Ajitesh Shukla

We're excited to announce a second physical location for NeurIPS 2025, in Mexico City, which we hope will address concerns around skyrocketing attendance and difficulties in travel visas that some attendees have experienced in previous years.

Read more in our blog:
blog.neurips.cc/2025/07/16/n...

The list of accepted papers at #FOCS2025 is up!

focs.computer.org/2025/accepte...

Understanding Quantum Information and Computation This is a course on the theory of quantum computing. It consists of 16 lessons, each with a video and written component, covering the basics of quantum information, quantum algorithms (including query...

After 3 1/2 years of work my course on quantum computing is finally finished — the "Director's Cut" of Understanding Quantum Information and Computation is now available.

arxiv.org/abs/2507.11536

Learning distributed representations with efficient SoftMax normalization

Lorenzo Dall'Amico, Enrico Maria Belliardo

Action editor: Manzil Zaheer

https://openreview.net/forum?id=9M4NKMZOPu

#softmax #embeddings #embedding

Symplectic Hecke eigenbases from Ehrhart polynomials For $n\in\mathbb{N}$ and $\ell\in\{0,1,\dots,n\}$, we consider the function extracting the $\ell$th coefficient of the Ehrhart polynomials of lattice polytopes in $\mathbb{R}^n$. These functions form ...

arxiv.org/abs/2507.11728
/Symplectic Hecke eigenbases from Ehrhart polynomials/
Claudia Alfes, Joshua Maglione, Christopher Voll

Breaking and Fixing Content-Defined Chunking Content-defined chunking (CDC) algorithms split streams of data into smaller blocks, called chunks, in a way that preserves chunk boundaries when the data is partially changed. CDC is ubiquitous in ap...

Oh fun! "Breaking and Fixing Content-Defined Chunking" uses G6K in one of the attacks: worlds colliding, lattice reduction in the wild something something.

eprint.iacr.org/2025/558
github.com/fplll/g6k

The Davis-Kahan sin(θ) theorem bounds the difference between the subspaces spanned by eigenvectors of two symmetric matrices, based on the difference between the matrices. It quantifies how small perturbations in a matrix affect its eigenvectors. www.jstor.org/stable/29495...

Ringworlds and Dyson spheres can be stable

It's been known since forever that a ringworld orbiting a star isn't stable. But that's just when there's one star. If there are two then stability becomes possible. This is getting closer to what Iain Banks called […]

[Original post on mathstodon.xyz]

Nonparametric Factor Analysis and Beyond Nearly all identifiability results in unsupervised representation learning inspired by, e.g., independent component analysis, factor analysis, and causal representation learning, rely on assumptions o...

Interesting identifiability results relevant to disentangling (for nonparametric models w nonlinear generating processes). Identify conditions in which latent variables can be identified up to permutation and component-wise invertible transformations. arxiv.org/abs/2503.16865

First page of the instagram post

A new #CosmicDistanceLadder post on why lunar and solar eclipses tend to come in pairs (for instance, the solar eclipse next week is paired with the lunar eclipse from last week). www.instagram.com/p/DHkS3EcA40L

LaTeX source: https://pastebin.com/BeABGVqE Let $\pi(n)$ denote the number of prime numbers $\le n$. The prime number theorem states that \begin{equation} \lim_{n \to \infty} \frac{~\pi(n)~}{~\frac{n}{\log n}~} = 1. \label{eq:primes} \end{equation} Here's a weaker, one-sided (but non-asymptotic) result with a simpler proof: \begin{theorem}\label{thm:primes} For all $n \in \mathbb{N}$, we have $\pi(n) \ge \frac{n-2}{\log_2 n}$. \end{theorem} \begin{lemma}\label{lem:lcm} Define $\mathsf{lcm}(n) := \min\{m \in \mathbb{N} : \forall k \in [n] ~ \frac{m}{k} \in \mathbb{N}\}$ to be the least common multiple of $[n] := \{1,2,\cdots,n\}$. Then $\mathsf{lcm}(n) \ge 2^{n-2}$ for all $n \in \mathbb{N}$. \end{lemma}

Prime numbers are plentiful.
Here's a simple proof that the number of primes ≤n is ≥Ω(n / log n), which is a (small) constant factor from optimal.

