Publications (276)
Methods for Rapidly Processing Angular Masks of Next-Generation Galaxy Surveys
Molly E. C. Swanson, Max Tegmark, Andrew J. S. Hamilton +1
As galaxy surveys become larger and more complex, keeping track of the completeness, magnitude limit, and other survey parameters as a function of direction on the sky becomes an i…
On the inevitability of reionization: implications for cosmic microwave background fluctuations
Max Tegmark, Joseph Silk, Alain Blanchard
Early photoionization of the intergalactic medium is discussed in a nearly model-independent way, in order to investigate whether early structures corresponding to rare Gaussian pe…
Machine-learning hidden symmetries
Ziming Liu, Max Tegmark
We present an automated method for finding hidden symmetries, defined as symmetries that become manifest only in a new coordinate system that must be discovered. Its core idea is t…
A scheme to deal accurately and efficiently with complex angular masks in galaxy surveys
A. J. S. Hamilton, Max Tegmark
This paper presents a scheme to deal accurately and efficiently with complex angular masks, such as occur typically in galaxy surveys. An angular mask is taken to be an arbitrary u…
Grokking as Compression: A Nonlinear Complexity Perspective
Ziming Liu, Ziqian Zhong, Max Tegmark
We attribute grokking, the phenomenon where generalization is much delayed after memorization, to compression. To do so, we define linear mapping number (LMN) to measure network co…
How to measure CMB power spectra without losing information
Max Tegmark
A new method for estimating the angular power spectrum C_l from cosmic microwave background (CMB) maps is presented, which has the following desirable properties: (1) It is unbeata…
The Angular Power Spectrum of BATSE 3B Gamma-Ray Burst
Max Tegmark, Dieter Hartmann, Michael Briggs +1
We compute the angular power spectrum C_l from the BATSE 3B catalog of 1122 gamma-ray bursts, and find no evidence for clustering on any scale. These constraints bridge the entire…
A Resource Model For Neural Scaling Law
Jinyeop Song, Ziming Liu, Max Tegmark +1
Neural scaling laws characterize how model performance improves as the model size scales up. Inspired by empirical observations, we introduce a resource model of neural scaling. A…
OptPDE: Discovering Novel Integrable Systems via AI-Human Collaboration
Subhash Kantamneni, Ziming Liu, Max Tegmark
Integrable partial differential equation (PDE) systems are of great interest in natural science, but are exceedingly rare and difficult to discover. To solve this, we introduce Opt…
Opening the AI black box: program synthesis via mechanistic interpretability
Eric J. Michaud, Isaac Liao, Vedang Lad +7
We present MIPS, a novel method for program synthesis based on automated mechanistic interpretability of neural networks trained to perform the desired task, auto-distilling the le…
The Singapore Consensus on Global AI Safety Research Priorities
Yoshua Bengio, Tegan Maharaj, Luke Ong +84
Rapidly improving AI capabilities and autonomy hold significant promise of transformation, but are also driving vigorous debate on how to ensure that AI is safe, i.e., trustworthy,…
Mapping our Universe in 3D with MITEoR
Haoxuan Zheng, Max Tegmark, Victor Buza +33
Mapping our universe in 3D by imaging the redshifted 21 cm line from neutral hydrogen has the potential to overtake the cosmic microwave background as our most powerful cosmologica…
Inflationary Constraints on Type IIA String Theory
Mark P. Hertzberg, Shamit Kachru, Washington Taylor +1
We prove that inflation is forbidden in the most well understood class of semi-realistic type IIA string compactifications: Calabi-Yau compactifications with only standard NS-NS 3-…
Poisson Flow Generative Models
Yilun Xu, Ziming Liu, Max Tegmark +1
We propose a new "Poisson flow" generative model (PFGM) that maps a uniform distribution on a high-dimensional hemisphere into any data distribution. We interpret the data points a…
Task Force on Cosmic Microwave Background Research
James Bock, Sarah Church, Mark Devlin +11
One of the most spectacular scientific breakthroughs in past decades was using measurements of the fluctuations in the cosmic microwave background (CMB) to test precisely our under…
Measuring cosmological parameters with galaxy surveys
Max Tegmark
We assess the accuracy with which future galaxy surveys can measure cosmological parameters by deriving a handy approximation that we validate numerically. We find that galaxy surv…
Criticality in Formal Languages and Statistical Physics
Henry W. Lin, Max Tegmark
We show that the mutual information between two symbols, as a function of the number of symbols between the two, decays exponentially in any probabilistic regular grammar, but can…
How accurately can 21 cm tomography constrain cosmology?
