In-memory mechanical computing

Abstract

Mechanical computing requires matter to adapt behavior according to retained knowledge, often through integrated sensing, actuation, and control of deformation. However, inefficient access to mechanical memory and signal propagation limit mechanical computing modules. To overcome this, we developed an in-memory mechanical computing architecture where computing occurs within the interaction network of mechanical memory units. Interactions embedded within data read-write interfaces provided function-complete and neuromorphic computing while reducing data traffic and simplifying data exchange. A reprogrammable mechanical binary neural network and a mechanical self-learning perceptron were demonstrated experimentally in 3D printed mechanical computers, as were all 16 logic gates and truth-table entries that are possible with two inputs and one output. The in-memory mechanical computing architecture enables the design and fabrication of intelligent mechanical systems.

Fig. 1. Schematic of an in-memory mechanical computing system.

a An in-memory mechanical computing system consisting of binary mechanical memory units and their interactions (i.e., shifter register, XNOR, and perceptron operations). b Its computing process as the state evolution of the memory units. c Interaction serving as a shifter register. d Interaction serving as an XNOR gate, together with its truth table. e Interaction serving as a perceptron operation.

Fig. 2. Mechanical shift register.

a Structural design for mechanical shift register operation, comprising a binary mechanical memory unit (bi-stable buckled beam), links, springs, and support. The boundary condition of the components is also marked. The memory unit in (i) and (ii) is in state 0 and 1, respectively. b The theoretical compressive force-displacement response of the buckled beam in a. c Mechanical register structure receiving the time signal defined as the force F. For (i) and (ii), the memory unit is at state 0 and 1 before being excited by F, respectively. d The theoretical compressive force-displacement response of the buckled beam in c and e. e Mechanical register structure receiving the time signal and the displacement load Δ. For (i) and (ii), the memory unit is at state 0 and 1 before being excited, respectively. f State transformation map of the mechanical register unit.

Fig. 3. Mechanical XNOR and perceptron operations.

a Structural design for mechanical XNOR operation before receiving a time signal. It consists of mechanical memory units, springs, balanced bars, links, slider bar, slider block, and support. The state of the left two memory units is (0, 0) and serves as input. b The mechanical XNOR structure in a after receiving a time signal. The right memory unit serves as output and will be state 1. c The mechanical XNOR structure with input (1, 0) before receiving a time signal. d The mechanical XNOR structure in c after receiving a time signal. It will output 0. e and f Construction of the mechanical perceptron operation. The input is the state of the left memory units before receiving the time signal, (1,0) in e and (1,1) in f. g Definition of the critical stiffness k* which determines whether the compressed buckled beam will become state 1 after releasing the time signal. If k > (<) k*, the compressed beam arches to the right (left) and becomes state 1 (0) after releasing the time signal.

Fig. 4. Mechanical binary neural network.

a Binary neuron model. b An equivalent mechanical binary neural model corresponding to a. Once the system receives a time signal, it executes the calculation below. c A binary neural network with an input, a hidden, and an output layer. d An equivalent mechanical binary neural network of c. e The mechanical binary neural network in the experiment. f Three typical computation steps when the mechanical binary neural network is used for judging the parity of input Morse code numbers. g The error evolution during the training process for a BNN to distinguish labeled images of handwritten digits.

Fig. 5. Mechanical self-learning perceptron.

a A perceptron model with one input and bias. The weight and bias can be updated in the backward propagation process. b An equivalent mechanical self-learning perceptron with one input x and bias. The mechanical interactions related to the backward propagation process are represented by the symbols shown in brown. The data selector outputs the input data corresponding to the control information c. The mechanical memory x can also serve as a switch to determine whether a time signal can be transmitted to a certain part of the system. c A self-learning mechanical perceptron with one input and bias in the experiment. The functions of some typical parts are marked. d Four computation steps in a self-learning time period of the mechanical perceptron. e A typical evolution process of the mechanical self-learning perceptron. It can gradually acquire the target input-output relationship in a supervised learning paradigm. Here, the target input-output relationships are: input x = 0 output y = 1 and input x = 1 output y = 1. f, g The evolution of error and weight during the learning process for the mechanical perceptron with 10 inputs for case 1, 20 inputs for case 2, and 30 inputs for case 3.