Representation

Proposed in Holographic reduced representations, this model uses real valued hypervectors.

bind(other: HRRTensor) → HRRTensor[source]

Bind the hypervector with other using circular convolution.

This produces a hypervector dissimilar to both.

Binding is used to associate information, for instance, to assign values to variables.

Parameters:

other (HRR) – other input hypervector

Shapes:

  • Self: \((*)\)

  • Other: \((*)\)

  • Output: \((*)\)

Examples:

>>> a, b = torchhd.HRRTensor.random(2, 6)
>>> a
HRR([ 0.0101, -0.2474, -0.0097, -0.0788,  0.1541, -0.1766])
>>> b
HRR([-0.0338,  0.0340,  0.0289, -0.1498,  0.1178, -0.2822])
>>> a.bind(b)
HRR([ 0.0786, -0.0260,  0.0591, -0.0706,  0.0799, -0.0216])

>>> a, b = torchhd.HRRTensor.random(2, 6, dtype=torch.float64)
>>> a
HRR([ 0.0354, -0.0818,  0.0216,  0.0384,  0.2961,  0.1976], dtype=torch.float64)
>>> b
HRR([ 0.3640, -0.0640, -0.1033, -0.1454,  0.0999,  0.0299], dtype=torch.float64)
>>> a.bind(b)
HRR([-0.0362, -0.0910,  0.0114,  0.0445,  0.1244,  0.0388], dtype=torch.float64)
bundle(other: HRRTensor) → HRRTensor[source]

Bundle the hypervector with other using element-wise sum.

This produces a hypervector maximally similar to both.

The bundling operation is used to aggregate information into a single hypervector.

Parameters:

other (HRR) – other input hypervector

Shapes:

  • Self: \((*)\)

  • Other: \((*)\)

  • Output: \((*)\)

Examples:

>>> a, b = torchhd.HRRTensor.random(2, 6)
>>> a
HRR([ 0.1916, -0.1451, -0.0678,  0.0829,  0.3816, -0.0906])
>>> b
HRR([-0.2825,  0.3788,  0.0885, -0.1269, -0.0481, -0.3029])
>>> a.bundle(b)
HRR([-0.0909,  0.2336,  0.0207, -0.0440,  0.3336, -0.3935])

>>> a, b = torchhd.HRRTensor.random(2, 6, dtype=torch.float64)
>>> a
HRR([ 0.3879, -0.0452, -0.0082, -0.2262, -0.2764,  0.0166], dtype=torch.float64)
>>> b
HRR([ 0.0738, -0.0306,  0.4948,  0.1209,  0.1482,  0.1268], dtype=torch.float64)
>>> a.bundle(b)
HRR([ 0.4618, -0.0758,  0.4866, -0.1053, -0.1281,  0.1434], dtype=torch.float64)
cosine_similarity(others: HRRTensor, *, eps=1e-08) → Tensor[source]

Cosine similarity with other hypervectors

dot_similarity(others: HRRTensor) → Tensor[source]

Inner product with other hypervectors

classmethod empty(num_vectors: int, dimensions: int, *, dtype=None, device=None, requires_grad=False) → HRRTensor[source]

Creates a set of hypervectors representing empty sets.

When bundled with a random-hypervector \(x\), the result is \(x\). The empty vector of the HRR model is simply a set of 0 values.

Parameters:

  • num_vectors (int) – the number of hypervectors to generate.

  • dimensions (int) – the dimensionality of the hypervectors.

  • dtype (torch.dtype, optional) – the desired data type of returned tensor. Default: if None is torch.get_default_dtype().

  • device (torch.device, optional) – the desired device of returned tensor. Default: if None, uses the current device for the default tensor type (see torch.set_default_tensor_type()). device will be the CPU for CPU tensor types and the current CUDA device for CUDA tensor types.

  • requires_grad (bool, optional) – If autograd should record operations on the returned tensor. Default: False.

Examples:

>>> torchhd.HRRTensor.empty(3, 6)
HRR([[0., 0., 0., 0., 0., 0.],
    [0., 0., 0., 0., 0., 0.],
    [0., 0., 0., 0., 0., 0.]])
>>> torchhd.HRRTensor.empty(3, 6, dtype=torch.float64)
HRR([[0., 0., 0., 0., 0., 0.],
    [0., 0., 0., 0., 0., 0.],
    [0., 0., 0., 0., 0., 0.]], dtype=torch.float64)
exact_inverse() → HRRTensor[source]

Unstable, but exact, inverse

classmethod identity(num_vectors: int, dimensions: int, *, dtype=None, device=None, requires_grad=False) → HRRTensor[source]

Creates a set of identity hypervectors.

When bound with a random-hypervector \(x\), the result is \(x\).

Parameters:

  • num_vectors (int) – the number of hypervectors to generate.

  • dimensions (int) – the dimensionality of the hypervectors.

  • dtype (torch.dtype, optional) – the desired data type of returned tensor. Default: if None is torch.get_default_dtype().

  • device (torch.device, optional) – the desired device of returned tensor. Default: if None, uses the current device for the default tensor type (see torch.set_default_tensor_type()). device will be the CPU for CPU tensor types and the current CUDA device for CUDA tensor types.

  • requires_grad (bool, optional) – If autograd should record operations on the returned tensor. Default: False.

