Daily Papers

We establish a fundamental connection between score-based diffusion models and non-equilibrium thermodynamics by deriving performance limits based on entropy rates. Our main theoretical contribution is a lower bound on the negative log-likelihood of the data that relates model performance to entropy rates of diffusion processes. We numerically validate this bound on a synthetic dataset and investigate its tightness. By building a bridge to entropy rates - system, intrinsic, and exchange entropy - we provide new insights into the thermodynamic operation of these models, drawing parallels to Maxwell's demon and implications for thermodynamic computing hardware. Our framework connects generative modeling performance to fundamental physical principles through stochastic thermodynamics.

Partial differential equations (PDEs) are important tools to model physical systems, and including them into machine learning models is an important way of incorporating physical knowledge. Given any system of linear PDEs with constant coefficients, we propose a family of Gaussian process (GP) priors, which we call EPGP, such that all realizations are exact solutions of this system. We apply the Ehrenpreis-Palamodov fundamental principle, which works like a non-linear Fourier transform, to construct GP kernels mirroring standard spectral methods for GPs. Our approach can infer probable solutions of linear PDE systems from any data such as noisy measurements, or pointwise defined initial and boundary conditions. Constructing EPGP-priors is algorithmic, generally applicable, and comes with a sparse version (S-EPGP) that learns the relevant spectral frequencies and works better for big data sets. We demonstrate our approach on three families of systems of PDE, the heat equation, wave equation, and Maxwell's equations, where we improve upon the state of the art in computation time and precision, in some experiments by several orders of magnitude.

Modern deep learning approaches usually transform inputs into a modality-specific form. For example, the most common deep learning approach to image classification involves decoding image file bytes into an RGB tensor which is passed into a neural network. Instead, we investigate performing classification directly on file bytes, without the need for decoding files at inference time. Using file bytes as model inputs enables the development of models which can operate on multiple input modalities. Our model, ByteFormer, achieves an ImageNet Top-1 classification accuracy of 77.33% when training and testing directly on TIFF file bytes using a transformer backbone with configuration similar to DeiT-Ti (72.2% accuracy when operating on RGB images). Without modifications or hyperparameter tuning, ByteFormer achieves 95.42% classification accuracy when operating on WAV files from the Speech Commands v2 dataset (compared to state-of-the-art accuracy of 98.7%). Additionally, we demonstrate that ByteFormer has applications in privacy-preserving inference. ByteFormer is capable of performing inference on particular obfuscated input representations with no loss of accuracy. We also demonstrate ByteFormer's ability to perform inference with a hypothetical privacy-preserving camera which avoids forming full images by consistently masking 90% of pixel channels, while still achieving 71.35% accuracy on ImageNet. Our code will be made available at https://github.com/apple/ml-cvnets/tree/main/examples/byteformer.

The upcoming space-based gravitational wave (GW) observatory, LISA, is expected to detect GW signals from supermassive black hole (SMBH) mergers occurring at high redshifts. However, understanding the origin and growth of SMBHs in the early Universe remains an open problem in astrophysics. In this work, we utilize the First Light And Reionization Epoch Simulations (FLARES), a suite of cosmological hydrodynamical zoom-in simulations, to study SMBH mergers at 5 lesssim z lesssim 10 across a wide range of environments. Most mergers in FLARES involve secondary SMBHs near the seed mass (m_{seed} approx 1.5 times 10^{5} M_{odot}) while primary SMBHs span up to 10^{9} M_{odot}, resulting in mass ratios from q sim 10^{-4} to 1, with a peak at q sim 1. The number of mergers increases rapidly towards lower redshifts, and the comoving total number density scales with overdensity as n_{merger} = 10^{-3.80} (1 + delta)^{4.56}. Denser regions host more massive mergers, with higher merger redshifts and lower mass ratios. Within the FLARES redshift range, LISA is expected to detect mergers with 10^{5} lesssim M_{tot} / M_{odot} lesssim 10^{8} and q gtrsim 10^{-2}, corresponding to a detection rate of 0.030 yr^{-1} for events with signal-to-noise ratio SNR geq 10. Our study demonstrates the sensitivity of GW predictions at high redshifts to SMBH seed models and merger time delays, highlighting the need for improved modeling in future cosmological simulations to maximize LISA's scientific return.