This work presents a modification of the self-attention dynamics proposed by Geshkovski et al. (2023b) to better reflect the practically relevant, causally masked attention used in transformer architectures for generative AI. This modification translates into an interacting particle system that cannot be interpreted as a mean-field gradient flow. Despite this loss of structure, we significantly strengthen the results of Geshkovski et al. (2023b) in this context: While previous rigorous results focused on cases where all three matrices (Key, Query, and Value) were scaled identities, we prove asymptotic convergence to a single cluster for arbitrary key-query matrices and a value matrix equal to the identity. Additionally, we establish a connection to the classical Rényi parking problem from combinatorial geometry to make initial theoretical steps towards demonstrating the existence of meta-stable states.

We introduce Unbalanced Sobolev Descent (USD), a particle descent algorithm for transporting a high dimensional source distribution to a target distribution that does not necessarily have the same mass.

We introduce Unbalanced Sobolev Descent (USD), a particle descent algorithm for transporting a high dimensional source distribution to a target distribution that does not necessarily have the same mass. We define the Sobolev-Fisher discrepancy between distributions and show that it relates to advection-reaction transport equations and the Wasserstein-Fisher-Rao metric between distributions. USD transports particles along gradient flows of the witness function of the Sobolev-Fisher discrepancy (advection step) and reweighs the mass of particles with respect to this witness function (reaction step). The reaction step can be thought of as a birth-death process of the particles with rate of growth proportional to the witness function. When the Sobolev-Fisher witness function is estimated in a Reproducing Kernel Hilbert Space (RKHS), under mild assumptions we show that USD converges asymptotically (in the limit of infinite particles) to the target distribution in the Maximum Mean Discrepancy (MMD) sense. We then give two methods to estimate the Sobolev-Fisher witness with neural networks, resulting in two Neural USD algorithms. The first one implements the reaction step with mirror descent on the weights, while the second implements it through a birthdeath process of particles. We show on synthetic examples that USD transports distributions with or without conservation of mass faster than previous particle descent algorithms, and finally demonstrate its use for molecular biology analyses where our method is naturally suited to match developmental stages of populations of differentiating cells based on their single-cell RNA sequencing profile. Code is available at http://github.com/ibm/usd.

This manuscript contributes a general and practical framework for casting a Markov process model of a system at equilibrium as a structural causal model, and carrying out counterfactual inference. Markov processes mathematically describe the mechanisms in the system, and predict the system's equilibrium behavior upon intervention, but do not support counterfactual inference. In contrast, structural causal models support counterfactual inference, but do not identify the mechanisms.

SL techniques to be studied.

B.1 Background on Successive Halving Successive Halving (SH) divides a total budget of T iterations into L " rlog This results in an exponential distribution of resources allocated to the different candidates, with more resources allocated to those that are more promising after intermediate evaluation. Adapting it to our setting of treating the problem as a top-m identification is done by simply using L " rlog The online variant of the algorithm is useful if a user is unsure about the total iteration budget that they want to spend on the input program. We therefore need to adapt Algo. 1 so that it can be'restarted' after it has terminated. A naive approach to this would be to simply run Algo. 1 again but re-use the q's for the SLPs that have already been discovered and only initialize the q However, this scheme is limited as it disproportionately favours SLPs which were discovered in the previous run. This is because for those SLPs the local ELBOs will already be relatively large compared to the newly added SLPs.

While humans effortlessly discern intrinsic dynamics and adapt to new scenarios, modern AI systems often struggle. Current methods for visual grounding of dynamics either use pure neural-network-based simulators (black box), which may violate physical laws, or traditional physical simulators (white box), which rely on expert-defined equations that may not fully capture actual dynamics. We propose the Neural Material Adaptor (NeuMA), which integrates existing physical laws with learned corrections, facilitating accurate learning of actual dynamics while maintaining the generalizability and interpretability of physical priors. Additionally, we propose Particle-GS, a particle-driven 3D Gaussian Splatting variant that bridges simulation and observed images, allowing back-propagate image gradients to optimize the simulator. Comprehensive experiments on various dynamics in terms of grounded particle accuracy, dynamic rendering quality, and generalization ability demonstrate that NeuMA can accurately capture intrinsic dynamics.

In the past decade, deep conditional generative models have revolutionized the generation of realistic images, extending their application from entertainment to scientific domains. Single-particle cryo-electron microscopy (cryo-EM) is crucial in resolving near-atomic resolution 3D structures of proteins, such as the SARS-COV-2 spike protein. To achieve high-resolution reconstruction, a comprehensive data processing pipeline has been adopted. However, its performance is still limited as it lacks high-quality annotated datasets for training. To address this, we introduce physics-informed generative cryo-electron microscopy (CryoGEM), which for the first time integrates physics-based cryo-EM simulation with a generative unpaired noise translation to generate physically correct synthetic cryo-EM datasets with realistic noises. Initially, CryoGEM simulates the cryo-EM imaging process based on a virtual specimen. To generate realistic noises, we leverage an unpaired noise translation via contrastive learning with a novel mask-guided sampling scheme. Extensive experiments show that CryoGEM is capable of generating authentic cryo-EM images. The generated dataset can be used as training data for particle picking and pose estimation models, eventually improving the reconstruction resolution.

Breakthroughs, discoveries, and DIY tips sent every weekday. The world's harbor seals (Phoca vitulina) are masters in seeing through the cloudy coastal waters they call home. Equipped with dexterous whiskers, these pinnipeds use a suite of senses to navigate their surroundings with ease. Harbor seals may also use an important part of their vision to determine which direction they are moving, even with such an opaque view of the world. Now, we might know a bit more about how they can tell which direction they are heading.

Cryo-electron microscopy (cryo-EM) is an experimental technique for protein structure determination that images an ensemble of macromolecules in nearphysiological contexts. While recent advances enable the reconstruction of dynamic conformations of a single biomolecular complex, current methods do not adequately model samples with mixed conformational and compositional heterogeneity. In particular, datasets containing mixtures of multiple proteins require the joint inference of structure, pose, compositional class, and conformational states for 3D reconstruction.