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steppion An end to pop?

Thanks for the recommendations. All of my music equipment is in storage now, but I hope to set up a small studio later this year. Will definitely check this stuff out.

steppion An end to pop?

I’ve recorded at home with a similar setup. Getting things to sound just right takes a lot of effort and tinkering though which I just don’t have time for due to the demands of work and family. I might have a couple hours per week to devote to music. If I could go from writing a song to making a professional sounding recording in a couple hours, that would be amazing. This isn’t a hypothetical either. I’m an ML researcher and plan to experiment with stuff like this when I have time. Making it stupid easy to produce professional sounding recordings would absolutely be democratizing in my opinion.

steppion An end to pop?

A Radiohead album is an incredibly sophisticated feat of audio engineering requiring a team of people beyond the band itself to make. The production costs are substantial. It takes more than just practicing enough to make something like that. If AI gets to the point where I can record something in my bedroom with similar production values, I’d count that as democratization.

steppion Permutation Group Visualizer

D1 and D2 are a little weird. The way they’re usually defined, they can’t be defined as subgraphs of S1 and S2 respectively. See this relevant stackexchange answer [0].

By the symmetry of the n-gon you should, in this case, think of the group of all the isometries of the plane that fix the outline of the n-gon. For n=1 there are two such isometries, namely the identity and the reflection through the midline.

What’s being shown in the linked visualizer is actually the action of D2 on the labeled vertices of a 2-gon. I suspect two identical generators are shown because this is how each of the two generators of D2 (180 degree rotation and reflection about midpoint of 2-gon) act on the vertices.

[0] https://math.stackexchange.com/questions/470570/the-small-di...

steppion Permutation Group Visualizer

Yes, checkout the Steinhaus-Johnson-Trotter algorithm [0].

[0] https://en.m.wikipedia.org/wiki/Steinhaus%E2%80%93Johnson%E2...

steppion Editors quit top neuroscience journal to protest against open-access charges

Researchers do post PDFs on their websites, and on preprint servers like the arXiv, bioaRxiv, etc. Unfortunately, publishers act like gatekeepers towards career progress in academia. Climbing the ladder depends on getting publications in high impact journals and getting your papers cited by other publications. Competition for academic jobs and funding is already very high, and anyone who refuses to play the game will most likely fall behind.

steppion New Orleans teenagers found a new proof of the Pythagorean Theorem

This is a really great book. It’s very accessible but the insights can also be appreciated by a mathematically sophisticated audience. I’m particularly fond of Chapter 11 on understanding complex analytic functions and the part in Chapter 2 that gives a very clear explanation why the determinant formula gives the (signed) volume of the parallelepiped determined by the column vectors of a matrix.

steppion The perils of polishing old Fortran libraries

This is tricky, but it is at least a PEP 8 violation to compare a Boolean expression to True or False with ==, and a linter will complain. Programming in Python without a linter can be perilous in general.

steppion Kelly ‘Aloria’ Lum has died

Not all medications for bipolar are zombifying, though it took me 10 years to find something that worked well. On Lamotrigine I’ve been largely symptom free for nearly 7 years now, with few if any noticeable cognitive side effects. The problem with untreated bipolar is that it can be a progressive degenerative condition. It seems to have a physical component involving immune disregulation and neuroinflammation (mediated by life stress and exposure to pathogens) which medication can help. I’d strongly urge anyone in the early stages of illness who thinks they can manage on their own to seek help and try different medications until they find something that works for them.

steppion In Namibia, lions are king of the beach

"When I was your age I was before the mast on a square rigged ship that ran to Africa and I have seen lions on the beaches in the evening."

[…]

He no longer dreamed of storms, nor of women, nor of great occurrences, nor of great fish, nor fights, nor contests of strength, nor of his wife. He only dreamed of places now and of the lions on the beach.

Ernest Hemingway. The Old Man and the Sea.

I’d read this long ago, and never gave a thought to it that this detail must have been rooted in reality. It’s interesting to learn what the lions were doing there.

steppion Most data work seems fundamentally worthless

Yes, completely agree, I omitted the part about not just modeling binary outcomes for the sake of brevity. I was even considering linking the article Capital One: Exploiting an Information-Based Strategy [0], showing that one of Capital One's innovations was successfully modeling more complicated outcomes like profitability.

[0] https://www.computer.org/csdl/proceedings-article/hicss/1998...

steppion Most data work seems fundamentally worthless

Yes, that's a common approach. You can take a dataset of consumer features at the point in time when loans were opened along with information about the loan outcomes and try to predict the loan outcomes. You can't just take a kitchen sink approach with the features though because there are regulations that demand a level of explainability. To get a sense of the basics, I think the book Intelligent Credit Scoring by Naeem Siddiqi [0] is very good.

[0] https://towardsdatascience.com/book-review-intelligent-credi...

steppion Most data work seems fundamentally worthless

Working in the ML/data space and have been fortunate to have largely steered clear of this problem so far. My heuristic when evaluating potential jobs is only to consider positions where the output of statistical analysis and machine learning models has a clear and immediate impact within the organization, while avoiding adtech for ethical reasons and because of concerns toxic work could enable a toxic environment.

