"Why yet another book on learning theory? ...the main reason is that I felt that the current trend in the mathematical analysis of machine learning was leading to overly complicated arguments and results that are often not relevant to practitioners. Therefore, my aim was to propose the simplest formulations that can be derived from first principles, trying to remain rigorous without overwhelming readers with more powerful results that require too much mathematical sophistication."
From my own reading and experience on the mathematical analysis approach of this "training goes brrr" approach, I thought the material in Chapter 12, Overparameterized Models, was interesting and coherent with 12.2.4 Linear Regression with Gaussian Projections being an especially elegant explanation. It would be interesting to hear if you had read/skimmed/purused this section and found it wanting etc.
This is the PDF of the following 2011 book focused on FFTs and fast arithmetic for both real numbers and finite fields. https://www.amazon.com/Matters-Computational-Ideas-Algorithm...
The author is Jörg Arndt: born 1964 in Berlin, Germany. Study of theoretical physics at the University of Bayreuth, and the Technical University of Berlin, Diploma in 1995. PhD in Mathematics, supervised by Richard Brent, at the Australian National University, Canberra, in 2010.
Interesting that the underlying model, a LoRA fine-tune of Qwen2.5-Coder-32B, relies on synthetic data from Claude[1]:
But we had a classic chicken-and-egg problem—we needed data to train the model, but we didn't have any real examples yet. So we started by having Claude generate about 50 synthetic examples that we added to our dataset. We then used that initial fine-tune to ship an early version of Zeta behind a feature flag and started collecting examples from our own team's usage.
...
This approach let us quickly build up a solid dataset of around 400 high-quality examples, which improved the model a lot!
I checked the training set, but couldn't quickly identify which were 'Claude' produced[2]. Would be interesting to see them distinguished out.
Defer to other experts, but (briefly) normalizing flows are a method for constructing complex distributions by transforming a probability density through a series of invertible transformations. Normalizing flows are trained using
a plain log-likelihood function, and they are capable of exact density evaluation and efficient sampling. See:
Laurent Dinh, David Krueger, and Yoshua Bengio. Nice: Non-linear independent components estimation. In ICLR Workshop, 2015. Link: https://arxiv.org/pdf/1410.8516
And for your direct question, the following paper "Efficient Bayesian Sampling Using Normalizing Flows to Assist Markov Chain Monte Carlo Methods" appears upon a superficial glance to be relevant. Link: https://arxiv.org/pdf/2107.08001
This actually seems like just a very clever market segmentation solution since the GPU was already limited to 8x PCIe lanes (its a laptop GPU see https://www.notebookcheck.net/NVIDIA-GeForce-RTX-4060-Laptop...). The 'addition' of the M.2 SSD makes it a unique offering. Limiting it to only one drive is another way to keep the thermal envelope down. Kudos to the Asus design and product development folks.
The paper, Trigger-Level Event Reconstruction for Neutrino Telescopes Using Sparse Submanifold Convolutional Neural Networks, is here https://arxiv.org/abs/2303.08812.
The crucial advantage of SSCNN are that they "replaces traditional convolutions with sparse submanifold convolutions" which operate "only on the non-zero elements" and creates efficiencies.
The author, David Mumford, is known for his distinguished work in algebraic geometry, and was awarded the Fields Medal in 1974. [2]
Pattern theory was formulated by Ulf Grenander to describe knowledge of the world as patterns. [3]
Prof. Mumford explains that "[s]everal essential ideas brought me to realize how Grenander's Pattern Theory was the right way to understand almost all cognitive skills and especially vision. One was the emphasis on pattern synthesis as well as pattern analysis." [0]. Second, "was that natural signals given by functions f vary not only by random additive perturbations but often by composition with random rearrangements of their domain. The resulting probability distribution in the vector space of signals is nothing like Gaussian. Its support is usually a twisted snakey submanifold. This puts the lie to all simplistic Gaussian pattern recognition algorithms." [0]. And third, "graphical structures were everywhere in the representations of ideas in cognitive domains" [0].