Yi Mao, Max Tegmark, Matthew McQuinn +2
There is growing interest in using 3-dimensional neutral hydrogen mapping with the redshifted 21 cm line as a cosmological probe, as it has been argued to have a greater long-term…
Parallel Universes
Max Tegmark
I survey physics theories involving parallel universes, which form a natural four-level hierarchy of multiverses allowing progressively greater diversity. Level I: A generic predic…
The last stand before MAP: cosmological parameters from lensing, CMB and galaxy clustering
Xiaomin Wang, Max Tegmark, Bhuvnesh Jain +1
Cosmic shear measurements have now improved to the point where they deserve to be treated on par with CMB and galaxy clustering data for cosmological parameter analysis, using the…
Comparing and combining the Saskatoon, QMAP and COBE CMB maps
Yongzhong Xu, Max Tegmark, Angelica de Oliveira-Costa +5
We present a method for comparing and combining maps with different resolutions and beam shapes, and apply it to the Saskatoon, QMAP and COBE/DMR data sets. Although the Saskatoon…
The end of unified dark matter?
Havard Sandvik, Max Tegmark, Matias Zaldarriaga +1
Despite the interest in dark matter and dark energy, it has never been shown that they are in fact two separate substances. We provide the first strong evidence that they are separ…
PFGM++: Unlocking the Potential of Physics-Inspired Generative Models
Yilun Xu, Ziming Liu, Yonglong Tian +3
We introduce a new family of physics-inspired generative models termed PFGM++ that unifies diffusion models and Poisson Flow Generative Models (PFGM). These models realize generati…
Searching for Inflation in Simple String Theory Models: An Astrophysical Perspective
Mark P. Hertzberg, Max Tegmark, Shamit Kachru +2
Attempts to connect string theory with astrophysical observation are hampered by a jargon barrier, where an intimidating profusion of orientifolds, Kahler potentials, etc. dissuade…
Machine-Learning media bias
Samantha D'Alonzo, Max Tegmark
We present an automated method for measuring media bias. Inferring which newspaper published a given article, based only on the frequencies with which it uses different phrases, le…
Ensemble Inhibition and Excitation in the Human Cortex: an Ising Model Analysis with Uncertainties
Cristian Zanoci, Nima Dehghani, Max Tegmark
The pairwise maximum entropy model, also known as the Ising model, has been widely used to analyze the collective activity of neurons. However, controversy persists in the literatu…
Cosmological Parameters from Eigenmode Analysis of Sloan Digital Sky Survey Galaxy Redshifts
Adrian C. Pope, Takahiko Matsubara, Alexander S. Szalay +23
We present estimates of cosmological parameters from the application of the Karhunen-Loeve transform to the analysis of the 3D power spectrum of density fluctuations using Sloan Di…
Constraining Torsion with Gravity Probe B
Yi Mao, Max Tegmark, Alan Guth +1
It is well-entrenched folklore that torsion gravity theories predict observationally negligible torsion in the solar system, since torsion (if it exists) couples only to the intrin…
Symbolic Pregression: Discovering Physical Laws from Distorted Video
Silviu-Marian Udrescu, Max Tegmark
We present a method for unsupervised learning of equations of motion for objects in raw and optionally distorted unlabeled video. We first train an autoencoder that maps each video…
Uncorrelated measurements of the CMB power spectrum
Max Tegmark, Andrew Hamilton
We describe how to compute estimates of the power spectrum C_l from Cosmic Microwave Background (CMB) maps that not only retain all the cosmological information, but also have unco…
Spherical Harmonic Analysis of the Angular Distribution of Gamma-Ray Bursts
Max Tegmark, Dieter Hartmann, Michael Briggs +1
We compute the angular power spectrum C_l of the BATSE 3B catalog, and find no evidence for clustering on any scale. These constraints bridge the entire range from small scales, pr…
What does inflation really predict?