Jobs like this exist, though you may have to take a pay cut compared to the bullshit. My first job after finishing my PhD was as a staff scientist in an academic lab using ML engineering + data science to support scientific research. There seems to be a fair number of grant supported jobs like this and pay isn’t terrible. Just under or just at 6 figures. You can make more in industry, but scientific work feels very meaningful.

Now I’m working in credit risk modeling, something I never expected to be doing, but so far it’s been a good fit. The models are applied directly in decision making for the business, and there’s a real incentive to get everything right because mistakes could harm real people’s lives. The team I’m on is strong and ethically sound and I feel good about what I’m doing.

For anyone in the data space who’s despairing about the state of the industry, non-bullshit jobs do exist, you just have to look for them, and use your judgment when scoping out new roles.

steppion Physics and Mathematics Self-Study Project

I did something like this and ended up just substituting graduate classes for my math and physics requirements while taking regular undergraduate classes for everything else. I made a lot of great friends and was not the only undergrad in those graduate classes. I don't see it as a curse at all. I think the author will be fine if he stays motivated and finds the right peers and the right path.

steppion A Critical Field Guide for Working with Machine Learning Datasets

This hasn’t been my experience. I don’t think this knowledge has been lost and it’s often still applied when incentivized, such as when quality output of machine learning models serves an immediate business need, or in scientific applications of machine learning. By your reference to web scraping I assume your referring to datasets for large language models, but I don’t think the kitchen sink approach is applied out of ignorance, but out of a principled decision to forgo data hygiene in order to collect datasets large enough to feed such large models. Also, strictly speaking, one only needs to apply the critical approach when constructing and using validation datasets, and it’s typical for larger noisier training datasets to outperform smaller more rigorous ones when models trained on both are tested on carefully constructed validation datasets.

steppion Polynomial interpolation

Right, and if we are trying to get all coefficients and are thus performing the polynomial multiplications symbolically, then performing the multiplications naively will take O(n^2) time but using FFT allows it to be done in O(n log n) time.

steppion Polynomial interpolation

I think you're talking about evaluating the interpolating polynomial at a single value, but others are talking about getting all of the coefficients of the interpolating polynomial.

steppion Polynomial interpolation

Example please?

steppion Polynomial interpolation

That’s pretty neat. I didn’t even think of finite fields when I made my other comment. Another example where mathematical curiosities prove useful in cryptography.

steppion Polynomial interpolation

There's an aside in the linked section of CLRS that mentions that FFT based polynomial multiplication can be used for fast evaluation of Lagrange interpolation. I'm not aware of applications though, Lagrange interpolation isn't numerically stable; there are better interpolation methods for large datasets. It's more of a mathematical curiosity.

steppion Just know stuff (or, how to achieve success in a machine learning PhD)

Knowing things is good, but I think the real benefit of a PhD is in developing the skill to learn new things quickly and fill in any gaps as needed. It’s important to get practice learning many things in depth but the goal isn’t to become a storehouse of knowledge, it’s to develop the ability assimilate existing knowledge and apply it to figuring new things out.

The amount of topics I’ve studied in depth dwarfs this list (and the same is certainly true of its author) but the set of things I could teach a class on today without preparation is much smaller. The important thing is that if I have a problem, I can use the impressions from all I’ve learned before to get a sense of where to look next. My memory isn’t great but it doesn’t matter because I can refresh, learn, and figure things out as needed.

steppion Pattern Theory: The Mathematics of Perception (2002)

Along those lines, have you ever checked out the book Neurocomputing, Foundations of Research [0]? It's a compendium of old foundational papers that I think would be up your alley.

Researchers will find Neurocomputing an essential guide to the concepts employed in this field that have been taken from disciplines as varied as neuroscience, psychology, cognitive science, engineering, and physics. A number of these important historical papers contain ideas that have not yet been fully exploited, while the more recent articles define the current direction of neurocomputing and point to future research. Each article has an introduction that places it in historical and intellectual perspective.

[0] https://mitpress.mit.edu/9780262510486/neurocomputing/

steppion Pattern Theory: The Mathematics of Perception (2002)

Would you consider doing a write-up somewhere after getting further into your investigation of pattern theory? I'd certainly be interested in a distillation of any insights you find and I imagine others would too.

steppion Pattern Theory: The Mathematics of Perception (2002)

Having once studied just enough algebraic geometry to appreciate the true excellence of Mumford’s work in the field I’ve wondered before if I should study his Pattern Theory book [0] to mine it for insights that the ML community may have missed as a whole. I'd forgotten about that though.

Has anyone here worked through it? It seems like much of it is rooted in methods that have kind of fallen by the wayside due to the incredible success of modern techniques. I’d also be very interested to know David Mumford’s thoughts on modern deep learning and how he thinks it fits into his pattern theory framework. It looks like he goes into this to some extent in a 2019 blog post on whether AI can achieve consciousness [1] and another on the convergence between ML methods and the human brain [2].

