Zotero Catalogue

In this article we present pictorially the foundation of differential geometry which is a crucial tool for multiple areas of physics, notably general and special relativity, but also mechanics, thermodynamics and solving differential equations. As all the concepts are presented as pictures, there are no equations in this article. As such this article may be read by pre-university students who enjoy physics, mathematics and geometry. However it will also greatly aid the intuition of an undergraduate and masters students, learning general relativity and similar courses. It concentrates on the tools needed to understand Maxwell's equations thus leading to the goal of presenting Maxwell's equations as 3 pictures.

We introduce a method to measure uncertainty in large language models. For tasks like question answering, it is essential to know when we can trust the natural language outputs of foundation models. We show that measuring uncertainty in natural language is challenging because of ‘semantic equivalence’—different sentences can mean the same thing. To overcome these challenges we introduce semantic entropy—an entropy which incorporates linguistic invariances created by shared meanings. Our method is unsupervised, uses only a single model, and requires no modifications to ‘off-the-shelf’ language models. In comprehensive ablation studies we show that the semantic entropy is more predictive of model accuracy on question answering data sets than comparable baselines.

Today we will pour one out for the vaunted technical interview process, which is on its last leg. And we’ll talk a little about what’s…

It can be hard running a small business. If you want to sell to a large organisation like the UK Government, there are forms to fill in, checks to comply with, tenders to bid on, and a hundred other things. Luckily, there's the RM6237 Low Value Purchase System to make everything better. If a department wants to buy something below a certain threshold, they can contact any of the registered…

AI is doing to programming what framework-brain did to the frontend before. Deskilling, or just working at a higher level of abstraction?

We implemented the entire LLM decode pass in a single persistent kernel, no kernel launches, no interruptions, achieving 3,000+ tokens/s per request on AMD MI300X.

Today, Kog AI launches a tech preview of the Kog Inference Engine (KIE): 3,000 output tokens/s per request on 8× AMD MI300X GPUs and 2,100 on 8× NVIDIA H200 (FP16, no speculative decoding). This preview runs a 2B model, with support for large third-party MoE models coming next at similar speeds.

A new movie sets its doomed entrepreneurs amidst 17th-century “tulipmania”—but historians of the phenomenon have their own bubble to burst

Creative Commons Attribution license (reuse allowed)

Hundreds of University of California professors are urging the system to reinstate the SAT or ACT requirement for STEM majors by 2027, saying that the test-optional policy has created a widening preparation gap that threatens the value of UC science, technology, engineering and math degrees.

In this work, we propose a machine learning-based approach to address a specific aspect of the Quantum Marginal Problem: reconstructing a global density matrix compatible with a given set of quantum marginals. Our method integrates a quantum marginal imposition technique with convolutional denoising autoencoders. The loss function is carefully designed to enforce essential physical constraints, including Hermiticity, positivity, and normalization. Through extensive numerical simulations, we demonstrate the effectiveness of our approach, achieving high success rates and accuracy. Furthermore, we show that, in many cases, our model offers a faster alternative to state-of-the-art semidefinite programming solvers without compromising solution quality. These results highlight the potential of machine learning techniques for solving complex problems in quantum mechanics.

We present an algorithm for error correction in topological codes that exploits modern machine learning techniques. Our decoder is constructed from a stochastic neural network called a Boltzmann machine, of the type extensively used in deep learning. We provide a general prescription for the training of the network and a decoding strategy that is applicable to a wide variety of stabilizer codes with very little specialization. We demonstrate the neural decoder numerically on the well-known two dimensional toric code with phase-flip errors.

Entangled states are an important resource for quantum computation, communication, metrology, and the simulation of many-body systems. However, noise limits the experimental preparation of such states. Classical data can be efficiently denoised by autoencoders---neural networks trained in unsupervised manner. We develop a novel quantum autoencoder that successfully denoises Greenberger-Horne-Zeilinger states subject to spin-flip errors and random unitary noise. Various emergent quantum technologies could benefit from the proposed unsupervised quantum neural networks.

Resource-efficient quantum state tomography is one of the key ingredients of future quantum technologies. In this work, we propose a new tomography protocol combining standard quantum state reconstruction methods with an attention-based neural network architecture. We show how the proposed protocol is able to improve the averaged fidelity reconstruction over linear inversion and maximum-likelihood estimation in the finite-statistics regime, reducing at least by an order of magnitude the amount of necessary training data. We demonstrate the potential use of our protocol in physically relevant scenarios, in particular, to certify metrological resources in the form of many-body entanglement generated during the spin squeezing protocols. This could be implemented with the current quantum simulator platforms, such as trapped ions, and ultra-cold atoms in optical lattices.

Quantum state tomography (QST) is a challenging task in intermediate-scale quantum devices. Here, we apply conditional generative adversarial networks (CGANs) to QST. In the CGAN framework, two duelling neural networks, a generator and a discriminator, learn multi-modal models from data. We augment a CGAN with custom neural-network layers that enable conversion of output from any standard neural network into a physical density matrix. To reconstruct the density matrix, the generator and discriminator networks train each other on data using standard gradient-based methods. We demonstrate that our QST-CGAN reconstructs optical quantum states with high fidelity orders of magnitude faster, and from less data, than a standard maximum-likelihood method. We also show that the QST-CGAN can reconstruct a quantum state in a single evaluation of the generator network if it has been pre-trained on similar quantum states.

