FHRRTensor

class torchhd.FHRRTensor[source]

Fourier Holographic Reduced Representation

Proposed in Holographic Reduced Representation: Distributed Representation for Cognitive Structures, this model uses complex phaser hypervectors.

bind(other: FHRRTensor) → FHRRTensor[source]

Bind the hypervector with other using element-wise multiplication.

This produces a hypervector dissimilar to both.

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

Parameters:

other (FHRR) – other input hypervector

Shapes:

  • Self: \((*)\)

  • Other: \((*)\)

  • Output: \((*)\)

Examples:

>>> a, b = torchhd.FHRRTensor.random(2, 6)
>>> a
FHRR([ 0.9317-0.3632j,  0.7320+0.6813j, -0.8588+0.5123j, -0.9723-0.2339j, -0.9631-0.2692j, -0.4093-0.9124j])
>>> b
FHRR([ 0.9983+0.0578j, -0.5043-0.8635j,  0.5505-0.8349j,  0.9805+0.1966j, 0.9656+0.2599j, -0.5609-0.8279j])
>>> a.bind(b)
FHRR([ 0.9511-0.3087j,  0.2191-0.9757j, -0.0450+0.9990j, -0.9073-0.4204j, -0.8600-0.5102j, -0.5257+0.8507j])

>>> a, b = torchhd.FHRRTensor.random(2, 6, dtype=torch.complex128)
>>> a
FHRR([ 0.7838-0.6210j, -0.0258+0.9997j,  0.0263+0.9997j,  0.9617+0.2742j, 0.1281-0.9918j, -0.4321+0.9018j],
dtype=torch.complex128)
>>> b
FHRR([-0.9995+0.0308j,  0.4550-0.8905j,  0.2793+0.9602j,  0.0025-1.0000j, 0.4470+0.8946j,  0.8314-0.5557j],
dtype=torch.complex128)
>>> a.bind(b)
FHRR([-0.7643+0.6449j,  0.8785+0.4778j, -0.9525+0.3045j,  0.2766-0.9610j, 0.9444-0.3287j,  0.1419+0.9899j],
dtype=torch.complex128)
bundle(other: FHRRTensor) → FHRRTensor[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 (FHRR) – other input hypervector

Shapes:

  • Self: \((*)\)

  • Other: \((*)\)

  • Output: \((*)\)

Examples:

>>> a, b = torchhd.FHRRTensor.random(2, 6)
>>> a
FHRR([ 0.9556-0.2948j,  0.1746+0.9846j, -0.6270-0.7790j, -0.2423-0.9702j, 0.6358+0.7719j,  0.9965-0.0834j])
>>> b
FHRR([-0.9539-0.3000j, -0.1279+0.9918j, -0.4610+0.8874j, -0.3638-0.9315j, 0.9554+0.2952j,  0.8659+0.5003j])
>>> a.bundle(b)
FHRR([-1.6885+0.4104j, -0.4094-1.4874j,  0.0090-0.0058j,  0.1039-0.9365j, 0.0413-1.8657j,  0.6276+1.8385j])

>>> a, b = torchhd.FHRRTensor.random(2, 10, dtype=torch.complex128)
>>> a
FHRR([ 0.4521-0.8920j,  0.7917-0.6109j,  0.5414-0.8408j, -0.9550-0.2967j, 0.9320+0.3626j, -0.8509-0.5253j],
dtype=torch.complex128)
>>> b
FHRR([ 0.6954-0.7186j, -0.5621-0.8270j,  0.4685+0.8835j, -0.9319+0.3627j, -0.8310-0.5563j,  0.2545+0.9671j],
dtype=torch.complex128)
>>> a.bundle(b)
FHRR([ 1.1475-1.6106j,  0.2296-1.4379j,  1.0099+0.0427j, -1.8869+0.0660j, 0.1010-0.1937j, -0.5964+0.4417j],
dtype=torch.complex128)
cosine_similarity(others: FHRRTensor, *, eps=1e-08) → Tensor[source]

Cosine similarity with other hypervectors

dot_similarity(others: FHRRTensor) → Tensor[source]

Inner product with other hypervectors

classmethod empty(num_vectors: int, dimensions: int, *, dtype=torch.complex64, device=None, requires_grad=False) → FHRRTensor[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 FHRR model is a set of 0 values in both real and imaginary part.

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.complex64.

  • 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.FHRRTensor.empty(3, 6)
FHRR([[0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],
        [0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],
        [0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j]])

>>> torchhd.FHRRTensor.empty(3, 6, dtype=torch.complex128)
FHRR([[0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],
        [0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],
        [0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j]],
       dtype=torch.complex128)
classmethod identity(num_vectors: int, dimensions: int, *, dtype=torch.complex64, device=None, requires_grad=False) → FHRRTensor[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.complex64.

  • 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.FHRRTensor.identity(3, 6)
FHRR([[1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j],
        [1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j],
        [1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j]])

>>> torchhd.FHRRTensor.identity(3, 6, dtype=torch.complex128)
FHRR([[1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j],
        [1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j],
        [1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j]],
       dtype=torch.complex128)
inverse() → FHRRTensor[source]

Invert the hypervector for binding.

For FHRR the inverse of hypervector is its conjugate, this returns the conjugate of the hypervector.

