Sébastien Darses

Math. Assoc. Prof. (on leave) / Act. Int. Agent?
Research: Prob / Stat / Ant
👨‍🎓Teaching project

[Gabriel Peyré @gabrielpeyre]

The alpha version of my new book "Optimal Transport
for Machine Learners" is out, with in particular an online version with interactive figures
https://t.co/xEdZpMXgjx

[Guillaume Lample @ NeurIPS 2024 @GuillaumeLample]

🚀 We are hiring Research Interns !

We are looking for Master's and PhD students (final year) with a strong background in AI / ML / NLP who want to work on cutting-edge AI systems alongside Mistral AI researchers.

📍 Location: Paris, London, or Palo Alto
⏳ Duration: 4-6 months
🎓 For Master's students: opportunity to continue with a PhD at Mistral after the internship (via the CIFRE program).

Links below:

[Probability and Statistics @probnstat]

Eigenvalues of large random matrices are a central object of modern probability known as random matrix theory, which studies how the spectrum of a matrix with random entries behaves as its dimension grows. Remarkably, despite the randomness, the eigenvalues follow universal laws such as the semicircle law or Marchenko–Pastur law, allowing one to predict the distribution of variance and correlations in high-dimensional systems. In probability, these results explain fluctuations in complex interacting systems, from particle gases to queuing networks. In machine learning, the eigenvalues of data covariance matrices and neural network weight matrices reveal effective dimensionality, overfitting, and training dynamics, guiding practices like PCA, ridge regression, and deep network initialization. In real life, random matrix eigenvalues appear in wireless communication, where they determine channel capacity, in finance to separate signal from noise in correlation matrices of assets, and in physics to model energy levels of heavy nuclei, showing how order can emerge from apparent randomness.

Image: https://t.co/OlbyfMc2mp

[Physics In History @PhysInHistory]

Richard Feynman's way of learning ✍️

[Ken Ono @KenOno691]

I've spent my career thinking about hard math problems.

I am excited to share that I've joined Axiom @axiommathai as Founding Mathematician working with my former student @CarinaLHong.

AI for mathematical discovery in WSJ today.

[級数・積分bot @SeriesIntegral]

series 2-1 : 多重ゼータスター値の特殊値

[Frank Nielsen @FrnkNlsn]

Singular learning theory is a theory of machine learning of singular models, either non-identifiable models or having degenerate Fisher information matrix.

Regular non-singular statistical models are handled as manifolds and singular models as algebraic varieties

[Cliff Pickover @pickover]

Mathematics.

Coffee cup for caffeinated topologists.

[Paysages Mathématiques @paysmaths]

"Our notion of set is too vague for the continuum hypothesis to have a positive or negative answer." – Serge Lang (1927–2005), on Paul Cohen's result (proof of the independence of the continuum hypothesis).
#quote #mathematics #maths #math

[Paysages Mathématiques @paysmaths]

"My whole life, my ambition as a mathematician, or rather my joy and my passion, have always been to discover the obvious things." – Alexandre Grothendieck (1928-2014)
#quote #mathematics #math #maths

[Probability and Statistics @probnstat]

Trigonometry is crucial in real-world applications like GPS, which uses it for triangulation to find your location, and in computer graphics to rotate objects and calculate perspectives. In machine learning, its primary role is to represent cyclical data. Features like time of day or month of the year are encoded using sine and cosine functions. This transforms the data into a circular format, helping the model understand that 11 PM is close to 1 AM, which is vital for time-series forecasting and analyzing any wave-like data.

Image Source: https://t.co/qqcxUaEVJ4

[Paysages Mathématiques @paysmaths]

29 sept.1803: #CeJourLà naissance de Charles Sturm (†18/12/1855), mathématicien français connu pour avoir démontré le th qui porte son nom(calcul du nb de racines réelles distinctes d'un polynôme sur un intervalle donné) & pour la théorie de S.-Liouville
https://t.co/d1nQ5njUyc

[Pedro Domingos @pmddomingos]

Matrix multiplication is now a multi-trillion dollar business.

[Paysages Mathématiques @paysmaths]

"Mathematicians start with certain facts – which we call axioms – and deduce consequences, theorems. In physics, in a sense, it's the other way around: The physicists have a lot of facts, lots of relations [...]" – Stanislaw Ulam (1909–1984)
#quote #mathematics #physics #math

[Fermat's Library @fermatslibrary]

Square Roots

[The Math Flow @TheMathFlow]

Conic Sections.

[級数・積分bot @SeriesIntegral]

series 4-7 :

[Frank Nielsen @FrnkNlsn]

Visualizing curvatures on embedded manifolds via parallel transports along loops:

Left: flat cylinder, no angle defect after a round
Right: curved sphere, angle defect after a round

Curvature = connection property
https://t.co/0meDMQVofd

Images courtesy https://t.co/SOoQo72Peg