Neural ODE Transformers: Analyzing Internal Dynamics and Adaptive Fine-tuning
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Abstract (arXiv)
Recent advancements in large language models (LLMs) based on transformer architectures have sparked significant interest in understanding their inner workings. In this paper, we introduce a novel approach to modeling transformer architectures using highly flexible non-autonomous neural ordinary differential equations (ODEs). Our proposed model parameterizes all weights of attention and feed-forward blocks through neural networks, expressing these weights as functions of a continuous layer index. Through spectral analysis of the model's dynamics, we uncover an increase in eigenvalue magnitude that challenges the weight-sharing assumption prevalent in existing theoretical studies. We also leverage the Lyapunov exponent to examine token-level sensitivity, enhancing model interpretability. Our neural ODE transformer demonstrates performance comparable to or better than vanilla transformers across various configurations and datasets, while offering flexible fine-tuning capabilities that can adapt to different architectural constraints.
Key facts. Cited by 13 papers in the map (data through 14 Oct 2026). Builds on 42 of its 67 references that are in the map. First posted on arXiv 3 Mar 2025.
Builds on
42 of 67 references.
References · 42
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Citing papers per year: 2025: 6; 2026: 7.
13 papers.
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- 2026Deep Delta Learningcited by 9
- 2026Semantic Tube Prediction: Beating LLM Data Efficiency with JEPAcited by 7
- 2025Recurrent Self-Attention Dynamics: An Energy-Agnostic Perspective from Jacobianscited by 5
- 2025Interpretability as Alignment: Making Internal Understanding a Design Principlecited by 3
- 2026Multi-Headed Transformer Architectures as Time-dependent Wasserstein Gradient Flowscited by 1
- 2025TANDEM: Temporal Attention-guided Neural Differential Equations for Missingness in Time Series Classificationcited by 0
- 2025IIET: Efficient Numerical Transformer via Implicit Iterative Euler Methodcited by 0
- 2025PCARNN-DCBF: Minimal-Intervention Geofence Enforcement for Ground Vehiclescited by 0
- 2025ODE-ViT: Plug & Play Attention Layer from the Generalization of the ViT as an Ordinary Differential Equationcited by 0
- 2026The Hamilton-Jacobi Theory of Deep Learningcited by 0
- 2026From Self-Attention to Connection Laplacian: A Unified Operator View of Transformerscited by 0
- 2026DynImmune-BERT: Dynamic Immune Repertoire Modeling with Neural ODE Driven Continuous Transformerscited by 0
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- 2026ODE-Based Transformer Decoders for Iterative Sign Language Translation11 Aug 2026
- 2026DynImmune-BERT: Dynamic Immune Repertoire Modeling with Neural ODE Driven Continuous Transformers19 Jul 2026
- 2026From Self-Attention to Connection Laplacian: A Unified Operator View of Transformers12 Jul 2026
- 2026The Hamilton-Jacobi Theory of Deep Learning27 May 2026
- 2026Multi-Headed Transformer Architectures as Time-dependent Wasserstein Gradient Flows15 May 2026
- 2026Semantic Tube Prediction: Beating LLM Data Efficiency with JEPA26 Feb 2026
- 2026Deep Delta Learning1 Jan 2026
- 2025ODE-ViT: Plug & Play Attention Layer from the Generalization of the ViT as an Ordinary Differential Equation20 Nov 2025
- 2025PCARNN-DCBF: Minimal-Intervention Geofence Enforcement for Ground Vehicles19 Nov 2025
- 2025IIET: Efficient Numerical Transformer via Implicit Iterative Euler Method26 Sep 2025
- 2025Interpretability as Alignment: Making Internal Understanding a Design Principle10 Sep 2025
- 2025TANDEM: Temporal Attention-guided Neural Differential Equations for Missingness in Time Series Classification24 Aug 2025
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- 2026Deep Delta Learningcited by 9
- 2026Semantic Tube Prediction: Beating LLM Data Efficiency with JEPAcited by 7
- 2025Recurrent Self-Attention Dynamics: An Energy-Agnostic Perspective from Jacobianscited by 5
- 2025Interpretability as Alignment: Making Internal Understanding a Design Principlecited by 3
- 2026Multi-Headed Transformer Architectures as Time-dependent Wasserstein Gradient Flowscited by 1
- 2025TANDEM: Temporal Attention-guided Neural Differential Equations for Missingness in Time Series Classificationcited by 0
- 2025IIET: Efficient Numerical Transformer via Implicit Iterative Euler Methodcited by 0
- 2025PCARNN-DCBF: Minimal-Intervention Geofence Enforcement for Ground Vehiclescited by 0
- 2025ODE-ViT: Plug & Play Attention Layer from the Generalization of the ViT as an Ordinary Differential Equationcited by 0
- 2026The Hamilton-Jacobi Theory of Deep Learningcited by 0
- 2026From Self-Attention to Connection Laplacian: A Unified Operator View of Transformerscited by 0
- 2026DynImmune-BERT: Dynamic Immune Repertoire Modeling with Neural ODE Driven Continuous Transformerscited by 0
12 most cited of 13 All 13 (JSON)
- 2026ODE-Based Transformer Decoders for Iterative Sign Language Translation11 Aug 2026
- 2026DynImmune-BERT: Dynamic Immune Repertoire Modeling with Neural ODE Driven Continuous Transformers19 Jul 2026
- 2026From Self-Attention to Connection Laplacian: A Unified Operator View of Transformers12 Jul 2026
- 2026The Hamilton-Jacobi Theory of Deep Learning27 May 2026
- 2026Multi-Headed Transformer Architectures as Time-dependent Wasserstein Gradient Flows15 May 2026
- 2026Semantic Tube Prediction: Beating LLM Data Efficiency with JEPA26 Feb 2026
- 2026Deep Delta Learning1 Jan 2026
- 2025ODE-ViT: Plug & Play Attention Layer from the Generalization of the ViT as an Ordinary Differential Equation20 Nov 2025
- 2025PCARNN-DCBF: Minimal-Intervention Geofence Enforcement for Ground Vehicles19 Nov 2025
- 2025IIET: Efficient Numerical Transformer via Implicit Iterative Euler Method26 Sep 2025
- 2025Interpretability as Alignment: Making Internal Understanding a Design Principle10 Sep 2025
- 2025TANDEM: Temporal Attention-guided Neural Differential Equations for Missingness in Time Series Classification24 Aug 2025
12 newest of 13 All 13 (JSON)
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