Science - Advancing Understanding with Interpretable and symbolic Machine Learning using Kolmogorov-Arnold Networks

Amazing stuff!

"[machine learning models] ... But despite such successes, these data-driven approaches suffer a major drawback in that they are generally “black boxes” that offer no human-accessible understanding of how they make their predictions. This shortcoming also extends to the models’ inputs: It is often desirable to build known domain knowledge into these models, but the data-driven approach excludes that option. [Researchers] have now made a notable step toward addressing these challenges by developing a machine-learning method designed to discover simple, interpretable laws from data ... This method could potentially enable the automated discovery of the physical laws governing a wide range of systems. ...

KANs have since been used to parameterize multivariate functions via such a composition of sums and univariate functions and learn the univariate functions in this representation from a set of training data. Since the learned part of a KAN is a collection of univariate functions, one can potentially gain insight into the function represented by the KAN―and thus understand what the KAN has learned―by inspecting these univariate functions after training. This arguably makes KANs more interpretable than standard neural networks. ...

By necessity, these initial tests are toy experiments where the correct answer is already known. It will be exciting to see how KANs perform on problems of real scientific interest, where the correct physical laws are not yet known. Applied to such problems, this approach has the potential to significantly accelerate the scientific process. ..."

From the abstract:

"A major challenge of AI plus science lies in its inherent incompatibility: Today’s AI is primarily based on connectionism, while science depends on symbolism.
To bridge the two worlds, we propose a framework to seamlessly synergize Kolmogorov-Arnold networks (KANs) and science. The framework highlights KANs’ usage for three aspects of scientific discovery:
identifying relevant features,
revealing modular structures, and
discovering symbolic formulas.
The synergy is bidirectional: science to KAN (incorporating scientific knowledge into KANs), and KAN to science (extracting scientific insights from KANs).
We highlight major new functionalities in pykan:
(1) MultKAN, KANs with multiplication nodes,
(2) kanpiler, a KAN compiler that compiles symbolic formulas into KANs;
(3) tree converter, convert KANs (or any neural networks) into tree graphs.
Based on these tools, we demonstrate KANs’ capability to discover various types of physical laws, including conserved quantities, Lagrangians, symmetries, and constitutive laws."

Physics - Advancing Physical Understanding with Interpretable Machine Learning "A new artificial neural-network architecture opens a window into the workings of a tool previously regarded as a black box."

Kolmogorov-Arnold Networks Meet Science

KAN: Kolmogorov-Arnold Networks (I believe, this is the original work on KANs by the same first author Ziming Liu published in April 2024)

Notice MultKAN have additional multiplication nodes

How the famous Three Sisters survived (about traditional farming)

Recommendable!

Scientists Are So Blind

Posted: 8/28/2018

Trigger

Just read 3-D Cell Environment Crucial for Divvying Up Chromosomes – Find Could Help Explain Cancer Hallmark. It is very hard to believe that scientists only now realized that cell division (mitosis) does not function well in cells grown in a flat Petri dish as opposed to cells inserted into a living tissue. And this after more than 100 years of intensive research!

Similarities And Synergy

This reminds me that I recently blogged about following, similar discoveries:

1. Cell organelles have contact sites and tether together (here)
2. Human fascial system from head to toe (here)

It almost appears that scientists finally discover that the whole is greater than the sum of its parts or that by drilling down into ever more minute details obscures the view of the bigger picture (not seeing the forest for the trees).

Subatomic Particle Physics

Just today (8/28/2018) I read following news from Brookhaven National Laboratory: LHC Scientists Detect Most Favored Higgs Decay Scientists now know the fate of the vast majority of all Higgs bosons produced in the LHC. Quote: “Today at CERN, the Large Hadron Collider collaborations ATLAS and CMS jointly announced the discovery of the Higgs boson transforming into bottom quarks as it decays. This is predicted to be the most common way for Higgs bosons to decay, yet was a difficult signal to isolate because background processes closely mimic the subtle signal.” (emphasis added)

Yes, there was lots of excitement in 2012, when scientists at the  Large Hadron Collider (LHC) of CERN were able to detect the existence of this crucial particle. However, what are we actually dealing with here:

1. The all so important Higgs boson has a mean lifetime of about 1.6×10−22 s.
2. “Higgs bosons are only produced in roughly one out of a billion LHC collisions and live only a tiny fraction of a second before their energy is converted into a cascade of other particles.”
3. “Since its discovery in 2012, scientists have been able to identify only about thirty percent of all the predicted Higgs boson decays.”

To me, it appears that particle physics is going down a dead end. I have previously written some critical comments on particle physics (see e.g. here, here)

Like the once astonishing recognition of the duality of particle and waves, scientists have yet to make sense of the ever growing and more bizarre zoo of subatomic particles. Are they too missing the forest for the trees?

Like Gravity Or Synergy

Something is important is escaping scientists in their quest to further explain the universe we live in and beyond or life therein!

Guess, we have to wait for the next Galileo, Newton, or Einstein!