Examples:

>>> torchhd.HRRTensor.identity(3, 6)
HRR([[1., 0., 0., 0., 0., 0.],
     [1., 0., 0., 0., 0., 0.],
     [1., 0., 0., 0., 0., 0.]])
>>> torchhd.HRRTensor.identity(3, 6, dtype=torch.float64)
HRR([[1., 0., 0., 0., 0., 0.],
     [1., 0., 0., 0., 0., 0.],
     [1., 0., 0., 0., 0., 0.]], dtype=torch.float64)
inverse() → HRRTensor[source]

Stable inversion of the hypervector for binding.

For HRR the stable inverse of hypervector is its conjugate in the frequency domain, this returns the conjugate of the hypervector.

Shapes:

  • Self: \((*)\)

  • Output: \((*)\)

Examples:

>>> a = torchhd.HRRTensor.random(1, 6)
>>> a
HRR([[ 0.1406,  0.0014, -0.0502,  0.2888,  0.2969, -0.2637]])
>>> a.inverse()
HRR([[ 0.1406, -0.2637,  0.2969,  0.2888, -0.0502,  0.0014]])

>>> a = torchhd.HRRTensor.random(1, 6, dtype=torch.float64)
>>> a
HRR([[ 0.0090,  0.2620,  0.0836,  0.0441, -0.2351, -0.1744]], dtype=torch.float64)
>>> a.inverse()
HRR([[ 0.0090, -0.1744, -0.2351,  0.0441,  0.0836,  0.2620]], dtype=torch.float64)
multibind() → HRRTensor[source]

Bind multiple hypervectors

multibundle() → HRRTensor[source]

Bundle multiple hypervectors

negative() → HRRTensor[source]

Negate the hypervector for the bundling inverse.

Shapes:

  • Self: \((*)\)

  • Output: \((*)\)

Examples:

>>> a = torchhd.HRRTensor.random(1, 6)
>>> a
HRR([[ 0.2658, -0.2808,  0.1436,  0.1131,  0.1567, -0.1426]])
>>> a.negative()
HRR([[-0.2658,  0.2808, -0.1436, -0.1131, -0.1567,  0.1426]])

>>> a = torchhd.HRRTensor.random(1, 6, dtype=torch.float64)
>>> a
HRR([[ 0.0318,  0.1944,  0.1229,  0.0193,  0.0135, -0.2521]], dtype=torch.float64)
>>> a.negative()
HRR([[-0.0318, -0.1944, -0.1229, -0.0193, -0.0135,  0.2521]], dtype=torch.float64)
permute(shifts: int = 1) → HRRTensor[source]

Permute the hypervector.

The permutation operator is used to assign an order to hypervectors.

Parameters:

shifts (int, optional) – The number of places by which the elements of the tensor are shifted.

Shapes:

  • Self: \((*)\)

  • Output: \((*)\)

Examples:

>>> a = torchhd.HRRTensor.random(1, 6)
>>> a
HRR([[-0.2521,  0.1140, -0.1647, -0.1490, -0.2091, -0.0618]])
>>> a.permute()
HRR([[-0.0618, -0.2521,  0.1140, -0.1647, -0.1490, -0.2091]])

>>> a = torchhd.HRRTensor.random(1, 6, dtype=torch.float64)
>>> a
HRR([[-0.0495, -0.0318,  0.3923, -0.3205,  0.1587,  0.1926]], dtype=torch.float64)
>>> a.permute()
HRR([[ 0.1926, -0.0495, -0.0318,  0.3923, -0.3205,  0.1587]], dtype=torch.float64)
classmethod random(num_vectors: int, dimensions: int, *, generator=None, dtype=None, device=None, requires_grad=False) → HRRTensor[source]

Creates a set of random independent hypervectors.

The resulting hypervectors are sampled at random from a normal with mean 0 and standard deviation 1/dimensions.

Parameters:

  • num_vectors (int) – the number of hypervectors to generate.

  • dimensions (int) – the dimensionality of the hypervectors.

  • generator (torch.Generator, optional) – a pseudorandom number generator for sampling.

  • dtype (torch.dtype, optional) – the desired data type of returned tensor. Default: if None is torch.get_default_dtype().

  • device (torch.device, optional) – the desired device of returned tensor. Default: if None, uses the current device for the default tensor type (see torch.set_default_tensor_type()). device will be the CPU for CPU tensor types and the current CUDA device for CUDA tensor types.

  • requires_grad (bool, optional) – If autograd should record operations on the returned tensor. Default: False.

Examples:

>>> torchhd.HRRTensor.random(3, 6)
HRR([[ 0.2520, -0.0048, -0.0351,  0.2067,  0.0638, -0.0729],
     [-0.2695,  0.0815,  0.0103,  0.2211, -0.1202,  0.2134],
     [ 0.0086, -0.1748, -0.1715,  0.3215, -0.1353,  0.0044]])
>>> torchhd.HRRTensor.random(3, 6, dtype=torch.float64)
HRR([[-0.1327, -0.0396, -0.0065,  0.0886, -0.4665,  0.2656],
     [-0.2879, -0.1070, -0.0851, -0.4366, -0.1311,  0.3976],
     [-0.0472,  0.2987, -0.1567,  0.1496, -0.0098,  0.0344]], dtype=torch.float64)