Max Tegmark
If the inflaton potential has multiple minima, as may be expected in, e.g., the string theory "landscape", inflation predicts a probability distribution for the cosmological parame…
Twenty-one centimeter tomography with foregrounds
Xiaomin Wang, Max Tegmark, Mario Santos +1
Twenty-one centimeter tomography is emerging as a powerful tool to explore the end of the cosmic dark ages and the reionization epoch, but it will only be as good as our ability to…
A brute force analysis of the COBE DMR data
Max Tegmark, Emory Bunn
More than a dozen papers analyzing the COBE data have now appeared. We review the different techniques and compare them to a ``brute force" likelihood analysis where we invert the…
Is cosmology consistent?
Xiaomin Wang, Max Tegmark, Matias Zaldarriaga
We perform a detailed analysis of the latest CMB measurements (including BOOMERaNG, DASI, Maxima and CBI), both alone and jointly with other cosmological data sets involving, e.g.,…
Measuring quantum states: an experimental setup for measuring the spatial density matrix
Max Tegmark
To quantify the effect of decoherence in quantum measurements, it is desirable to measure not merely the square modulus of the spatial wavefunction, but the entire density matrix,…
An icosahedron-based method for pixelizing the celestial sphere
Max Tegmark
For power spectrum estimation it's important that the pixelization of a CMB sky map be smooth and regular to high degree. With this criterion in mind the ``COBE sky cube" was defin…
CMB Observables and Their Cosmological Implications
Wayne Hu, Masataka Fukugita, Matias Zaldarriaga +1
We show that recent measurements of the power spectrum of cosmic microwave background anisotropies by BOOMERanG and MAXIMA can be characterized by four observables, the position of…
Divide-and-Conquer Dynamics in AI-Driven Disempowerment
Peter S. Park, Max Tegmark
AI companies are attempting to create AI systems that outperform humans at most economically valuable work. Current AI models are already automating away the livelihoods of some ar…
Cosmology from the Highly-Redshifted 21 cm Line
Steven Furlanetto, Adam Lidz, Abraham Loeb +26
One of the next decade's most exciting prospects is to explore the cosmic "dark ages," during which the first stars in the Universe formed, with the 21 cm line of neutral hydrogen.…
Sycophancy Towards Researchers Drives Performative Misalignment
David D. Baek, Xinnuo Li, Anay Gupta +4
The increasing situational awareness of language models raises safety concerns: models might be aware when they are evaluated, and adjust their behavior to evade monitoring and res…
The large-scale polarization of the microwave background and foreground
Angelica de Oliveira-Costa, Max Tegmark, Chris O'Dell +4
The DASI discovery of CMB polarization has opened a new chapter in cosmology. Most of the useful information about inflationary gravitational waves and reionization is on large ang…
DafnyBench: A Benchmark for Formal Software Verification
Chloe Loughridge, Qinyi Sun, Seth Ahrenbach +7
We introduce DafnyBench, the largest benchmark of its kind for training and evaluating machine learning systems for formal software verification. We test the ability of LLMs such a…
Overcoming real-world obstacles in 21 cm power spectrum estimation: A method demonstration and results from early Murchison Widefield Array data
Joshua S. Dillon, Adrian Liu, Christopher L. Williams +16
We present techniques for bridging the gap between idealized inverse covariance weighted quadratic estimation of 21 cm power spectra and the real-world challenges presented univers…
Physics-Augmented Learning: A New Paradigm Beyond Physics-Informed Learning
Ziming Liu, Yunyue Chen, Yuanqi Du +1
Integrating physical inductive biases into machine learning can improve model generalizability. We generalize the successful paradigm of physics-informed learning (PIL) into a more…
Joint Efficient Dark-energy Investigation (JEDI): a Candidate Implementation of the NASA-DOE Joint Dark Energy Mission (JDEM)
Arlin Crotts, Peter Garnavich, William Priedhorsky +15
JEDI will probe dark energy in three independent ways by measuring the expansion history of the universe: (1) using type Ia supernovae as cosmological standard candles over a range…
Friendly Artificial Intelligence: the Physics Challenge
Max Tegmark
Relentless progress in artificial intelligence (AI) is increasingly raising concerns that machines will replace humans on the job market, and perhaps altogether. Eliezer Yudkowski…
Is "the theory of everything'' merely the ultimate ensemble theory?
