Oversmoothing in Graph Neural Networks (GNNs) refers to the phenomenon where increasing network depth leads to homogeneous node representations. While previous work has established that Graph Convolutional Networks (GCNs) exponentially lose expressive power, it remains controversial whether the graph attention mechanism can mitigate oversmoothing. In this work, we provide a definitive answer to this question through a rigorous mathematical analysis, by viewing attention-based GNNs as nonlinear time-varying dynamical systems and incorporating tools and techniques from the theory of products of inhomogeneous matrices and the joint spectral radius. We establish that, contrary to popular belief, the graph attention mechanism cannot prevent oversmoothing and loses expressive power exponentially. The proposed framework extends the existing results on oversmoothing for symmetric GCNs to a significantly broader class of GNN models, including random walk GCNs, Graph Attention Networks (GATs) and (graph) transformers.

In sampling-based Bayesian models of brain function, neural activities are assumed to be samples from probability distributions that the brain uses for probabilistic computation. However, a comprehensive understanding of how mechanistic models of neural dynamics can sample from arbitrary distributions is still lacking. We use tools from functional analysis and stochastic differential equations to explore the minimum architectural requirements for recurrent neural circuits to sample from complex distributions. We first consider the traditional sampling model consisting of a network of neurons whose outputs directly represent the samples (sampler-only network). We argue that synaptic current and firing-rate dynamics in the traditional model have limited capacity to sample from a complex probability distribution. We show that the firing rate dynamics of a recurrent neural circuit with a separate set of output units can sample from an arbitrary probability distribution. We call such circuits reservoir-sampler networks (RSNs). We propose an efficient training procedure based on denoising score matching that finds recurrent and output weights such that the RSN implements Langevin sampling. We empirically demonstrate our model's ability to sample from several complex data distributions using the proposed neural dynamics and discuss its applicability to developing the next generation of sampling-based Bayesian brain models.

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When you purchase through links in our articles, we may earn a small commission. I asked AI to book dinner. ChatGPT, Claude, and Gemini may be aces at coding, but they're less than magical when it comes to booking a table for three. I can clearly see the day when we'll be able to summon ChatGPT, Claude, or Gemini on our phones, say something like "Hey ChatGPT, book a table for two at Outback Steakhouse tonight at 8," and ChatGPT will simply take care of it. All of the big AI providers are busy unveiling integrations for everyday services ranging from Spotify and DoorDash to AllTrails and the dinner reservation app Resy, with varying degrees of success.

OpenAI is racing to catch up to its greatest rival. OpenAI does not like to be left out. The week after Anthropic announced Claude Mythos Preview --an AI model that has put governments around the world on edge because of its potential ability to hack into banks, energy grids, and military systems--OpenAI shared a program that is uncannily similar. And just like Anthropic did with its model, OpenAI has, for cybersecurity purposes, restricted access to this new bot, called GPT-5.4-Cyber, to a small group of trusted users. This sequence has become something of a pattern: First Anthropic will make an announcement, and then OpenAI will follow suit.

In recent years, AI-assisted drug design methods have been proposed to generate molecules given the pockets' structures of target proteins. Most of them are atomlevel-based methods, which consider atoms as basic components and generate atom positions and types. In this way, however, it is hard to generate realistic fragments with complicated structures. To solve this, we propose D3FG, a functional-groupbased diffusion model for pocket-specific molecule generation and elaboration. D3FG decomposes molecules into two categories of components: functional groups defined as rigid bodies and linkers as mass points. And the two kinds of components can together form complicated fragments that enhance ligand-protein interactions. To be specific, in the diffusion process, D3FG diffuses the data distribution of the positions, orientations, and types of the components into a prior distribution; In the generative process, the noise is gradually removed from the three variables by denoisers parameterized with designed equivariant graph neural networks. In the experiments, our method can generate molecules with more realistic 3D structures, competitive affinities toward the protein targets, and better drug properties. Besides, D3FG as a solution to a new task of molecule elaboration, could generate molecules with high affinities based on existing ligands and the hotspots of target proteins.