The NFM framework utilizes the classical idea of multiplicative frailty in survival analysis as a principled way of extending the proportional hazard assumption, at the same time being able to leverage the strong approximation power of neural architectures for handling nonlinear covariate dependence. Two concrete models are derived under the framework that extends neural proportional hazard models and nonparametric hazard regression models. Both models allow efficient training under the likelihood objective. Theoretically, for both proposed models, we establish statistical guarantees of neural function approximation with respect to nonparametric components via characterizing their rate of convergence. Empirically, we provide synthetic experiments that verify our theoretical statements. We also conduct experimental evaluations over 6 benchmark datasets of different scales, showing that the proposed NFM models achieve predictive performance comparable to or sometimes surpassing state-of-the-art survival models.

Theorem proving in natural mathematical language - the mixture of symbolic and natural language used by humans - plays a central role in mathematical advances and education, and tests aspects of reasoning that are core to intelligence. Yet it has remained underexplored with modern generative models. We study largescale language models on two new generation tasks: suggesting the next step in a mathematical proof, and full proof generation. We develop NATURALPROVER,a language model that generates proofs by conditioning on background references (e.g.

Human Intelligence (HI) excels at combining basic skills to solve complex tasks. This capability is vital for Artificial Intelligence (AI) and should be embedded in comprehensive AIAgents, enabling them to harness expert models for complex task-solving towards Artificial General Intelligence (AGI). Large Language Models (LLMs) show promising learning and reasoning abilities, and can effectively use external models, tools, plugins, or APIs to tackle complex problems. In this work, we introduce OpenAGI, an open-source AGI research and development platform designed for solving multi-step, real-world tasks. Specifically, OpenAGI uses a dual strategy, integrating standard benchmark tasks for benchmarking and evaluation, and open-ended tasks including more expandable models, tools, plugins, or APIs for creative problem-solving. Tasks are presented as natural language queries to the LLM, which then selects and executes appropriate models. We also propose a Reinforcement Learning from Task Feedback (RLTF) mechanism that uses task results to improve the LLM's task-solving ability, which creates a self-improving AI feedback loop. While we acknowledge that AGI is a broad and multifaceted research challenge with no singularly defined solution path, the integration of LLMs with domain-specific expert models, inspired by mirroring the blend of general and specialized intelligence in humans, offers a promising approach towards AGI.

Message passing neural networks (MPNN) have seen a steep rise in popularity since their introduction as generalizations of convolutional neural networks to graph structured data, and are now considered state-of-the-art tools for solving a large variety of graph-focused problems. We study the generalization error of MPNNs in graph classification and regression. We assume that graphs of different classes are sampled from different random graph models. We show that, when training a MPNN on a dataset sampled from such a distribution, the generalization gap increases in the complexity of the MPNN, and decreases, not only with respect to the number of training samples, but also with the average number of nodes in the graphs. This shows how a MPNN with high complexity can generalize from a small dataset of graphs, as long as the graphs are large. The generalization bound is derived from a uniform convergence result, that shows that any MPNN, applied on a graph, approximates the MPNN applied on the geometric model that the graph discretizes.