Bit-Ordered Multiplier-Accumulator for Single-Cycle Vector-Matrix Summation
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Solution Overview
Problem
Conventional vector-matrix multiplication operations require significant processing resources and energy, and are inefficient in terms of clock cycles and space due to their digital or hybrid analog implementations.
Innovation Solution
The method involves converting digital input vectors into analog signals using one-bit digital-to-analog converters (DACs) and performing vector-matrix multiplication using an analog vector matrix multiplier, with bit-ordered weighted summation achieved in a single clock cycle through charge accumulation and redistribution in an analog summation circuit.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If conventional digital or hybrid analog componentry is used for vector-matrix multiplication, then the operation can be performed with standard digital circuits, but it consumes significant processing resources and energy while requiring a relatively large number of clock cycles and large area of space
Solution Approach 1:
The patent replaces digital computational systems with an analog physical system that performs vector-matrix multiplication through natural physical processes. Digital input vectors are converted to analog signals, and the multiplication operation is performed using analog circuitry that inherently computes the result through continuous signal processing, eliminating the need for sequential digital computation steps and significantly reducing energy consumption.
Solution Approach 2:
The patent changes the fundamental parameter domain from digital discrete values to analog continuous signals. By representing input vectors as analog signals and performing multiplication in the analog domain, the system achieves parallel computation that completes in a single clock cycle rather than requiring multiple sequential digital operations, thereby improving productivity while reducing energy use.
2Loss of time
If conventional digital or hybrid analog componentry is used for vector-matrix multiplication, then the operation can be implemented with standard circuits, but it requires a relatively large number of clock cycles to complete
Solution Approach 1:
The patent replaces sequential digital computation with parallel analog computation. The analog vector matrix multiplier performs the entire vector-matrix multiplication operation simultaneously through continuous signal processing, reducing the time required from multiple clock cycles to a single clock cycle, despite the increased complexity of the analog circuitry.
3Area of stationary object
If conventional digital or hybrid analog componentry is used for vector-matrix multiplication, then the operation can be performed with standard digital logic, but it requires a relatively large area of space to implement
Solution Approach 1:
The patent transitions from digital discrete parameter representation to analog continuous parameter representation. This allows the computation to be performed in parallel using analog signals, achieving high computation efficiency in a compact area by utilizing the continuous nature of analog physics rather than requiring extensive digital logic arrays.
4Measurement precision
If bit-ordered binary-weighted analog summation is used, then the weighted summation can be performed in a single clock cycle through charge accumulation, but it requires precise analog circuitry for charge storage and redistribution
Solution Approach 1:
The patent introduces capacitors as intermediary energy storage elements that hold analog signals during the computation process. These capacitors temporarily store charge representing the product values, allowing precise analog summation to be performed by redistributing charge among capacitors according to binary weights, thereby achieving accurate results while managing the complexity of analog circuitry.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
This approach reduces the number of clock cycles required for vector-matrix multiplication by up to 25.6 times compared to conventional analog designs, while also providing significant space savings and efficient computation, allowing for faster and more energy-efficient operations.
Implementation Method 1
The bit-ordered weighted summation can be performed based on an amount of charge stored by the summation circuit
Implementation Method 2
The bit-ordered weighted summation can be performed in a single clock cycle through charge accumulation and redistribution in an analog summation circuit
Data Source
AI summary
Various arrangements for performing vector-matrix multiplication are provided here. Digital input vectors that include binary-encoded values can be converted into a plurality of analog signals using a plurality of one-bit digital to analog converters (DACs). Using an analog vector matrix multiplier, a vector-matrix multiplication operation can be performed using a weighting matrix for each bit-order of the plurality of analog signals. For each performed vector-matrix multiplication operation, a bit-ordered indication of an output of the analog vector matrix multiplier may be stored. A bit-order weighted summation of the sequentially performed vector-matrix multiplication operation may be performed.