Papers with sampling
Fighting FIRe with FIRE: Assessing the Validity of Text-to-Video Retrieval Benchmarks (2023.findings-eacl)
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Pedro Rodriguez, Mahmoud Azab, Becka Silvert, Renato Sanchez, Linzy Labson, Hardik Shah, Seungwhan Moon
| Challenge: | Existing benchmarks for text-to-video retrieval are incomplete, resulting in false negatives . a recent state-of-the-art model gains 25% recall points, but this is not the case for TVR. |
| Approach: | They propose to retire video captioning datasets as TVR benchmarks . they propose to annotate and release additional caption-video pairs to mitigate this flaw . |
| Outcome: | The proposed method fails to accurately reflect reality, despite lack of purpose-built benchmarks. |
Resisting the Lure of the Skyline: Grounding Practices in Active Learning for Morphological Inflection (2024.acl-short)
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| Challenge: | Several approaches to active learning are available, including confidence-based, diversity-based and committee-based. |
| Approach: | They propose to use a baseline and a skyline to measure the accuracy of the unannotated sample pool. |
| Outcome: | The proposed model outperforms a random selection baseline and a skyline approach. |
Best Practices for Data-Efficient Modeling in NLG:How to Train Production-Ready Neural Models with Less Data (2020.coling-industry)
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Ankit Arun, Soumya Batra, Vikas Bhardwaj, Ashwini Challa, Pinar Donmez, Peyman Heidari, Hakan Inan, Shashank Jain, Anuj Kumar, Shawn Mei, Karthik Mohan, Michael White
| Challenge: | Natural language generation (NLG) is a critical component in conversational systems . Traditionally, NLG components have been deployed using template-based solutions . however, deployment of such model-based systems has been challenging due to high latency and data needs. |
| Approach: | They propose a family of techniques to deploy data-efficient neural solutions for NLG in conversational systems to production. |
| Outcome: | The proposed techniques achieve production quality with light-weight neural network models using fraction of the data needed otherwise. |
RankGen: Improving Text Generation with Large Ranking Models (2022.emnlp-main)
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| Challenge: | Modern language models assign high probabilities to output sequences that are repetitive, incoherent, or irrelevant to the prefix. |
| Approach: | They propose a 1.2B parameter encoder model for English that scores model generations given a prefix. |
| Outcome: | The proposed model outperforms decoding algorithms on automatic metrics and human evaluations with English writers. |
Long Warm-up and Self-Training: Training Strategies of NICT-2 NMT System at WAT-2019 (D19-52)
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| Challenge: | NICT-2 neural machine translation system was presented at the 6th Workshop on Asian Translation (WAT-2019) |
| Approach: | They describe a NICT-2 neural machine translation system at the 6th Workshop on Asian Translation . they employ a long warm-up strategy and a self-training strategy that uses multiple back-translations generated by sampling to improve the translation quality. |
| Outcome: | The proposed system improves translation quality and learning rate by using the long warm-up and self-training strategies. |
Too Correct to Learn: Reinforcement Learning on Saturated Reasoning Data (2026.acl-short)
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| Challenge: | Strong base models saturate benchmarks, resulting in weaker performance, a paradox . a new approach to Reinforcement Learning (RL) is needed to improve performance . |
| Approach: | They propose a method that uses constrained uniform top-k sampling to flatten the local optimization landscape by sampling uniformly from constrained high-confidence candidates. |
| Outcome: | Experiments show that the proposed approach prevents policy degeneration and boosts out-of-domain generalization. |
Soft Self-Consistency Improves Language Models Agents (2024.acl-short)
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| Challenge: | Current “sample and select” methods rely on majority voting to score answers . however, when tasks have many distinct and valid answers, selection by voting requires a large number of samples. |
| Approach: | They introduce a method that replaces SC's discontinuous scoring with a continuous score computed from model likelihoods to increase selection even when actions are sparsely distributed. |
| Outcome: | The proposed method improves performance and efficiency on long-horizon interactive tasks by replacing SC’s discontinuous scoring with a continuous score computed from model likelihoods. |
ReEx-SQL: Reasoning with Execution-Aware Reinforcement Learning for Text-to-SQL (2026.acl-long)
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Yaxun Dai, Wenxuan Xie, Xialie Zhuang, Tianyu Yang, Ziyi Liu, Haiqin Yang, Yiying Yang, Yuhang Zhao, Pingfu Chao, Wenhao Jiang
| Challenge: | Current Text-to-SQL reasoning models lack integrated execution feedback during generation. |