Differentially Private Algorithms that Never Fail [Side Note: We’ve migrated email subscriptions from feedburner (RIP) to follow.it, so they should start working again.] Most differentially private algorithms fail with some nonzero probability. For...

Differentially Private Algorithms that Never Fail
differentialprivacy.org/fail-prob/

2) They find that GRPO is biased.
- The length normalization prefers shorter correct answers, and longer incorrect answers. -> length bias
- The std normalization prefers too easy or too hard questions over average questions. -> difficulty bias

They introduce Dr. GRPO to remove above biases.

Compute Optimal Scaling of Skills: Knowledge vs Reasoning Scaling laws are a critical component of the LLM development pipeline, most famously as a way to forecast training decisions such as 'compute-optimally' trading-off parameter count and dataset size, a...

Paper: Compute Optimal Scaling of Skills: Knowledge vs Reasoning ( arxiv.org/abs/2503.10061 )

Understanding R1-Zero-Like Training: A Critical Perspective

1) There are biases in the base model pretraining: self-reflection behaviors, math-solving abilities are already infused before RL reinforces them by reward signals.

RWC 2025 Real World Crypto Symposium

Looking forward to attending Real-World Crypto '25 rwc.iacr.org/2025/ next week. I should be there from Tuesday afternoon to Friday evening.

I will present our Tor Directory Authorities (zhtluo.com/paper/Attack...) work on Friday afternoon.

A Collatz-like function f(n) that bifurcates on the primes, I posed a decade ago. It remains unknown if it always falls into a 2/4 cycle. For n=229, f(n) shoots off to 10^{376} before returning to that cycle after 6309 iterations. mathoverflow.net/questions/20...
#MathSky

Only one week left to submit a contributed talk to QEC 25!
qec25.yalepages.org
August 11 - 15, 2025, hosted at Yale University.

This promises to be the best QEC yet!

Please repost!

Case Study: Verified Vampire Proofs in the LambdaPi-calculus Modulo The Vampire automated theorem prover is extended to output machine-checkable proofs in the Dedukti concrete syntax for the LambdaPi-calculus modulo. This significantly reduces the trusted computing ba...

Case study: Verified Vampire proofs in the LambdaPi-calculus modulo. ~ Anja Petković Komel, Michael Rawson, Martin Suad. arxiv.org/abs/2503.155... #ATP #Vampire #Dedukti

ComfyUI now natively supports Hunyuan3D 2.0 and Hunyuan3D 2.0 MV (Multi-View) model series!

3 workflows to get started:

🔹Hunyuan3D-2 mv: multi-view to 3D
🔹Hunyuan3D-2 mv Turbo: accelerated multi-view
🔹Hunyuan3D-2: single image to 3D

Division polynomials for arbitrary isogenies Following work of Mazur-Tate and Satoh, we extend the definition of division polynomials to arbitrary isogenies of elliptic curves, including those whose kernels do not sum to the identity. In analogy...

arxiv.org/abs/2503.15428
/Division polynomials for arbitrary isogenies/
Katherine E. Stange

A commutative diagram showing * [0,1]^3, meaning the product of the unit interval with itself three times * its three projections into [0,1]^2 * inclusions of the letters G, E, and B into each of those unit squares * the universal property of the maximal subset of [0,1]^3 such that its three projections lie inside the letters G, E and B

I think it's a limit (a slightly generalised pullback), the universal thing that completes this diagram

