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We propose a new class of deep reinforcement learning (RL) algorithms that model latent representations in hyperbolic space. Sequential decision-making requires reasoning about the possible future consequences of current behavior.…
Multi-step reasoning is a fundamental challenge in artificial intelligence, with applications ranging from mathematical problem-solving to decision-making in dynamic environments. Reinforcement Learning (RL) has shown promise in enabling…
Hyperbolic spaces have recently gained momentum in the context of machine learning due to their high capacity and tree-likeliness properties. However, the representational power of hyperbolic geometry is not yet on par with Euclidean…
We examine five setups where an agent (or two agents) seeks to explore unknown environment without any prior information. Although seemingly very different, all of them can be formalized as Reinforcement Learning (RL) problems in hyperbolic…
Foundation models pre-trained on massive datasets, including large language models (LLMs), vision-language models (VLMs), and large multimodal models, have demonstrated remarkable success in diverse downstream tasks. However, recent studies…
Hierarchical reinforcement learning deals with the problem of breaking down large tasks into meaningful sub-tasks. Autonomous discovery of these sub-tasks has remained a challenging problem. We propose a novel method of learning sub-tasks…
Hyperbolic Neural Networks (HNNs), operating in hyperbolic space, have been widely applied in recent years, motivated by the existence of an optimal embedding in hyperbolic space that can preserve data hierarchical relationships (termed…
Hyperbolic spaces, which have the capacity to embed tree structures without distortion owing to their exponential volume growth, have recently been applied to machine learning to better capture the hierarchical nature of data. In this…
Retrieval-augmented generation (RAG) enables large language models (LLMs) to access external knowledge, helping mitigate hallucinations and enhance domain-specific expertise. Graph-based RAG enhances structural reasoning by introducing…
Deep reinforcement learning (RL) agents commonly rely on high-dimensional neural representations, despite growing evidence that task-relevant value and policy structure may be intrinsically low-dimensional. In this work, we present a simple…
Recently, there has been a surge of interest in representation learning in hyperbolic spaces, driven by their ability to represent hierarchical data with significantly fewer dimensions than standard Euclidean spaces. However, the viability…
Reinforcement learning (RL) has emerged as a powerful approach for tackling complex problems. The recent introduction of multi-objective reinforcement learning (MORL) has further expanded the scope of RL by enabling agents to make…
This paper investigates the notion of learning user and item representations in non-Euclidean space. Specifically, we study the connection between metric learning in hyperbolic space and collaborative filtering by exploring Mobius…
Many high-dimensional practical data sets have hierarchical structures induced by graphs or time series. Such data sets are hard to process in Euclidean spaces and one often seeks low-dimensional embeddings in other space forms to perform…
Metric learning plays a critical role in training image retrieval and classification. It is also a key algorithm in representation learning, e.g., for feature learning and its alignment in metric space. Hyperbolic embedding has been…
Hyperbolic networks have shown prominent improvements over their Euclidean counterparts in several areas involving hierarchical datasets in various domains such as computer vision, graph analysis, and natural language processing. However,…
In order to improve reproducibility, deep reinforcement learning (RL) has been adopting better scientific practices such as standardized evaluation metrics and reporting. However, the process of hyperparameter optimization still varies…
Hyperbolic geometry is an effective geometry for embedding hierarchical data structures. Hyperbolic learning has therefore become increasingly prominent in machine learning applications where data is hierarchically organized or governed by…
Reinforcement learning (RL) applications, where an agent can simply learn optimal behaviors by interacting with the environment, are quickly gaining tremendous success in a wide variety of applications from controlling simple pendulums to…
Due to its geometric properties, hyperbolic space can support high-fidelity embeddings of tree- and graph-structured data, upon which various hyperbolic networks have been developed. Existing hyperbolic networks encode geometric priors not…