Processing complex packed tensors using integrated circuit of real and complex packed tensors in complex domain
An example system includes a processor that can receive a number of complex packed tensors, wherein each of the complex packed tensors include real numbers encoded as imaginary parts of complex numbers. The processor can execute a single instruction, multiple data (SIMD) operation on the complex packed tensors using an integrated circuit of real and complex packed tensors in a complex domain to generate a result.
1 . A computer system comprising:
a processor set;
one or more computer-readable storage media; and
program instructions stored on the one or more computer-readable storage media to cause the processor set to perform operations comprising:
receiving a plurality of non-complex packed tensors and complex packed tensors, wherein each of the complex packed tensors comprises real numbers encoded as imaginary parts of complex numbers;
transforming a non-complex packed tensor into a complex-packed tensor of the plurality of complex packed tensors; and
executing a homomorphically encrypted single instruction, multiple data (SIMD) operation on the complex packed tensors using an integrated circuit of real and complex packed tensors corresponding to SIMD-based registers in a complex domain to generate a result.
2 . The system of claim 1 , wherein the complex packed tensors comprise complex packed tile tensors.
3 . The system of claim 1 , wherein the homomorphically encrypted SIMD operation is executed securely using a fully homomorphic encryption scheme and the result comprises an encrypted result.
4 . The system of claim 1 , wherein the complex packed tensors correspond to ciphertexts.
5 . The system of claim 1 , wherein the complex packed tensors correspond to the SIMD-based registers of a hardware processing unit.
6 . The system of claim 1 , wherein the plurality of complex packed tensors correspond to a single data set packed using imaginary parts of complex numbers to represent half of the single data set.
7 . The system of claim 1 , wherein the plurality of complex packed tensors correspond to two data sets with similar dimensions, and a first data set is represented by real parts of complex numbers and a second data set is represented by imaginary parts of the complex numbers.
8 . The system of claim 1 , wherein the SIMD operation approximates a function of a layer of a neural network.
9 . The system of claim 8 , wherein the layer of the neural network comprises a convolutional layer.
10 . The system of claim 8 , wherein the layer of the neural network comprises a fully-connected layer.
11 . The system of claim 1 , wherein the non-complex packed tensor is transformed using a complex packing method.
12 . A computer-implemented method, comprising:
receiving, via a processor, a plurality of non-complex packed tensors and complex packed tensors, wherein each of the complex packed tensors comprise real numbers encoded as imaginary parts of complex numbers;
transforming a non-complex packed tensor into a complex-packed tensor of the plurality of complex packed tensors; and
executing, via the processor, a homomorphically encrypted single instruction, multiple data (SIMD) operation on the complex packed tensors using an integrated circuit of real and complex packed tensors corresponding to SIMD-based registers in a complex domain to generate a result.
13 . The computer-implemented method of claim 12 , wherein executing the SIMD operation comprises performing a dot product operation on the plurality of complex packed tensors.
14 . The computer-implemented method of claim 12 , wherein executing the SIMD operation comprises performing a matrix-vector multiplication using an operation between a ciphertext corresponding to a vector and a set of values of an encrypted matrix corresponding to an underlying plaintext matrix, wherein each row of the encrypted matrix is complex packed in an additional ciphertext.
15 . The computer-implemented method of claim 12 , comprising adding complex packed dimensions to a tile tensor shape information, and additional operators a set of operators supported by a tile tensor, wherein executing the SIMD operation comprises performing an operation on a set of complex packed tile tensors.
16 . The computer-implemented method of claim 12 , comprising generating the plurality of complex packed tensors using an interleaving complex packing operation on pairs of ciphertexts, and in response to detecting an odd number of ciphertexts, leaving a last ciphertext non-complex-packed.
17 . The computer-implemented method of claim 12 , wherein executing the SIMD operation comprises performing a dot product operation, wherein the plurality of complex packed tensors comprise a first vector encoded with odd indexed elements as real parts and a negation of event indexed elements as imaginary parts and a second vector encoded with odd indexed elements as real parts and even indexed elements as imaginary parts, wherein performing the dot product operation comprises computing a dot product of the first vector and the second vector and outputting a real part of the dot product.
18 . The computer-implemented method of claim 12 , wherein executing the SIMD operation comprises performing a diagonalization operation comprising a sum operation implemented on a complex packed vector with a non-complex-packed matrix using a rotate-one operator.
19 . A computer program product for packing real numbers, the computer program product comprising a computer-readable storage medium having program code embodied therewith, the program code executable by a processor to cause the processor to:
receive a plurality of non-complex packed tensors and complex packed tensors, wherein each of the complex packed tensors comprise real numbers encoded as imaginary parts of complex numbers;
transform a non-complex packed tensor into a complex-packed tensor of the plurality of complex packed tensors; and
execute a homomorphically encrypted single instruction, multiple data (SIMD) operation on encrypted complex packed tensors using an integrated circuit of real and complex packed tensors corresponding to SIMD-based registers in a complex domain to generate a result.
20 . The computer program product of claim 19 , wherein the complex packed tensors and the generated result are encrypted, further comprising program code executable by the processor to send the result to a client device to be decrypted.