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)
normalize() → HRRTensor[source]

Normalize the hypervector.

The normalization preserves the direction of the hypervector but makes it unit norm. This means that it is mapped to the closest point on the unit sphere.

Shapes:

  • Self: \((*)\)

  • Output: \((*)\)

Examples:

>>> x = torchhd.HRRTensor.random(4, 6).multibundle()
>>> x
HRRTensor([-0.6150,  0.4260,  0.6975,  0.3110,  0.9387,  0.0696])
>>> x.normalize()
HRRTensor([-0.4317,  0.2990,  0.4897,  0.2184,  0.6590,  0.0489])
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 uniformly at random from the (dimensions - 1)-unit sphere.

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)