His most recent work seems to be "Pattern Theory, the Stochastic Analysis of Real World Signals" [1]
A more detailed source: https://www.pulitzer.org/winners/staff-quanta-magazine-new-y..., explaining "For coverage that revealed the complexities of building the James Webb Space Telescope, designed to facilitate groundbreaking astronomical and cosmological research."
An interesting take from Mike Pondsmith given his heavy involvement in the venture at the end of (at least in my opinion) well-written article: "[C]omparing the tabletop experience with its video-game incarnation, he noted that the latter doesn’t really compare to the former when it comes to self-expression. “You could be you in a tabletop game and bring all the stuff that you wanted to bring into it,” he said. “A tabletop game is limitless. A video game, by its very nature of how it’s designed, has some limits.” "
The paper itself is here: https://arxiv.org/abs/2111.09259 with the key conclusion that "Examining the evolution of human concepts using probing showed that many human concepts can be accurately regressed from the AZ network after training, even though AlphaZero has never seen a human game of chess, and there is no objective function promoting human-like play or activations" and "[t]he fact that human concepts can be located even in a superhuman system trained by self-play
broadens the range of systems in which we should expect to find human-understandable concepts"
A nice summary of the current understanding (from a lay perspective) on manifold "sameness".
From the article:
"But Freedman’s [1981] proof left open the “smooth” four-dimensional Poincaré conjecture, which says that any four-dimensional smooth manifold that is homotopy equivalent to the four-dimensional sphere is also diffeomorphic to the four-dimensional sphere. This is an even stronger statement than the one Freedman proved — since a diffeomorphism is a stronger form of equivalence than a homeomorphism — and one that mathematicians today have no idea how to settle.
This leaves them in the strange position of being unable to perform one of the most basic classification tasks of all: recognizing when a smooth four-dimensional manifold is really a sphere."
"Due to Facebook stopping announcing their DNS prefix routes through BGP, our and everyone else's DNS resolvers had no way to connect to their nameservers. Consequently, 1.1.1.1, 8.8.8.8, and other major public DNS resolvers started issuing (and caching) SERVFAIL responses.
But that's not all. Now human behavior and application logic kicks in and causes another exponential effect. A tsunami of additional DNS traffic follows.
This happened in part because apps won't accept an error for an answer and start retrying, sometimes aggressively, and in part because end-users also won't take an error for an answer and start reloading the pages, or killing and relaunching their apps, sometimes also aggressively."
This Economist article is from October of 2020. Peter Turchin is not a historian. He is instead in the Department of Ecology and Evolutionary Biology at the Universtiy of Connecticut. He advocates for a field of 'cliodynamics' which tries to apply math to meaningfully describe and predict social trends, especially large ones such as collapse. The Nature article from about decade ago: https://www.nature.com/articles/454034a
A large project he directs and uses to study this: http://seshatdatabank.info/seshat-about-us/
Sone of the work [0] has been criticized on methodological grounds [1] and some recent (2017) related work [2]. Finally, in his own words, a comparison of Psychohistory and Cliodynamics (2012) [3]
Francis Bach, the author, makes a good faith effort to explain exactly why this material is beneficial (see https://francisbach.com/my-book-is-out/):
"Why yet another book on learning theory? ...the main reason is that I felt that the current trend in the mathematical analysis of machine learning was leading to overly complicated arguments and results that are often not relevant to practitioners. Therefore, my aim was to propose the simplest formulations that can be derived from first principles, trying to remain rigorous without overwhelming readers with more powerful results that require too much mathematical sophistication."
From my own reading and experience on the mathematical analysis approach of this "training goes brrr" approach, I thought the material in Chapter 12, Overparameterized Models, was interesting and coherent with 12.2.4 Linear Regression with Gaussian Projections being an especially elegant explanation. It would be interesting to hear if you had read/skimmed/purused this section and found it wanting etc.