From p.1 of https://math.jhu.edu/~eriehl/context.pdf: In 1941, Saunders Mac Lane gave a lecture at the University of Michigan in which he computed for a prime p that Ext(Z[ 1 p ]/Z, Z)  Zp, the group of p-adic integers, where Z[ 1 p ]/Z is the Prüfer p-group. When he explained this result to Samuel Eilenberg, who had missed the lecture, Eilenberg recognized the calculation as the homology of the 3-sphere complement of the p-adic solenoid, a space formed as the infinite intersection of a sequence of solid tori, each wound around p times inside the preceding torus. In teasing apart this connection, the pair of them discovered what is now known as the universal coefficient theorem in algebraic topology, which relates the homology H∗ and cohomology groups H ∗ associated to a space X via a group extension [ML05]: (1.0.1) 0 → Ext(Hn−1(X),G) → H n (X,G) → Hom(Hn(X),G) → 0 . To obtain a more general form of the universal coefficient theorem, Eilenberg and Mac Lane needed to show that certain isomorphisms of abelian groups expressed by this group extension extend to spaces constructed via direct or inverse limits. And indeed this is the case, precisely because the homomorphisms in the diagram (1.0.1) are natural with respect to continuous maps between topological spaces.

So Mac Lane and Eilenberg invented category theory so they could prove the universal coefficient theorem, which they discovered because Saunders showed an algebra computation to Sammy and Sammy went "Huh. That's how I compute the complement of the p-adic solenoid inside a 3-sphere."

Stability-Aware Training of Machine Learning Force Fields with Differentiable Boltzmann Estimators

Sanjeev Raja, Ishan Amin, Fabian Pedregosa, Aditi S. Krishnapriyan

Action editor: Stratis Gavves

https://openreview.net/forum?id=ZckLMG00sO

#boltzmann #molecular #molecules

Dynamics of disordered quantum systems with two- and three-dimensional tensor networks Quantum spin glasses form a good testbed for studying the performance of various quantum annealing and optimization algorithms. In this work we show how two- and three-dimensional tensor networks can ...

In a new preprint arxiv.org/abs/2503.05693, led by Joseph Tindall and Antonio Mello at Flatiron CCQ, we simulate annealing of disordered quantum magnets 🧲 ⌛ and in many cases find better accuracy than recent results from D-Wave devices and leading classical methods (c.f. arxiv.org/abs/2403.00910).

A note on the twisted degree $6$ $L$-function for Hermitian cusp forms of degree $2$ Let $F$ be a cuspidal Hermitian eigenform of degree two over $\mathbb{Q}(i)$, with first Fourier-Jacobi coefficient not identically zero. Building on a paper by Das and Jha, we prove the meromorphic c...

arxiv.org/abs/2503.03615
/A note on the twisted degree 6 L-function for Hermitian cusp forms of degree 2/
Rafail Psyroukis

Distributed Certifiably Correct Range-Aided SLAM

Alexander Thoms, @alanpapalia.bsky.social, Jared Velasquez, David M. Rosen, Sriram Narasimhan

tl;dr: RA-SLAM->QCQP->SDR->Riemannian Staircase

arxiv.org/abs/2503.03192

A distribution related to Farey sequences -- I We study some arithmetical properties of Farey sequences by the method introduced by F.Boca, C.Cobeli and A.Zaharescu (2001). Let $Φ_{Q}$ be the classical Farey sequence of order $Q$. Having the fixed...

arxiv.org/abs/2502.19881
/A distribution related to Farey sequences -- I/
Maxim A. Korolev

Comment on "InAs-Al hybrid devices passing the topological gap protocol", Microsoft Quantum, Phys. Rev. B 107, 245423 (2023) The topological gap protocol (TGP) is presented as "a series of stringent experimental tests" for the presence of topological superconductivity and associated Majorana bound states. Here, we show that...

I had made Microsoft Quantum aware of issues before publication of this latest Nature paper (which uses it tune up their devices).

Since they seem to not care, I have make these issues public.

In short: The topological gap protocol and all claims based on it are flawed.

arxiv.org/abs/2502.19560