# Temporal Attention for Adaptive Control of Euler-Lagrange Systems with Unobservable Memory

arXiv: https://arxiv.org/abs/2605.06877 · HTML: https://mlsanity.com/paper/2605.06877/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 24 references that are in the map.
- First posted on arXiv 7 May 2026.

## Builds on (most cited first, 9 of 9)

- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [DARTS: Differentiable Architecture Search](https://mlsanity.com/paper/1806.09055/) (2018)
- [Constrained Policy Optimization](https://mlsanity.com/paper/1705.10528/) (2017)
- [Efficient Neural Architecture Search via Parameter Sharing](https://mlsanity.com/paper/1802.03268/) (2018)
- [Control Barrier Functions: Theory and Applications](https://mlsanity.com/paper/1903.11199/) (2019)
- [Responsive Safety in Reinforcement Learning by PID Lagrangian Methods](https://mlsanity.com/paper/2007.03964/) (2020)
- [A Lyapunov-based Approach to Safe Reinforcement Learning](https://mlsanity.com/paper/1805.07708/) (2018)
- [Differentiable Architecture Search for Reinforcement Learning](https://mlsanity.com/paper/2106.02229/) (2021)
- [INCRT: An Incremental Transformer That Determines Its Own Architecture](https://mlsanity.com/paper/2604.10703/) (2026)

## Built on by (most cited first, 1 of 1)

- [Runtime-Incremental Transformer for Reinforcement-Learning-Based Adaptive Control](https://mlsanity.com/paper/2609.13545/) (2026)

## Abstract (arXiv)

Adaptive control of Euler-Lagrange systems is challenging when friction is governed by a finite-horizon internal state that is not directly observable from joint measurements. In this setting, the measured closed-loop state is no longer Markovian, and standard certainty-equivalence adaptive laws may lose their convergence guarantees. The paper proposes a meta-control architecture in which the gains of a computed-torque controller are generated by a self-attention block processing a short window of recent motion history. The number of attention heads is selected before policy training through a surrogate analysis of the autocovariance of the memory-state gradient along the temporal window. This surrogate is based on a temporal adaptation of an incremental rank-tracking framework previously developed by the authors. The selected head count is then fixed and used as an architectural hyperparameter in a reinforcement-learning stage, where the policy is trained under a shielded admissibility constraint. The approach is tested on a 2-DOF manipulator with nonlinear friction and variable payload. In the short and matched memory regimes, the single-layer attention-only meta-controller outperforms a deeper Transformer baseline, with tracking-error reductions of 12 and 19 percentage points, respectively. The reported effect sizes are large, with d approximately -1.1 and -2.1, and Mann-Whitney p < 0.05 in both cases. In the long memory regime, however, the advantage disappears. Four out of ten training runs show either divergence or payload-invariant policy collapse, revealing a weakness in the static Phase-1 head-count prescription. This motivates moving rank-tracking inside the reinforcement-learning loop, allowing attention heads to be pruned or grown at runtime instead of fixed before training.