From my experience of working in this problem domain for the last year, I'd say it is pretty powerful but the "too good to be true part" comes from that EML buys elegance through exponential expression blow-up. Multiplication alone requires depth-8 trees with 41+ leaves i.e. minimal operator vocabulary trades off against expression length. There's likely an information-theoretic sweet spot between these extremes.

It's interesting to see his EML approach whereas mine was more on generating a context sensitive homoiconic grammar.

I've had lots of success combining spectral neural nets (GNNs, FNOs, Neural Tangent Kernels) with symbolic regression and using Operad Theory and Category Theory as my guiding mathematical machinery

While I'm really enjoying this paper, I think you are way overstating the significance here. This is mathematically interesting, and conceptually elegant, but there is nothing in this paper that suggests a competitive regression or optimisation approach.

I might have misunderstood, but from the two "Why do X when you can do just Y with EML" sentences, I think you are describing symbolic regression, which has been around for quite some time and is a serious grown-up technique these days. But even the best symbolic regression tools do not typically "replace" other regression approaches.

> Why use splines or polynomials or haphazardly chosen basis functions if you can just fit (gradient descent) your data or wave functions to the proper computational EML tree?

Same reason all boolean logic isn't performed with combinations of NAND – it's computationally inefficient. Polynomials are (for their expressivity) very quick to compute.

> Why use splines or polynomials or haphazardly chosen basis functions if you can just fit (gradient descent) your data or wave functions to the proper computational EML tree?

Because the EML basis makes simple functions (like +) hard to express.

Not to diminish this very cool discovery!

> I'm still reading this, but if this checks out, this is one of the most significant discoveries in years.

It seems like a neat parlour trick, indeed. But significant discovery?

The compute, energy, and physical cost of this versus a simple x+y is easily an order of magnitude. It will not replace anything in computing, except maybe fringe experiments.

I can't say I'm surprised at this result at all, in fact I'm surprised something like this wasn't already known.

Given this amazing work, an efficient EML operator HW implementation could revolutionize a bunch of things. So the next thing might be an efficient EML HW implementation.

This isn't all that significant to anyone who has done Calculus 2 and knows about Taylor's Series.

All this really says is that the Taylor's expansions of e^x and ln x are sufficient to express to express trig functions, which is trivially true from Euler's formula as long as you're in the complex domain.

Arithmetic operations follow from the fact that e^x and ln x are inverses, in particular that e^ln(x) = x.

Taylor's series seem a bit like magic when you first see them but then you get to Real Analysis and find out there are whole classes of functions that they can't express.

This paper is interesting but it's not revolutionary.

What URL should we change it to?