Resource-efficient quantum state tomography is one of the key ingredients of future quantum technologies. In this work, we propose a new tomography protocol combining standard quantum state reconstruction methods with an attention-based neural network architecture. We show how the proposed protocol is able to improve the averaged fidelity reconstruction over linear inversion and maximum-likelihood estimation in the finite-statistics regime, reducing at least by an order of magnitude the amount of necessary training data. We demonstrate the potential use of our protocol in physically relevant scenarios, in particular, to certify metrological resources in the form of many-body entanglement generated during the spin squeezing protocols. This could be implemented with the current quantum simulator platforms, such as trapped ions, and ultra-cold atoms in optical lattices.

We build a general quantum state tomography framework that makes use of machine learning techniques to reconstruct quantum states from a given set of coincidence measurements. For a wide range of pure and mixed input states we demonstrate via simulations that our method produces functionally equivalent reconstructed states to that of traditional methods with the added benefit that expensive computations are front-loaded with our system. Further, by training our system with measurement results that include simulated noise sources we are able to demonstrate a significantly enhanced average fidelity when compared to typical reconstruction methods. These enhancements in average fidelity are also shown to persist when we consider state reconstruction from partial tomography data where several measurements are missing. We anticipate that the present results combining the fields of machine intelligence and quantum state estimation will greatly improve and speed up tomography-based quantum experiments.

A few weeks ago my 5-year-old and I tried playing Cat Crimes, a puzzle game in which you work out which of your cats ate your shoes. We had a wonderful time - for about 20 minutes.

“What language is the Coffeescript compiler written in?” I asked my brilliant, witty and insightful colleague Grzegorz Kossakowski. “The Coffeescript compiler is written in Coffeescript,” he replied. Since this statement is clearly stupid, I denounced him as a liar and an idiot and took back all of the nice things I had said about him.

We provide an efficient method for computing the maximum likelihood mixed quantum state (with density matrix $ρ$) given a set of measurement outcome in a complete orthonormal operator basis subject to Gaussian noise. Our method works by first changing basis yielding a candidate density matrix $μ$ which may have nonphysical (negative) eigenvalues, and then finding the nearest physical state under the 2-norm. Our algorithm takes at worst $O(d^4)$ for the basis change plus $O(d^3)$ for finding $ρ$ where $d$ is the dimension of the quantum state. In the special case where the measurement basis is strings of Pauli operators, the basis change takes only $O(d^3)$ as well. The workhorse of the algorithm is a new linear-time method for finding the closest probability distribution (in Euclidean distance) to a set of real numbers summing to one.

A lot of people seem convinced that the point of AI coding is to write low-quality code as fast as possible. Spew out barely-passable slop, open massive PRs, and merge them unvetted. Ship it! But t…

When I was younger, I severally underestimated how valuable it is to compound, to focus in on a few things and do them well. There are things you can only discover 10,000 hours into a conversation with your best friend, experiences you can only have two decades into honing a craft or living in the same place. It takes dedication to not become blasé to the things we have around us, to maintain the serious attention and dedication necessary to discover new levels to something. But those levels are, in many ways, more rewarding than the rewards of doing new stuff (as fun as that is, and as important as it is to have that as part of the mix).

Hello! Quick throwaway post here. I was reading Normative Uncertainty by William MacAskill(Effective Altruism man) when I was flashbanged by the math. After some chatting with claude, apparently this is what makes analytic philosophy notable, as opposed to continental philosophy which is focused on society, culture, etc. What they don’t learn about apparently is analysis, which unlike logic, deals with continuous things.

Mac's Tech Blog

Painlessly quit pornography immediately, without willpower or any sense of deprivation or sacrifice.

Math Every Day Stevey's Drunken Blog Rants™

and now I'm a different person

TLDR: I’ve collected some tips for research that I’ve given to other people and/or used myself, which have sped things up and helped put people in th…

Different forms of attention mechanisms, used in modern diffusion models.

You Don't Have Writers' Block; Just Keep Going

We build a rigorous bridge between deep networks (DNs) and approximation theory via spline functions and operators. Our key result is that a large class of DNs can be written as a composition of max-affine spline operators (MASOs), which provide a powerful portal through which to view and analyze their inner workings. For instance, conditioned on the input signal, the output of a MASO DN can be written as a simple affine transformation of the input. This implies that a DN constructs a set of signal-dependent, class-specific templates against which the signal is compared via a simple inner product; we explore the links to the classical theory of optimal classification via matched filters and the effects of data memorization. Going further, we propose a simple penalty term that can be added to the cost function of any DN learning algorithm to force the templates to be orthogonal with each other; this leads to significantly improved classification performance and reduced overfitting with no change to the DN architecture. The spline partition of the input signal space opens up a new geometric avenue to study how DNs organize signals in a hierarchical fashion. As an application, we develop and validate a new distance metric for signals that quantifies the difference between their partition encodings.

We present a novel machine learning architecture that uses the exponential of a single input-dependent matrix as its only nonlinearity. The mathematical simplicity of this architecture allows a detailed analysis of its behaviour, providing robustness guarantees via Lipschitz bounds. Despite its simplicity, a single matrix exponential layer already provides universal approximation properties and can learn fundamental functions of the input, such as periodic functions or multivariate polynomials. This architecture outperforms other general-purpose architectures on benchmark problems, including CIFAR-10, using substantially fewer parameters.