  Currently there has been increasing demand for real-time training on
resource-limited IoT devices such as smart sensors, which realizes standalone
online adaptation for streaming data without data transfers to remote servers.
OS-ELM (Online Sequential Extreme Learning Machine) has been one of promising
neural-network-based online algorithms for on-chip learning because it can
perform online training at low computational cost and is easy to implement as a
digital circuit. Existing OS-ELM digital circuits employ fixed-point data
format and the bit-widths are often manually tuned, however, this may cause
overflow or underflow which can lead to unexpected behavior of the circuit. For
on-chip learning systems, an overflow/underflow-free design has a great impact
since online training is continuously performed and the intervals of
intermediate variables will dynamically change as time goes by. In this paper,
we propose an overflow/underflow-free bit-width optimization method for
fixed-point digital circuit of OS-ELM. Experimental results show that our
method realizes overflow/underflow-free OS-ELM digital circuits with 1.0x -
1.5x more area cost compared to an ordinary simulation-based optimization
method where overflow or underflow can happen.
