Traditional neural networks employ fixed weights during inference, limiting their ability to adapt to changing input conditions, unlike biological neurons that adjust signal strength dynamically based on stimuli. This discrepancy between artificial and biological neurons constrains neural network flexibility and adaptability. To bridge this gap, we propose a novel framework for adaptive neural networks, where neuron weights are modeled as functions of the input signal, allowing the network to adjust dynamically in real-time. Importantly, we achieve this within the same traditional architecture of an Artificial Neural Network, maintaining structural familiarity while introducing dynamic adaptability. In our research, we apply Chebyshev polynomials as one of the many possible decomposition methods to achieve this adaptive weighting mechanism, with polynomial coefficients learned during training. Of the 145 datasets tested, our adaptive Chebyshev neural network demonstrated a marked improvement over an equivalent MLP in approximately 83% of the cases, performing strictly better on 121 datasets. In the remaining 24 datasets, the performance of our algorithm matched that of the MLP, highlighting its ability to generalize the behavior of standard neural networks while offering enhanced adaptability. As a generalized form of MLP, this model seamlessly retains MLP performance where needed while extending its capabilities to achieve superior accuracy across a wide range of complex tasks. These results underscore the potential of adaptive neurons to enhance generalization, flexibility, and robustness in neural networks, particularly in applications with dynamic or non-linear data dependencies. • Dynamic weighting mechanism allows neurons to adapt their output based on input strength, mimicking biological adaptability. • Chebyshev polynomials provide mathematical flexibility, enabling nuanced and complex weight dynamics. • Improved generalization capability in tasks involving complex and non-linear input–output relationships.

The AI community has been exploring a pathway to artificial general intelligence (AGI) by developing “language agents”, which are complex large language models (LLMs) workflows involving both prompting techniques and tool usage methods. While language agents have demonstrated impressive capabilities for many real-world tasks, a fundamental limitation of current language agents research is that they are model-centric or engineering-centric. That is to say, the design of prompts, tools, and workflows of language agents requires substantial manual engineering efforts from human experts rather than automatically learning from data. We believe the transition from model-centric, or engineering-centric, to data-centric, i.e., the ability of language agents to autonomously learn and evolve in environments, is the key for them to possibly achieve AGI.In this work, we introduce agent symbolic learning, a systematic framework that enables language agents to optimize themselves on their own in a data-centric way using symbolic optimizers. Specifically, we consider agents as symbolic networks in which learnable weights are defined by prompts, tools, and the way they are stacked together. Agent symbolic learning is designed to optimize the symbolic network within language agents in a data-centric way by mimicking two fundamental algorithms in connectionist learning: back-propagation and gradient descent. Instead of dealing with numeric weights, agent symbolic learning works with text-based weights, loss, and gradients. We conduct proof-of-concept experiments on both standard benchmarks and complex real-world tasks and show substantial improvements over static agent frameworks and simple prompt/tool optimization methods. In addition, agent symbolic learning enables language agents to update themselves after being created and deployed in the wild, resulting in “self-evolving agents”. We will open-source the agent symbolic learning framework to facilitate future research on data-centric agent learning.