Yue Wu

Yue Wu, Jesús A. De Loera

Can agents be trained to answer difficult mathematical questions by playing a game? We consider the integer feasibility problem, a challenge of deciding whether a system of linear equations and inequalities has a solution with integer values. This is a famous NP-complete problem with applications in many areas of Mathematics and Computer Science. Our paper describes a novel algebraic reinforcement learning framework that allows an agent to play a game equivalent to the integer feasibility problem. We explain how to transform the integer feasibility problem into a game over a set of arrays with fixed margin sums. The game starts with an initial state (an array), and by applying a legal move that leaves the margins unchanged, we aim to eventually reach a winning state with zeros in specific positions. To win the game the player must find a path between the initial state and a final terminal winning state if one exists. Finding such a winning state is equivalent to solving the integer feasibility problem. The key algebraic ingredient is a Gröbner basis of the toric ideal for the underlying axial transportation polyhedron. The Gröbner basis can be seen as a set of connecting moves (actions) of the game. We then propose a novel RL approach that trains an agent to predict moves in continuous space to cope with the large size of action space. The continuous move is then projected onto the set of legal moves so that the path always leads to valid states. As a proof of concept we demonstrate in experiments that our agent can play well the simplest version of our game for 2-way tables. Our work highlights the potential to train agents to solve non-trivial mathematical queries through contemporary machine learning methods used to train agents to play games.

Yue Wu, Jesús A. De Loera

Recently discovered polyhedral structures of the value function for finite state-action discounted Markov decision processes (MDP) shed light on understanding the success of reinforcement learning. We investigate the value function polytope in greater detail and characterize the polytope boundary using a hyperplane arrangement. We further show that the value space is a union of finitely many cells of the same hyperplane arrangement and relate it to the polytope of the classical linear programming formulation for MDPs. Inspired by these geometric properties, we propose a new algorithm, Geometric Policy Iteration (GPI), to solve discounted MDPs. GPI updates the policy of a single state by switching to an action that is mapped to the boundary of the value function polytope, followed by an immediate update of the value function. This new update rule aims at a faster value improvement without compromising computational efficiency. Moreover, our algorithm allows asynchronous updates of state values which is more flexible and advantageous compared to traditional policy iteration when the state set is large. We prove that the complexity of GPI achieves the best known bound $\mathcal{O}\left(\frac{|\mathcal{A}|}{1 - γ}\log \frac{1}{1-γ}\right)$ of policy iteration and empirically demonstrate the strength of GPI on MDPs of various sizes.

Tianxiang Chen, Zhentao Tan, Xiaofan Bo et al.

Effectively handling long contexts is challenging for Large Language Models (LLMs) due to the rarity of long texts, high computational demands, and substantial forgetting of short-context abilities. Recent approaches have attempted to construct long contexts for instruction tuning, but these methods often require LLMs or human interventions, which are both costly and limited in length and diversity. Also, the drop in short-context performances of present long-context LLMs remains significant. In this paper, we introduce Flora, an effortless (human/LLM-free) long-context construction strategy. Flora can markedly enhance the long-context performance of LLMs by arbitrarily assembling short instructions based on categories and instructing LLMs to generate responses based on long-context meta-instructions. This enables Flora to produce contexts of arbitrary length and scale with rich diversity, while only slightly compromising short-context performance. Experiments on Llama3-8B-Instruct and QwQ-32B show that LLMs enhanced by Flora excel in three long-context benchmarks while maintaining strong performances in short-context tasks. Our data-construction code is available at \href{https://github.com/txchen-USTC/Flora}{https://github.com/txchen-USTC/Flora}.

Xiaolan Chen, Ziwei Zhao, Weiyi Zhang et al.

Artificial intelligence (AI) has gained significant attention in healthcare consultation due to its potential to improve clinical workflow and enhance medical communication. However, owing to the complex nature of medical information, large language models (LLM) trained with general world knowledge might not possess the capability to tackle medical-related tasks at an expert level. Here, we introduce EyeGPT, a specialized LLM designed specifically for ophthalmology, using three optimization strategies including role-playing, finetuning, and retrieval-augmented generation. In particular, we proposed a comprehensive evaluation framework that encompasses a diverse dataset, covering various subspecialties of ophthalmology, different users, and diverse inquiry intents. Moreover, we considered multiple evaluation metrics, including accuracy, understandability, trustworthiness, empathy, and the proportion of hallucinations. By assessing the performance of different EyeGPT variants, we identify the most effective one, which exhibits comparable levels of understandability, trustworthiness, and empathy to human ophthalmologists (all Ps>0.05). Overall, ur study provides valuable insights for future research, facilitating comprehensive comparisons and evaluations of different strategies for developing specialized LLMs in ophthalmology. The potential benefits include enhancing the patient experience in eye care and optimizing ophthalmologists' services.

Jingyi Liu, Zhongyu Li, Xiayue Fan et al.

Electrocardiogram (ECG) signals play critical roles in the clinical screening and diagnosis of many types of cardiovascular diseases. Despite deep neural networks that have been greatly facilitated computer-aided diagnosis (CAD) in many clinical tasks, the variability and complexity of ECG in the clinic still pose significant challenges in both diagnostic performance and clinical applications. In this paper, we develop a robust and scalable framework for the clinical recognition of ECG. Considering the fact that hospitals generally record ECG signals in the form of graphic waves of 2-D images, we first extract the graphic waves of 12-lead images into numerical 1-D ECG signals by a proposed bi-directional connectivity method. Subsequently, a novel deep neural network, namely CRT-Net, is designed for the fine-grained and comprehensive representation and recognition of 1-D ECG signals. The CRT-Net can well explore waveform features, morphological characteristics and time domain features of ECG by embedding convolution neural network(CNN), recurrent neural network(RNN), and transformer module in a scalable deep model, which is especially suitable in clinical scenarios with different lengths of ECG signals captured from different devices. The proposed framework is first evaluated on two widely investigated public repositories, demonstrating the superior performance of ECG recognition in comparison with state-of-the-art. Moreover, we validate the effectiveness of our proposed bi-directional connectivity and CRT-Net on clinical ECG images collected from the local hospital, including 258 patients with chronic kidney disease (CKD), 351 patients with Type-2 Diabetes (T2DM), and around 300 patients in the control group. In the experiments, our methods can achieve excellent performance in the recognition of these two types of disease.