Max Tegmark
We discuss some physical consequences of what might be called ``the ultimate ensemble theory'', where not only worlds corresponding to say different sets of initial data or differe…
How did it all begin?
Max Tegmark
How did it all begin? Although this question has undoubtedly lingered for as long as humans have walked the Earth, the answer still eludes us. Yet since my grandparents were born,…
The Hydrogen Epoch of Reionization Array Dish II: Characterization of Spectral Structure with Electromagnetic Simulations and its science Implications
Aaron Ewall-Wice, Richard Bradley, David DeBoer +25
We use time-domain electromagnetic simulations to determine the spectral characteristics of the Hydrogen Epoch of Reionization Arrays (HERA) antenna. These simulations are part of…
Why is the CMB fluctuation level 10^{-5}?
Max Tegmark, Martin Rees
We explore the qualitative changes that would occur if the amplitude Q ~ 10^{-5} of cosmological density fluctuations were different. If is less than about 10^{-6}, the cosmologica…
Discovering New Interpretable Conservation Laws as Sparse Invariants
Ziming Liu, Patrick Obin Sturm, Saketh Bharadwaj +2
Discovering conservation laws for a given dynamical system is important but challenging. In a theorist setup (differential equations and basis functions are both known), we propose…
Fault-Tolerant Neural Networks from Biological Error Correction Codes
Alexander Zlokapa, Andrew K. Tan, John M. Martyn +3
It has been an open question in deep learning if fault-tolerant computation is possible: can arbitrarily reliable computation be achieved using only unreliable neurons? In the grid…
Towards Understanding Distilled Reasoning Models: A Representational Approach
David D. Baek, Max Tegmark
In this paper, we investigate how model distillation impacts the development of reasoning features in large language models (LLMs). To explore this, we train a crosscoder on Qwen-s…
Decoherence produces coherent states: an explicit proof for harmonic chains
Max Tegmark, Harold S. Shapiro
We study the behavior of infinite systems of coupled harmonic oscillators as t->infinity, and generalize the Central Limit Theorem (CLT) to show that their reduced Wigner distribut…
The Angular Correlation Function of Galaxies from Early SDSS Data
SDSS Collaboration, Andrew Connolly, Ryan Scranton +22
The Sloan Digital Sky Survey is one of the first multicolor photometric and spectroscopic surveys designed to measure the statistical properties of galaxies within the local Univer…
Omnigrok: Grokking Beyond Algorithmic Data
Ziming Liu, Eric J. Michaud, Max Tegmark
Grokking, the unusual phenomenon for algorithmic datasets where generalization happens long after overfitting the training data, has remained elusive. We aim to understand grokking…
Cosmic microwave background maps from the HACME experiment
Max Tegmark, Angelica de Oliveira-Costa, John Staren +9
We present Cosmic Microwave Background (CMB) maps from the Santa Barbara HACME balloon experiment (Staren etal 2000), covering about 1150 square degrees split between two regions i…
Relativity Revisited
Flora Lopis, Max Tegmark
Was Einstein wrong? This paper provides a detailed technical review of Einstein's special and general relativity from an astrophysical perspective, including the historical develop…
Efficient Dictionary Learning with Switch Sparse Autoencoders
Anish Mudide, Joshua Engels, Eric J. Michaud +2
Sparse autoencoders (SAEs) are a recent technique for decomposing neural network activations into human-interpretable features. However, in order for SAEs to identify all features…
The power spectrum of the CfA/SSRS UZC galaxy redshift survey
