Interactive Symbolic Regression through Offline Reinforcement Learning: A Co-Design Framework

Symbolic Regression (SR) holds great potential for uncovering underlying mathematical and physical relationships from observed data. However, the vast combinatorial space of possible expressions poses significant challenges for both online search methods and pre-trained transformer models. Additionally, current state-of-the-art approaches typically do not consider the integration of domain experts' prior knowledge and do not support iterative interactions with the model during the equation discovery process. To address these challenges, we propose the Symbolic Q-network (Sym-Q), an advanced interactive framework for large-scale symbolic regression. Unlike previous large-scale transformer-based SR approaches, Sym-Q leverages reinforcement learning without relying on a transformer-based decoder. This formulation allows the agent to learn through offline reinforcement learning using any type of tree encoder, enabling more efficient training and inference. Furthermore, we propose a co-design mechanism, where the reinforcement learning-based Sym-Q facilitates effective interaction with domain experts at any stage of the equation discovery process. Users can dynamically modify generated nodes of the expression, collaborating with the agent to tailor the mathematical expression to best fit the problem and align with the assumed physical laws, particularly when there is prior partial knowledge of the expected behavior. Our experiments demonstrate that the pre-trained Sym-Q surpasses existing SR algorithms on the challenging SSDNC benchmark. Moreover, we experimentally show on real-world cases that its performance can be further enhanced by the interactive co-design mechanism, with Sym-Q achieving greater performance gains than other state-of-the-art models. Our reproducible code is available at https://github.com/EPFL-IMOS/Sym-Q.

X-LeBench: A Benchmark for Extremely Long Egocentric Video Understanding

Long-form egocentric video understanding provides rich contextual information and unique insights into long-term human behaviors, holding significant potential for applications in embodied intelligence, long-term activity analysis, and personalized assistive technologies. However, existing benchmark datasets primarily focus on single, short-duration videos or moderately long videos up to dozens of minutes, leaving a substantial gap in evaluating extensive, ultra-long egocentric video recordings. To address this, we introduce X-LeBench, a novel benchmark dataset specifically crafted for evaluating tasks on extremely long egocentric video recordings. Leveraging the advanced text processing capabilities of large language models (LLMs), X-LeBench develops a life-logging simulation pipeline that produces realistic, coherent daily plans aligned with real-world video data. This approach enables the flexible integration of synthetic daily plans with real-world footage from Ego4D-a massive-scale egocentric video dataset covers a wide range of daily life scenarios-resulting in 432 simulated video life logs that mirror realistic daily activities in contextually rich scenarios. The video life-log durations span from 23 minutes to 16.4 hours. The evaluation of several baseline systems and multimodal large language models (MLLMs) reveals their poor performance across the board, highlighting the inherent challenges of long-form egocentric video understanding and underscoring the need for more advanced models.

Sym-Q: Adaptive Symbolic Regression via Sequential Decision-Making

Symbolic regression holds great potential for uncovering underlying mathematical and physical relationships from empirical data. While existing transformer-based models have recently achieved significant success in this domain, they face challenges in terms of generalizability and adaptability. Typically, in cases where the output expressions do not adequately fit experimental data, the models lack efficient mechanisms to adapt or modify the expression. This inflexibility hinders their application in real-world scenarios, particularly in discovering unknown physical or biological relationships. Inspired by how human experts refine and adapt expressions, we introduce Symbolic Q-network (Sym-Q), a novel reinforcement learning-based model that redefines symbolic regression as a sequential decision-making task. Sym-Q leverages supervised demonstrations and refines expressions based on reward signals indicating the quality of fitting precision. Its distinctive ability to manage the complexity of expression trees and perform precise step-wise updates significantly enhances flexibility and efficiency. Our results demonstrate that Sym-Q excels not only in recovering underlying mathematical structures but also uniquely learns to efficiently refine the output expression based on reward signals, thereby discovering underlying expressions. Sym-Q paves the way for more intuitive and impactful discoveries in physical science, marking a substantial advancement in the field of symbolic regression.