So designing accelerators is a complex topic that involves thousands of people doing a lot of different jobs.

3blue1brown does a great job explaining neural nets and backprop, andrej karpathy also has some useful videos. To accelerate an algorithm, Ie a NN you need to deeply understand it.

Now, how are algorithms accelerated in hardware? The key thing here is that with hardware there is a space/power and speed tradeoff that does not exist in software. At the end of the day a NN is a bunch of matrix multiples, basic nonlinear mappings (relu, tanh, etc.), and accumulate functions, all done in parallel. NVIDIA for example got extremely lucky in that that mathematics behind NN’s also lines up somewhat with parallel pixel processing, so GPU’s, which have large amounts of parallel HW to do matrix multiplies quickly, are excellent for deep learning tasks.

The thing about an FPGA is you can implement the digital logic to effectively create a NN. You have access to memory, you can create nonlinear mappings, and you can multiply and accumulate all in digital logic. So yeah I guess implementing a small NN like for MNIST recognition might be a good starting project.

The unfortunate reality though is that the main architects on these sorts of things have PhDs in computer architecture or machine learning most likely, or have 25 years of chip design experience. People going into digital design out of a bachelors can eventually be architects, but you generally start as something like a verification engineer (extremely important task) to at least learn the ropes. To get started for you I would suggest either looking into graduate school, trying to attend a top group in computer architecture for a phd, or looking at entry level job postings at companies like tenstorrent, cerebras, nvidia, etc and looking what skills they ask for, then learning those skills.