Nikhil Padmanabhan, Max Tegmark, Andrew J. S. Hamilton
The combined CfA2/SSRS redshift catalog has recently been improved and made public. We compute the redshift-space power spectrum of this catalog using the regions at -2.5 < delta <…
Improved limits on gamma ray burst repetition
Max Tegmark, Dieter Hartmann, Michael Briggs +2
We tighten previous upper limits on gamma ray burst repetition by analyzing the angular power spectrum of the BATSE 3B catalog of 1122 bursts. At 95% confidence, we find that no mo…
Linear Redshift Distortions and Power in the PSCz Survey
A. J. S. Hamilton, Max Tegmark, Nikhil Padmanabhan
We present a state-of-the-art linear redshift distortion analysis of the recently published IRAS Point Source Catalog Redshift Survey (PSCz). The procedure involves linear compress…
The Intermediate-Scale Clustering of Luminous Red Galaxies
Idit Zehavi, Daniel J. Eisenstein, Robert C. Nichol +7
We report the intermediate-scale (0.3 to 40 Mpc/h) clustering of 35,000 luminous early-type galaxies at redshifts 0.16 to 0.44 from the Sloan Digital Sky Survey. We present the red…
Do Two AI Scientists Agree?
Xinghong Fu, Ziming Liu, Max Tegmark
When two AI models are trained on the same scientific task, do they learn the same theory or two different theories? Throughout history of science, we have witnessed the rise and f…
Seeing is Believing: Brain-Inspired Modular Training for Mechanistic Interpretability
Ziming Liu, Eric Gan, Max Tegmark
We introduce Brain-Inspired Modular Training (BIMT), a method for making neural networks more modular and interpretable. Inspired by brains, BIMT embeds neurons in a geometric spac…
Bias and beyond
Max Tegmark
It is becoming increasingly clear that galaxy bias is complicated, with evidence indicating that it can be time-dependent, morphology-dependent, scale-dependent, non-linear and non…
A Method for 21cm Power Spectrum Estimation in the Presence of Foregrounds
Adrian Liu, Max Tegmark
21cm tomography promises to be a powerful tool for estimating cosmological parameters, constraining the epoch of reionization, and probing the so-called dark ages. However, realizi…
Observationally Determining the Properties of Dark Matter
Wayne Hu, Daniel J. Eisenstein, Max Tegmark +1
Determining the properties of the dark components of the universe remains one of the outstanding challenges in cosmology. We explore how upcoming CMB anisotropy measurements, galax…
A Fast Method for Power Spectrum and Foreground Analysis for 21 cm Cosmology
Joshua S. Dillon, Adrian Liu, Max Tegmark
We develop and demonstrate an acceleration of the Liu & Tegmark quadratic estimator formalism for inverse variance foreground subtraction and power spectrum estimation in 21 cm tom…
Many Worlds in Context
Max Tegmark
Everett's Many-Worlds Interpretation of quantum mechanics is discussed in the context of other physics disputes and other proposed kinds of parallel universes. We find that only a…
Angular Clustering with Photometric Redshifts in the Sloan Digital Sky Survey: Bimodality in the Clustering Properties of Galaxies
Tamas Budavari, Andrew J. Connolly, Alexander S. Szalay +18
Understanding the clustering of galaxies has long been a goal of modern observational cosmology. Utilizing our photometric redshift technique a volume limited sample containing mor…
AI Feynman 2.0: Pareto-optimal symbolic regression exploiting graph modularity
Silviu-Marian Udrescu, Andrew Tan, Jiahai Feng +3
We present an improved method for symbolic regression that seeks to fit data to formulas that are Pareto-optimal, in the sense of having the best accuracy for a given complexity. I…
Weak Lensing: Prospects for Measuring Cosmological Parameters