Shapes:

  • Self: \((*)\)

  • Output: \((*)\)

Examples:

>>> a = torchhd.FHRRTensor.random(1, 6)
>>> a
FHRR([[ 0.9855+0.1698j, -0.0927-0.9957j, -0.8316-0.5554j, -0.1433-0.9897j, 0.8328+0.5536j,  0.2071+0.9783j]])
>>> a.inverse()
FHRR([[ 0.9855-0.1698j, -0.0927+0.9957j, -0.8316+0.5554j, -0.1433+0.9897j, 0.8328-0.5536j,  0.2071-0.9783j]])

>>> a = torchhd.FHRRTensor.random(1, 6, dtype=torch.complex128)
>>> a
FHRR([[-0.9983-0.0574j, -0.4825+0.8759j,  0.9631-0.2692j,  0.9066-0.4219j, 0.7099-0.7044j, -0.1313-0.9913j]],
dtype=torch.complex128)
>>> a.inverse()
>>> a.inverse()
FHRR([[-0.9983+0.0574j, -0.4825-0.8759j,  0.9631+0.2692j,  0.9066+0.4219j, 0.7099+0.7044j, -0.1313+0.9913j]],
dtype=torch.complex128)
multibind() → FHRRTensor[source]

Bind multiple hypervectors

multibundle() → FHRRTensor[source]

Bundle multiple hypervectors

negative() → FHRRTensor[source]

Negate the hypervector for the bundling inverse.

Shapes:

  • Self: \((*)\)

  • Output: \((*)\)

Examples:

>>> a = torchhd.FHRRTensor.random(1, 6)
>>> a
FHRR([[-0.0187-0.9998j,  0.1950-0.9808j,  0.5203+0.8540j,  0.8587+0.5124j, 0.9998+0.0203j, -0.6237-0.7816j]])
>>> a.negative()
FHRR([[ 0.0187+0.9998j, -0.1950+0.9808j, -0.5203-0.8540j, -0.8587-0.5124j, -0.9998-0.0203j,  0.6237+0.7816j]])

>>> a = torchhd.FHRRTensor.random(1, 6, dtype=torch.complex128)
>>> a
FHRR([[ 0.8255+0.5644j, -0.8352-0.5500j,  0.9751-0.2218j, -0.9808-0.1950j, -0.3840-0.9233j,  0.4106-0.9118j]],
dtype=torch.complex128)
>>> a.negative()
FHRR([[-0.8255-0.5644j,  0.8352+0.5500j, -0.9751+0.2218j,  0.9808+0.1950j, 0.3840+0.9233j, -0.4106+0.9118j]], dtype=torch.complex128)
permute(shifts: int = 1) → FHRRTensor[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.FHRRTensor.random(1, 6)
>>> a
FHRR([[-0.3286-0.9445j,  0.2161-0.9764j, -0.6484+0.7613j, -0.4020+0.9156j, 0.8282-0.5605j, -0.9869+0.1613j]])
>>> a.permute()
FHRR([[-0.9869+0.1613j, -0.3286-0.9445j,  0.2161-0.9764j, -0.6484+0.7613j, -0.4020+0.9156j,  0.8282-0.5605j]])

>>> a = torchhd.FHRRTensor.random(1, 6, dtype=torch.complex128)
>>> a
FHRR([[-0.9500-0.3123j, -0.0234+0.9997j, -0.1071-0.9943j, -0.8558-0.5174j, 0.9631-0.2690j,  0.5470-0.8371j]],
dtype=torch.complex128)
>>> a.permute()
FHRR([[ 0.5470-0.8371j, -0.9500-0.3123j, -0.0234+0.9997j, -0.1071-0.9943j, -0.8558-0.5174j,  0.9631-0.2690j]],
dtype=torch.complex128)
classmethod random(num_vectors: int, dimensions: int, *, dtype=torch.complex64, device=None, requires_grad=False, generator=None) → FHRRTensor[source]

Creates a set of random independent hypervectors.

The resulting hypervectors are sampled uniformly at random from the angle between -pi and +pi.

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.complex64.

  • 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.FHRRTensor.random(3, 6)
FHRR([[ 0.2082-0.9781j,  0.7038-0.7104j, -0.6297-0.7768j, -0.9632-0.2689j, -0.4941+0.8694j,  0.9771-0.2128j],
        [ 0.9820-0.1887j, -0.0395+0.9992j, -0.5139+0.8579j, -0.8415-0.5402j, -0.6696-0.7427j,  0.2312+0.9729j],
        [-0.9786+0.2057j,  0.1714+0.9852j, -0.5925-0.8056j, -0.5698-0.8218j, -0.4632-0.8863j,  0.6996-0.7145j]])

>>> torchhd.FHRRTensor.random(3, 6, dtype=torch.long)
FHRR([[-0.9996-0.0285j, -0.0688-0.9976j,  0.6900-0.7238j,  0.9519-0.3064j, 0.8131-0.5821j,  0.9942-0.1077j],
        [-0.9199-0.3922j,  0.8073-0.5902j,  0.8683+0.4960j,  0.1250+0.9922j, 0.6248+0.7808j, -0.2495+0.9684j],
        [ 0.0178+0.9998j, -0.3006-0.9538j, -0.9346+0.3557j,  0.9017-0.4324j, 0.4029-0.9153j,  0.4818-0.8763j]],
        dtype=torch.complex128)