# Tiny Recursive Models for Solving the J2-Perturbed Lambert Problem

arXiv: https://arxiv.org/abs/2606.00895 · HTML: https://mlsanity.com/paper/2606.00895/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 15 references that are in the map.
- First posted on arXiv 30 May 2026.

## Builds on (most cited first, 5 of 5)

- [RT-2: Vision-Language-Action Models Transfer Web Knowledge to Robotic Control](https://mlsanity.com/paper/2307.15818/) (2023)
- [Transformer-based Model Predictive Control: Trajectory Optimization via Sequence Modeling](https://mlsanity.com/paper/2410.23916/) (2024)
- [Tiny Recursive Control: Iterative Reasoning for Efficient Optimal Control](https://mlsanity.com/paper/2512.16824/) (2025)
- [Design and Guidance of a Multi-Active Debris Removal Mission](https://mlsanity.com/paper/2210.11701/) (2022)
- [Exploiting Scaling Constants to Facilitate the Convergence of Indirect Trajectory Optimization Methods](https://mlsanity.com/paper/2208.11273/) (2022)

## Abstract (arXiv)

This paper presents a fast, recursive neural solver for the J2-perturbed Lambert problem based on Tiny Recursive Models (TRM), termed the TRM-Perturbed Lambert (TRM-PL) model. TRM is a weight-shared architecture whose effective capacity emerges from iteration depth rather than parameter count: a compact reasoning module is applied repeatedly within a two-level latent hierarchy, refining a candidate departure velocity by simulating the J2 trajectory and correcting it from the resulting tracking error. This unifies initial-guess generation and iterative correction in a single, end-to-end differentiable architecture. The recursive refinement loop is a learned alternative to the homotopy and continuation schemes of classical perturbed-Lambert solvers: rather than following a hand-designed path from the Keplerian to the perturbed solution, the network learns its own sequence of corrections. We evaluate TRM-PL on three test cases of increasing difficulty: single-revolution low-Earth-orbit (LEO) transfers, multi-revolution LEO transfers, and multi-revolution Jovian transfers. Three training paradigms are compared: jointly learning the Lambert solution and the J2 correction; refining the Lambert initial velocity with target-position and J2-corrected velocity supervision; and refining it with target-position supervision alone. Across all cases, the refinement-only approaches are the most reliable. The position-supervised variant reduces the median terminal-position error from 21.7 km to 0.027 km on single-revolution LEO, from 340.9 km to 0.31 km on multi-revolution LEO, all with the same 2.3M-parameter architecture. A single Newton corrector iteration on the TRM-PL output tightens the Jovian median to 0.063 km, yielding compact models accurate enough for embedded deployment.