Wayne Hu, Max Tegmark
Weak lensing of galaxies by large scale structure can potentially measure cosmological quantities as accurately as the cosmic microwave background (CMB). However, the relation betw…
Measuring spacetime: from big bang to black holes
Max Tegmark
Nerd abstract: Observational constraints on spacetime are reviewed, focusing on how the underlying physics (dark matter, dark energy, gravity) can be tested rather than assumed. Po…
Meta-learning autoencoders for few-shot prediction
Tailin Wu, John Peurifoy, Isaac L. Chuang +1
Compared to humans, machine learning models generally require significantly more training examples and fail to extrapolate from experience to solve previously unseen challenges. To…
The power spectrum of galaxies in the 2dF 100k redshift survey
Max Tegmark, Andrew J. S. Hamilton, Yongzhong Xu
We compute the real-space power spectrum and the redshift-space distortions of galaxies in the 2dF 100k galaxy redshift survey using pseudo-Karhunen-Loeve eigenmodes and the stocha…
A method for subtracting foregrounds from multi-frequency CMB sky maps
Max Tegmark, George Efstathiou
An improved method for subtracting contaminants from Cosmic Microwave Background (CMB) sky maps is presented, and used to estimate how well future experiments will be able to recov…
The role of artificial intelligence in achieving the Sustainable Development Goals
Ricardo Vinuesa, Hossein Azizpour, Iolanda Leite +7
The emergence of artificial intelligence (AI) and its progressively wider impact on many sectors across the society requires an assessment of its effect on sustainable development.…
Shut up and calculate
Max Tegmark
I advocate an extreme "shut-up-and-calculate" approach to physics, where our external physical reality is assumed to be purely mathematical. This brief essay motivates this "it's a…
On Math, Matter and Mind
Piet Hut, Mark Alford, Max Tegmark
We discuss the nature of reality in the ontological context of Penrose's math-matter-mind triangle. The triangle suggests the circularity of the widespread view that math arises fr…
Large-Scale Sunyaev-Zel'dovich Effect: Measuring Statistical Properties with Multifrequency Maps
Asantha Cooray, Wayne Hu, Max Tegmark
We study the prospects for extracting detailed statistical properties of the Sunyaev-Zel'dovich (SZ) effect associated with large scale structure using upcoming multifrequency CMB…
Mapping the CMB I: the first flight of the QMAP experiment
Mark Devlin, Angelica de Oliveira-Costa, Tom Herbig +4
We report on the first flight of the balloon-borne QMAP experiment. The experiment is designed to make a map of the cosmic microwave background anisotropy on angular scales from 0.…
Physics of Skill Learning
Ziming Liu, Yizhou Liu, Eric J. Michaud +2
We aim to understand physics of skill learning, i.e., how skills are learned in neural networks during training. We start by observing the Domino effect, i.e., skills are learned s…
Likely values of the Higgs vev
John F. Donoghue, Koushik Dutta, Andreas Ross +1
We make an estimate of the likelihood function for the Higgs vacuum expectation value by imposing anthropic constraints on the existence of atoms while allowing the other parameter…
Scaling Laws For Scalable Oversight
Joshua Engels, David D. Baek, Subhash Kantamneni +1
Scalable oversight, the process by which weaker AI systems supervise stronger ones, has been proposed as a key strategy to control future superintelligent systems. However, it is s…
ESTIMATING MICROWAVE POWER SPECTRA
Max Tegmark
A new method for estimating the power spectrum from cosmic microwave background (CMB) maps was recently presented by the author and applied to the 2 year COBE data. It was fo…
