UniSymNet: A Unified Symbolic Network Guided by Transformer

• URL: http://arxiv.org/abs/2505.06091v1
• Date: Fri, 09 May 2025 14:38:25 GMT
• Title: UniSymNet: A Unified Symbolic Network Guided by Transformer
• Authors: Xinxin Li, Juan Zhang, Da Li, Xingyu Liu, Jin Xu, Junping Yin,
• Abstract summary: We propose a Unified Symbolic Network that unifies nonlinear binary operators into nested unary operators.<n>UniSymNet shows high fitting accuracy, excellent symbolic solution rate, and relatively low expression complexity.
• Score: 21.207141107201775
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Symbolic Regression (SR) is a powerful technique for automatically discovering mathematical expressions from input data. Mainstream SR algorithms search for the optimal symbolic tree in a vast function space, but the increasing complexity of the tree structure limits their performance. Inspired by neural networks, symbolic networks have emerged as a promising new paradigm. However, most existing symbolic networks still face certain challenges: binary nonlinear operators $\{\times, \div\}$ cannot be naturally extended to multivariate operators, and training with fixed architecture often leads to higher complexity and overfitting. In this work, we propose a Unified Symbolic Network that unifies nonlinear binary operators into nested unary operators and define the conditions under which UniSymNet can reduce complexity. Moreover, we pre-train a Transformer model with a novel label encoding method to guide structural selection, and adopt objective-specific optimization strategies to learn the parameters of the symbolic network. UniSymNet shows high fitting accuracy, excellent symbolic solution rate, and relatively low expression complexity, achieving competitive performance on low-dimensional Standard Benchmarks and high-dimensional SRBench.

