# Contextual Plackett-Luce: An Efficient Neural Model for Probabilistic Sequence Selection under Ambiguity

arXiv: https://arxiv.org/abs/2605.09112 · HTML: https://mlsanity.com/paper/2605.09112/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 40 references that are in the map.
- First posted on arXiv 9 May 2026.

## Builds on (most cited first, 22 of 22)

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- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [nuScenes: A multimodal dataset for autonomous driving](https://mlsanity.com/paper/1903.11027/) (2019)
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- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Planning with Diffusion for Flexible Behavior Synthesis](https://mlsanity.com/paper/2205.09991/) (2022)
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- [MultiPath: Multiple Probabilistic Anchor Trajectory Hypotheses for Behavior Prediction](https://mlsanity.com/paper/1910.05449/) (2019)
- [Pix2seq: A Language Modeling Framework for Object Detection](https://mlsanity.com/paper/2109.10852/) (2021)
- [CoverNet: Multimodal Behavior Prediction using Trajectory Sets](https://mlsanity.com/paper/1911.10298/) (2019)
- [MotionDiffuser: Controllable Multi-Agent Motion Prediction using Diffusion](https://mlsanity.com/paper/2306.03083/) (2023)
- [Fast Differentiable Sorting and Ranking](https://mlsanity.com/paper/2002.08871/) (2020)
- [Learning Latent Permutations with Gumbel-Sinkhorn Networks](https://mlsanity.com/paper/1802.08665/) (2018)
- [Stochastic Optimization of Sorting Networks via Continuous Relaxations](https://mlsanity.com/paper/1903.08850/) (2019)
- [Learning in an Uncertain World: Representing Ambiguity Through Multiple Hypotheses](https://mlsanity.com/paper/1612.00197/) (2016)
- [Structured Prediction Energy Networks](https://mlsanity.com/paper/1511.06350/) (2015)

## Abstract (arXiv)

Selecting a coherent sequence or subset of elements is a fundamental problem in structured prediction, arising in tasks such as detection, trajectory forecasting, and representative subset selection. In many such settings, the target is inherently ambiguous: each input admits multiple valid outputs, while supervision provides only a single sampled instance. This induces a mismatch between the underlying multi-modal target distribution and the observed training signal. We propose Contextual Plackett-Luce (CPL), a structured probabilistic model for sequence selection that extends the classical Plackett-Luce model to a context-dependent setting following an Ising-style parameterization with unary and pairwise interaction terms. CPL can be viewed as a hybrid between fully autoregressive prediction and parallel sequence selection: autoregressive models effectively capture uncertainty but are computationally expensive on modern parallel hardware such as GPUs, while parallel methods are efficient but struggle to represent multi-modal dependencies. CPL combines the strengths of both by constructing the parameters of a probabilistic selection model in a fully parallel manner, followed by a lightweight autoregressive selection process in which each step applies incremental updates to contextual logits. This decoupling of parallel scoring and sequential selection enables efficient computation without sacrificing expressivity. We evaluate CPL on two structured selection tasks: multi-modal path prediction and representative subset selection. CPL achieves improved structural consistency and robustness under ambiguous supervision compared to strong parallel baselines.