Pareto-optimal data compression for binary classification tasks
Max Tegmark, Tailin Wu
The goal of lossy data compression is to reduce the storage cost of a data set while retaining as much information as possible about something () that you care about. For ex…
Current cosmological constraints from a 10 parameter CMB analysis
Max Tegmark, Matias Zaldarriaga
We compute the constraints on a ``standard'' 10 parameter cold dark matter (CDM) model from the most recent CMB and data and other observations, exploring 30 million discrete model…
Towards Guaranteed Safe AI: A Framework for Ensuring Robust and Reliable AI Systems
David "davidad" Dalrymple, Joar Skalse, Yoshua Bengio +14
Ensuring that AI systems reliably and robustly avoid harmful or dangerous behaviours is a crucial challenge, especially for AI systems with a high degree of autonomy and general in…
Solving the Corner-Turning Problem for Large Interferometers
Andy Lutomirski, Max Tegmark, Nevada Sanchez +3
The so-called corner turning problem is a major bottleneck for radio telescopes with large numbers of antennas. The problem is essentially that of rapidly transposing a matrix that…
A Limit on the Large Angular Scale Polarization of the Cosmic Microwave Background
Brian G. Keating, Christopher W. O'Dell, Angelica de Oliveira-Costa +5
We present an upper limit on the polarization of the Cosmic Microwave Background at 7 degree angular scales in the frequency band between 26 and 36 GHz, produced by the POLAR exper…
Limits on non-Gaussianities from WMAP data
Paolo Creminelli, Alberto Nicolis, Leonardo Senatore +2
We develop a method to constrain the level of non-Gaussianity of density perturbations when the 3-point function is of the "equilateral" type. Departures from Gaussianity of this f…
KAN 2.0: Kolmogorov-Arnold Networks Meet Science
Ziming Liu, Pingchuan Ma, Yixuan Wang +2
A major challenge of AI + Science lies in their inherent incompatibility: today's AI is primarily based on connectionism, while science depends on symbolism. To bridge the two worl…
Removing point sources from CMB maps
Max Tegmark, Angelica de Oliveira-Costa
For high-precision cosmic microwave background (CMB) experiments, contamination from extragalactic point sources is a major concern. It is therefore useful to be able to detect and…
CMB multipole measurements in the presence of foregrounds
Angelica de Oliveira-Costa, Max Tegmark
Most analysis of Cosmic Microwave Background spherical harmonic coefficients a_lm has focused on estimating the power spectrum C_l=<|a_lm|^2> rather than the coefficients themselve…
Observing the Evolution of the Universe
James Aguirre, Alexandre Amblard, Amjad Ashoorioon +172
How did the universe evolve? The fine angular scale (l>1000) temperature and polarization anisotropies in the CMB are a Rosetta stone for understanding the evolution of the univers…
Language Models Use Trigonometry to Do Addition
Subhash Kantamneni, Max Tegmark
Mathematical reasoning is an increasingly important indicator of large language model (LLM) capabilities, yet we lack understanding of how LLMs process even simple mathematical tas…
How unlikely is a doomsday catastrophe?
Max Tegmark, Nick Bostrom
Numerous Earth-destroying doomsday scenarios have recently been analyzed, including breakdown of a metastable vacuum state and planetary destruction triggered by a "strangelet'' or…
Time Evolution of Galaxy Formation and Bias in Cosmological Simulations
Michael Blanton, Renyue Cen, Jeremiah P. Ostriker +2
The clustering of galaxies relative to the mass distribution declines with time because: first, nonlinear peaks become less rare events; second, the densest regions stop forming ne…