Related papers

• Neural Networks as Universal Finite-State Machines: A Constructive Feedforward Simulation Framework for NFAs [0.0]
  This work establishes a new bridge between symbolic automata theory and modern neural architectures.<n>We show that feedforward networks can perform precise, interpretable, and trainable symbolic computation.
  arXiv  Detail & Related papers  (2025-05-30T01:18:35Z)
• Compositional Generalization Across Distributional Shifts with Sparse Tree Operations [77.5742801509364]
  We introduce a unified neurosymbolic architecture called the Differentiable Tree Machine.<n>We significantly increase the model's efficiency through the use of sparse vector representations of symbolic structures.<n>We enable its application beyond the restricted set of tree2tree problems to the more general class of seq2seq problems.
  arXiv  Detail & Related papers  (2024-12-18T17:20:19Z)
• Enhancing lattice kinetic schemes for fluid dynamics with Lattice-Equivariant Neural Networks [79.16635054977068]
  We present a new class of equivariant neural networks, dubbed Lattice-Equivariant Neural Networks (LENNs) Our approach develops within a recently introduced framework aimed at learning neural network-based surrogate models Lattice Boltzmann collision operators. Our work opens towards practical utilization of machine learning-augmented Lattice Boltzmann CFD in real-world simulations.
  arXiv  Detail & Related papers  (2024-05-22T17:23:15Z)
• SymbolNet: Neural Symbolic Regression with Adaptive Dynamic Pruning for Compression [1.0356366043809717]
  We propose $ttSymbolNet$, a neural network approach to symbolic regression specifically designed as a model compression technique.<n>This framework allows dynamic pruning of model weights, input features, and mathematical operators in a single training process.
  arXiv  Detail & Related papers  (2024-01-18T12:51:38Z)
• A foundation for exact binarized morphological neural networks [2.8925699537310137]
  Training and running deep neural networks (NNs) often demands a lot of computation and energy-intensive specialized hardware. One way to reduce the computation and power cost is to use binary weight NNs, but these are hard to train because the sign function has a non-smooth gradient. We present a model based on Mathematical Morphology (MM), which can binarize ConvNets without losing performance under certain conditions.
  arXiv  Detail & Related papers  (2024-01-08T11:37:44Z)
• MetaSymNet: A Tree-like Symbol Network with Adaptive Architecture and Activation Functions [12.344379563265395]
  We propose MetaSymNet, a novel neural network that adjusts its structure in real-time, allowing for both expansion and contraction.<n>We evaluate MetaSymNet's performance against four state-of-the-art symbolic regression algorithms across more than 10 public datasets.
  arXiv  Detail & Related papers  (2023-11-13T13:27:59Z)
• A Neural-Guided Dynamic Symbolic Network for Exploring Mathematical Expressions from Data [12.964942755481585]
  Symbolic regression is a powerful technique for discovering the underlying mathematical expressions from observed data. Recent deep generative SR methods have shown promising results, but they face difficulties in processing high-dimensional problems. We propose DySymNet, a novel neural-guided Dynamic Symbolic Network for SR.
  arXiv  Detail & Related papers  (2023-09-24T17:37:45Z)
• Differentiable Tree Operations Promote Compositional Generalization [106.59434079287661]
  Differentiable Tree Machine (DTM) architecture integrates interpreter with external memory and agent that learns to sequentially select tree operations. DTM achieves 100% while existing baselines such as Transformer, Tree Transformer, LSTM, and Tree2Tree LSTM achieve less than 30%.
  arXiv  Detail & Related papers  (2023-06-01T14:46:34Z)
• Factorizers for Distributed Sparse Block Codes [45.29870215671697]
  We propose a fast and highly accurate method for factorizing distributed block codes (SBCs) Our iterative factorizer introduces a threshold-based nonlinear activation, conditional random sampling, and an $ell_infty$-based similarity metric. We demonstrate the feasibility of our method on four deep CNN architectures over CIFAR-100, ImageNet-1K, and RAVEN datasets.
  arXiv  Detail & Related papers  (2023-03-24T12:31:48Z)
• Iterative Soft Shrinkage Learning for Efficient Image Super-Resolution [91.3781512926942]
  Image super-resolution (SR) has witnessed extensive neural network designs from CNN to transformer architectures. This work investigates the potential of network pruning for super-resolution iteration to take advantage of off-the-shelf network designs and reduce the underlying computational overhead. We propose a novel Iterative Soft Shrinkage-Percentage (ISS-P) method by optimizing the sparse structure of a randomly network at each and tweaking unimportant weights with a small amount proportional to the magnitude scale on-the-fly.
  arXiv  Detail & Related papers  (2023-03-16T21:06:13Z)
• Symbolic Synthesis of Neural Networks [0.0]
  I present Graph-basedally Synthesized Neural Networks (GSSNNs) GSSNNs are a form of neural network whose topology and parameters are informed by the output of a symbolic program. I demonstrate that by developing symbolic abstractions at a population level, I can elicit reliable patterns of improved generalization with small quantities of data known to contain local and discrete features.
  arXiv  Detail & Related papers  (2023-03-06T18:13:14Z)
• Symbolic Visual Reinforcement Learning: A Scalable Framework with Object-Level Abstraction and Differentiable Expression Search [63.3745291252038]
  We propose DiffSES, a novel symbolic learning approach that discovers discrete symbolic policies. By using object-level abstractions instead of raw pixel-level inputs, DiffSES is able to leverage the simplicity and scalability advantages of symbolic expressions. Our experiments demonstrate that DiffSES is able to generate symbolic policies that are simpler and more scalable than state-of-the-art symbolic RL methods.
  arXiv  Detail & Related papers  (2022-12-30T17:50:54Z)
• Symbolic Distillation for Learned TCP Congestion Control [70.27367981153299]
  TCP congestion control has achieved tremendous success with deep reinforcement learning (RL) approaches. Black-box policies lack interpretability and reliability, and often, they need to operate outside the traditional TCP datapath. This paper proposes a novel two-stage solution to achieve the best of both worlds: first, to train a deep RL agent, then distill its NN policy into white-box, light-weight rules.
  arXiv  Detail & Related papers  (2022-10-24T00:58:16Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.