Circuit and method for estimating gradients

A circuit for implementing a N-dimensional gradient for a function f(), wherein N is greater than one, comprising:

• input means for receiving a plurality of input signals y.sub.i (t) and noise signals n.sub.i (t), where i represents the component of a signal and each of the noise signals n.sub.i (t) is independent and uncorrelated to the noise signals corresponding to other components;
• coupling means for combining an input signal and a noise signal of the same component to produce a combined signal for each component;
• means for determining an output signal of f() based on the combined signals input;
• N sub-circuits for determining a gradient estimate for the input signal of each component, each sub-circuit receiving as input the output of the function f() and the corresponding noise signal for the sub-circuit component, each sub-circuit comprising;
• a scale factor, coupled to receive the output of the function f() and outputting a scaled signal,
• a first differentiator for generating a derivative of the noise signal,
• a second differentiator for generating a derivative of the scaled signal,
• a multiplier for determining a correlation between the differentiated noise signal and the differentiated scaled signal, and
• a low pass filter for filtering the correlated signal to produce a gradient derivative for the corresponding dimension, wherein N derivative estimates for the N input signals are generated.

A method for implementing a N-dimensional gradient function for a function f(), said method comprising the steps of:

• inputting at least one input signal y.sub.i (t) and noise signal n.sub.i (t), where i represents a component of the signal;
• combining the input signal and a noise signal of the same component to produce a combined signal for each component;
• determining an output of the function f() based upon the combined signals input;
• generating a gradient estimate for the input signal of each component, based upon the output of f() and the corresponding noise signal of the component, comprising the steps of;
• correlating the output of the function and the noise signal, and
• filtering the correlated output to produce a gradient component for the dimension;
• such that N derivative estimates for the N input dimensions are generated.

A method for implementing a N-dimensional gradient function for a function f(), wherein N is greater than one, said method comprising the steps of:

• inputting a plurality of input signals y.sub.i (t) and noise signals n.sub.i (t), where i represents a component of the signal and each of the noise signals n.sub.i (t) is independent and uncorrelated to the noise signals corresponding to other components;
• combining the input signal and a noise signal of the same component to produce a combined signal for each component;
• determining an output of the function f();
• generating a gradient estimate for the input signal of each component, based upon the output of f() and the corresponding noise signal of the component, comprising the steps of;
• scaling the output of f() by a scale factor to produce a scaled output,
• differentiating the scaled output,
• differentiating the corresponding noise signal for the component,
• correlating the differentiated scaled output and the differentiated noise signal,
• low pass filtering the correlated output to produce a derivative estimate for the component;
• such that N derivative estimates for the N input dimensions are generated.

In a very large scale integration (VLSI) circuit, a circuit for implementing an N-dimensional gradient descent for minimizing an on-chip function f(), said circuit receiving N component noise signals n.sub.i (t) and N component input signals y.sub.i (t) and using the noise signals for estimating a gradient of an error measure, said circuit comprising:

• capacitive coupling means for combining an input signal and a noise signal of the same component to produce a combined signal for each component;
• means for determining an output of f() based on the combined signals input;
• N sub-circuits for determining a gradient estimate for the input signal of each component, each sub-circuit receiving as input the output of the function f() and the corresponding noise signal for the sub-circuit component, each sub-circuit comprising;
• a scale factor, coupled to receive the output of the function f() and outputting a scaled signal,
• a first differentiator for generating a derivative of the noise signal,
• a second differentiator for generating a derivative of the scaled signal,
• a multiplier for computing a correlation between the differentiated noise signal and the differentiated scaled signal, and
• an integrator for filtering the correlated signal to produce a derivative estimate for the corresponding component;
• wherein N derivative estimates for the N input signals are generated.