[0] https://www.routledge.com/Pattern-Theory-The-Stochastic-Anal...

[1] https://www.dam.brown.edu/people/mumford/blog/2019/conscious...

[2] https://www.dam.brown.edu/people/mumford/blog/2020/Astonishi...

steppion Ask HN: Math books that made you significantly better at math?

Some favorites below. Books 0-3 are accessible. The remaining books are more difficult but I'd highly recommend them to math students.

0. Jan Gullberg, Mathematics, From the Birth of Numbers. A highly accessible popular survey on different branches of higher mathematics. I read this over the Summer between high school and starting my undergraduate degree. It's what made me want to study math. Previously I'd wanted to be a guitar player, but had to find a new ambition after an injury left me unable to play.

1. The high school mathematics series by Israel Gelfand. Algebra, Trigonometry, The Method of Coordinates, and Functions and Graphs. I didn't have much mathematics background in high school, but working through these really solidified my grasp on the basics.

2. George Polya. How to Solve it. A short book giving excellent high level advice on mathematical problem solving.

3. George E. Andrews, Number Theory. I worked through this freshman year contemporaneously with my first proof based class on simple logic and set theory. A very beautiful and accessible introduction to basic number theory. The combinatorial/geometric proofs of Fermat's Little Theorem and Wilson's Theorem are lovely. It also includes a very nice proof of Chebyshev's theorem on the asymptotic density of primes and even the Rogers-Ramanujan identities for integer partitions.

4. Vladimir Arnold, Ordinary Differential Equations: Undergrad ODE classes are often taught in a cookbook fashion and if so, don't offer much enlightenment. This book explains what's going on at geometrical level. I didn't appreciate ODEs until I read this. See https://www.uni-muenster.de/Physik.TP/~munsteg/arnold.html for Arnold's views on teaching mathematics.

5. E.C. Titchmarsh The Theory of Functions: Recommended by my undergraduate advisor because he noticed that I liked reading older books. It contains sections on complex analysis and real analysis with measure theory, but I've only read the complex analysis sections. It's not for everyone, if I recall correctly, there is not a single picture, but it is very lively and has a lot of material you won't find in a standard complex analysis book, including Dirichlet series. Excellent as a supplement to a standard complex analysis book.

6. George Polya. Mathematics and Plausible Reasoning. An excellent expansion on Polya's ideas on How to Solve it. While the goal is to seek rigorous proofs, to get there it's powerful to be able to think based on intuition, heuristics, and plausible reasoning. A lot of math exposition is theorem/proof based and doesn't help develop these skills. In a similar vein, see also Terence Tao's classic post There's more to mathematics than rigour and proofs https://terrytao.wordpress.com/career-advice/theres-more-to-....

7. H.S.M Coxeter, An Introduction to Geometry. A book of very beautiful classical geometry. Something typically not touched on at all in a typical mathematics curriculum.

steppion A New Formula for the Determinant

From my read of the paper. This new formula also gives an exponential time algorithm. It’s not of interest as a practical method for computing determinants. It does however have interesting geometric and combinatorial properties and they used it to give new bounds for the tensor rank and Waring rank of a determinant respectively. You can think of these ranks loosely as measures of the “complexity” of a determinant (but not in the sense of computational complexity). These ranks are of interest in pure mathematics but I can’t really say more about them because it’s been too many years since I’ve studied related math.

steppion To Explain or to Predict? (2010) [pdf]

I think I would have eventually pushed through the dip, but I ended up badly injuring the elbow on my fretting hand side. This was when I was around 20. It was maybe for the best. I ended up getting into math instead which has lead me down an interesting path.

My impression is that real mastery requires periods of flow and periods of deliberate thought. When performing you want to flow, but practice should also incorporate the conscious and deliberate. Having the meta-cognition to reflect on where you are, where you want to be, and having the ability to plan how to get there are very important. I think this holds true beyond music.

steppion To Explain or to Predict? (2010) [pdf]

It’s an interesting example. I experienced something similar learning to play guitar by ear from a young age and then going back to learn proper music theory as an adult. I’d learned to improvise over chords in any key just by feel, without really understanding what was going on. My playing actually became more wooden as a result of thinking things through more. It seems like a lot of human learning is based on statistical/associative pattern matching like this and real expertise requires our brains to master both prediction and explanation and combine them skillfully.

steppion To Explain or to Predict? (2010) [pdf]

I think this paper really cuts to the heart of the distinction Leo Breiman was exploring in his classic Statistical Modeling: The Two Cultures [0]. The idea here is that real distinction is not essentially in terms of assumptions or philosophy, but in terms of goals. The boundaries are more fuzzy when it comes to the methods themselves, and there are always tradeoffs between building a model to predict or building a model to try to understand the underlying phenomena.

[0] https://projecteuclid.org/journals/statistical-science/volum...

steppion Bayesian statistics and machine learning: How do they differ?

Very cool. I’ve never tried fewer than 5. Will definitely keep that in mind. Yes, I know that paper.