# PLAN: Parallel Liquid-Inspired Approximation Network for Efficient Representation Learning in Flexible Job Shop Scheduling

arXiv: https://arxiv.org/abs/2608.03041 · HTML: https://mlsanity.com/paper/2608.03041/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in RL for energy, networks and operations, one of 15 directions in Deep reinforcement learning methods.
- Builds on 3 of its 12 references that are in the map.
- First posted on arXiv 4 Aug 2026.

## Placed in

- Deep reinforcement learning methods / [RL for energy, networks and operations](https://mlsanity.com/deeprl/rl-for-energy-networks-and-operations/)

## Builds on (most cited first, 3 of 3)

- [A Comprehensive Survey on Applications of Transformers for Deep Learning Tasks](https://mlsanity.com/paper/2306.07303/) (2023)
- [When Smaller Wins: Dual-Stage Distillation and Pareto-Guided Compression of Liquid Neural Networks for Edge Battery Prognostics](https://mlsanity.com/paper/2601.06227/) (2026)
- [ReLA: Representation Learning and Aggregation for Job Scheduling with Reinforcement Learning](https://mlsanity.com/paper/2601.03646/) (2026)

## Abstract (arXiv)

Deep reinforcement learning (DRL) approaches for flexible job shop scheduling (FJSP) heavily rely on attention-centric architectures to achieve state-of-the-art performance. However, these models suffer from excessive parameter counts and prohibitive inference latency as problem scales expand. While liquid neural networks (LNNs) offer a parameter-efficient alternative for modeling adaptive state evolution, their inherently sequential dynamics bottleneck computational efficiency. To resolve this trade-off, we propose PLAN (Parallel Liquid-inspired Approximation Network), a lightweight representation learning framework that reformulates continuous liquid-state dynamics into a discretized and parallelizable formulation. PLAN structurally decouples state evolution from context aggregation, where liquid-inspired updates handle the primary evolving state representation, and a lightweight context aggregation module provides complementary global context. Furthermore, PLAN acts as a versatile, plug-and-play backbone that generalizes to complex FJSP variants, pairing with a compact stochastic module for stochastic FJSP and replacing heavy heterogeneous graph transformers in multi-faceted dynamic FJSP. Extensive evaluations across deterministic, stochastic, and multi-faceted dynamic FJSP benchmarks show that PLAN reduces the average makespan by 1.2%, 1.4%, and 2.3%, respectively, compared with the corresponding state-of-the-art baselines, with the improvement reaching 10.2% in one benchmark setting. PLAN also reduces average inference latency by 13.2%, 31.7%, and 26.9%, respectively, with a maximum reduction of 69.2% on the largest instances, while using only 22-47% of the baseline parameters.