Pearl Yedidia’s Post

Could it be that the regularization problem in Quantum Field Theory actually be of a more fundamental mathematical nature? The paper below relates QFT regularization, to Ramanujan's famous -1/12 result, the Riemann zeta function and divergent infinite series. Worth a watch. The paper: https://lnkd.in/gkTtvxQU #featurenotabug

A interesting paper about Kolmogorov & Arnold theorem challenges Multi Layer Perceptrons. These so called KANs have activation functions that are not constant like in MLPs, instead they can be flexible, which opens a whole new range of possibilities. Interesting!

【Mathematical Modeling of Possibility Markov Chains by Possibility Theory】 Full article: https://lnkd.in/gSUJ6Vuw (Authored by Yoshiki Uemura, et al., from Analog Image Technology Development Laboratory (Japan), etc.) This paper takes up the entity efficiency evaluation problem as a case study of the posterior non-discriminable production possibility region and mentions Fuzzy DEA with fuzzy constraints, discusses the case study of the ex-ante non-discriminable event setting, and introduces the measure of the fuzzy number and the equality relation and attempt to model the #possibility_Markov_chain mathematically. #Ergodic_Condition #Direct_Sum_State 

NeRF proves to be very effective in view synthesis. Given a set of images of a scene, it can synthesize new photorealistic images taken from new points of view. NeRF, unfortunately, requires a large set of images, while it usually struggles in few-shot settings, i.e., with small sets. In our paper presented at the 2024 International Conference on 3D Vision we address this issue by introducing CombiNeRF, a framework that synergically combines different regularization techniques, some of which are novel, to allow NeRF to produce accurate results also in few-shot settings. Experiments on public datasets show that CombiNeRF generally outperforms both vanilla implementations of NeRF and other recent regularization techniques. With Matteo Bonotto, Luigi Sarrocco, Daniele Evangelista, and Marco Imperoli. Paper: https://lnkd.in/dB6hHjh4 Code: https://lnkd.in/dh8XRTjj Video: https://lnkd.in/dAqa98TP

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Towards Understanding Inductive Bias in Transformers: A View From Infinity Itay Lavie, Guy Gur-Ari, Zohar Ringel Abstract We study inductive bias in Transformers in the infinitely over-parameterized Gaussian process limit and argue transformers tend to be biased towards more permutation symmetric functions in sequence space. We show that the representation theory of the symmetric group can be used to give quantitative analytical predictions when the dataset is symmetric to permutations between tokens. We present a simplified transformer block and solve the model at the limit, including accurate predictions for the learning curves and network outputs. We show that in common setups, one can derive tight bounds in the form of a scaling law for the learnability as a function of the context length. Finally, we argue WikiText dataset, does indeed possess a degree of permutation symmetry. #machinelearning

Maybe you are familiar with the fact that Srinivasa Ramanujan and G.H. Hardy found a formula for the number of partitions of integers, as dramatized in "The Man Who Knew Infinity". The content of this video on Abelian groups is related to that! #ramanujan #math #maths #mathematics #grouptheory #abstractalgebra #mathematicseducation #iteachmath #infinity #infinityisreallybig #billkinney #billkinneymath https://lnkd.in/gUp7pWUG

Read #NewPaper: "Tunneling between Multiple Histories as a Solution to the Information Loss Paradox" by Pisin Chen et al. See more details at: https://lnkd.in/gjYnZzDF #blackhole #Hawkingevaporation #informationlossparadox #entanglemententropy #Pagetime

What is information? From Wheeler's theory of "it from bit" to Hawking's black hole information paradox, information keeps popping up in quantum theory. Let's look at a new way to define this. Tomorrow, we'll have Iago da Silva Rossetto lead the discussion on "Constructor theory of information" at Y225a (Riihi) and on Zoom (https://lnkd.in/gF6eNqBq), from 17:00 onwards. Paper: https://lnkd.in/g-5ud-2D

#BinaryBasics: The binary system uses only two digits, 0 and 1. Each digit represents a power of 2. Start from the right, each place value doubles. It's an easy way to express information using a series of on/off or true/false states. #PowerofTwo #DigitalLanguage #BinarySystem