# Neural ODE Transformers: Analyzing Internal Dynamics and Adaptive Fine-tuning

arXiv: https://arxiv.org/abs/2503.01329 · HTML: https://mlsanity.com/paper/2503.01329/

## 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 (most cited first, 30 of 42)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awareness](https://mlsanity.com/paper/2205.14135/) (2022)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [ALBERT: A Lite BERT for Self-supervised Learning of Language Representations](https://mlsanity.com/paper/1909.11942/) (2019)
- [Pythia: A Suite for Analyzing Large Language Models Across Training and Scaling](https://mlsanity.com/paper/2304.01373/) (2023)
- [Attention is not Explanation](https://mlsanity.com/paper/1902.10186/) (2019)
- [Training Deep Nets with Sublinear Memory Cost](https://mlsanity.com/paper/1604.06174/) (2016)
- [Transformers learn in-context by gradient descent](https://mlsanity.com/paper/2212.07677/) (2022)
- [What Can Transformers Learn In-Context? A Case Study of Simple Function Classes](https://mlsanity.com/paper/2208.01066/) (2022)
- [Scaling Vision Transformers to 22 Billion Parameters](https://mlsanity.com/paper/2302.05442/) (2023)
- [Attention is not not Explanation](https://mlsanity.com/paper/1908.04626/) (2019)
- [Transformer Interpretability Beyond Attention Visualization](https://mlsanity.com/paper/2012.09838/) (2020)
- [Deep Equilibrium Models](https://mlsanity.com/paper/1909.01377/) (2019)
- [Measuring the Intrinsic Dimension of Objective Landscapes](https://mlsanity.com/paper/1804.08838/) (2018)
- [Model evaluation for extreme risks](https://mlsanity.com/paper/2305.15324/) (2023)
- [Neural Stochastic Differential Equations: Deep Latent Gaussian Models in the Diffusion Limit](https://mlsanity.com/paper/1905.09883/) (2019)
- [Equinox: neural networks in JAX via callable PyTrees and filtered transformations](https://mlsanity.com/paper/2111.00254/) (2021)
- [Sinkformers: Transformers with Doubly Stochastic Attention](https://mlsanity.com/paper/2110.11773/) (2021)
- [XAI for Transformers: Better Explanations through Conservative Propagation](https://mlsanity.com/paper/2202.07304/) (2022)
- [Uncovering mesa-optimization algorithms in Transformers](https://mlsanity.com/paper/2309.05858/) (2023)
- [Branchformer: Parallel MLP-Attention Architectures to Capture Local and Global Context for Speech Recognition and Understanding](https://mlsanity.com/paper/2207.02971/) (2022)
- [Chaos as an interpretable benchmark for forecasting and data-driven modelling](https://mlsanity.com/paper/2110.05266/) (2021)
- [Memory-Efficient Backpropagation Through Time](https://mlsanity.com/paper/1606.03401/) (2016)
- [Lyapunov spectra of chaotic recurrent neural networks](https://mlsanity.com/paper/2006.02427/) (2020)

## Built on by (most cited first, 13 of 13)

- [Deep Delta Learning](https://mlsanity.com/paper/2601.00417/) (2026)
- [Semantic Tube Prediction: Beating LLM Data Efficiency with JEPA](https://mlsanity.com/paper/2602.22617/) (2026)
- [Recurrent Self-Attention Dynamics: An Energy-Agnostic Perspective from Jacobians](https://mlsanity.com/paper/2505.19458/) (2025)
- [Interpretability as Alignment: Making Internal Understanding a Design Principle](https://mlsanity.com/paper/2509.08592/) (2025)
- [Multi-Headed Transformer Architectures as Time-dependent Wasserstein Gradient Flows](https://mlsanity.com/paper/2605.18870/) (2026)
- [TANDEM: Temporal Attention-guided Neural Differential Equations for Missingness in Time Series Classification](https://mlsanity.com/paper/2508.17519/) (2025)
- [IIET: Efficient Numerical Transformer via Implicit Iterative Euler Method](https://mlsanity.com/paper/2509.22463/) (2025)
- [PCARNN-DCBF: Minimal-Intervention Geofence Enforcement for Ground Vehicles](https://mlsanity.com/paper/2511.15522/) (2025)
- [ODE-ViT: Plug & Play Attention Layer from the Generalization of the ViT as an Ordinary Differential Equation](https://mlsanity.com/paper/2511.16501/) (2025)
- [The Hamilton-Jacobi Theory of Deep Learning](https://mlsanity.com/paper/2605.28983/) (2026)
- [From Self-Attention to Connection Laplacian: A Unified Operator View of Transformers](https://mlsanity.com/paper/2607.10677/) (2026)
- [DynImmune-BERT: Dynamic Immune Repertoire Modeling with Neural ODE Driven Continuous Transformers](https://mlsanity.com/paper/2607.17244/) (2026)
- [ODE-Based Transformer Decoders for Iterative Sign Language Translation](https://mlsanity.com/paper/2608.11352/) (2026)

## 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.