| Approach: | They propose a text-to-SQL framework that interacts with the SQL execution engine during decoding and dynamically adjusts reasoning based on execution feedback. |
| Outcome: | The proposed framework achieves 89.1% accuracy on Spider and 65.3% on BIRD at the 7B scale. |
On the True Distribution Approximation of Minimum Bayes-Risk Decoding (2024.naacl-short)
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| Challenge: | Minimum Bayes-risk (MBR) decoding has recently gained renewed attention in text generation. |
| Approach: | They propose to use anomaly detection to measure the degree of approximation by sampling texts from a model and selecting the text with the highest similarity to the others. |
| Outcome: | The proposed method shows that previous hypotheses about samples do not correlate well with the variation, but the results support the core assumption of MBR decoding. |
A Survey of Methods for Addressing Class Imbalance in Deep-Learning Based Natural Language Processing (2023.eacl-main)
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| Challenge: | Developing methods to improve model performance in imbalanced data settings has been an active area for decades . |
| Approach: | They propose to use sampling, data augmentation, choice of loss function, staged learning, or model design to address class imbalance in NLP. |
| Outcome: | The proposed approaches are evaluated on a variety of NLP tasks or in the computer vision community. |
Understanding Back-Translation at Scale (D18-1)
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| Challenge: | An effective method to improve neural machine translation with monolingual data is to augment the parallel training corpus with back-translations of target language sentences. |
| Approach: | They propose to augment parallel training corpus with back-translations of target language sentences to improve neural machine translation with monolingual data. |
| Outcome: | The proposed method achieves a state-of-the-art of 35 BLEU on the WMT’14 English-German test set. |
Efficient Dependency Tree Sampling Without Replacement (2024.findings-naacl)
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| Challenge: | Existing algorithms for dependency tree sampling have been proposed for sampling without replacement. |
| Approach: | They propose an algorithm that adapts the Wilson Reject algorithm for sampling without replacement and combines it with a Trie data structure. |
| Outcome: | The proposed method is efficient in the case of sampling without replacement from dependency graphs with random weights. |
Interlocking-free Selective Rationalization Through Genetic-based Learning (2025.acl-long)
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| Challenge: | Existing approaches to selective rationalization suffer from interlocking, a phenomenon known as interlock. |
| Approach: | They propose a genetically-based disjoint training architecture for selective rationalization that avoids interlocking by performing genetic global search. |
| Outcome: | The proposed model outperforms state-of-the-art models on a synthetic and real-world benchmark. |
Using active learning to expand training data for implicit discourse relation recognition (D18-1)
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| Challenge: | Existing methods to determine semantic relations between text spans are limited in the field of discourse-level relation recognition. |
| Approach: | They propose to expand the training data set using the corpus of explicitly-related arguments by arbitrarily dropping the overtly presented discourse connectives. |
| Outcome: | The proposed model expands the training data set using the corpus of explicitly-related arguments, by arbitrarily dropping the overtly presented discourse connectives. |
Unbiased and Efficient Sampling of Dependency Trees (2022.emnlp-main)
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| Challenge: | linguistic constraints in dependency trees are not part of the definition of spanning trees. |
| Approach: | They propose to use a constraint that requires a single root to be incorporated into dependency tree sampling . they propose to reduce the asymptotic runtime of sampling k trees without replacement to O(kn3) |
| Outcome: | The proposed algorithms are asymptotically and practically more efficient . they reduce the runtime of the fastest algorithm for sampling with replacement to O(kn3) |
Non-Exchangeable Conformal Language Generation with Nearest Neighbors (2024.findings-eacl)
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| Challenge: | Existing methods to evaluate reliability of generated text are lacking in natural language generation. |
| Approach: | They propose a non-exchangeable conformal prediction method that provides bounds on coverage . they validated their method with k-NN retrieval and show that it produces encouraging results . |
| Outcome: | The proposed method produces encouraging results in machine translation and language modeling tasks. |
Don’t Mess with Mister-in-Between: Improved Negative Search for Knowledge Graph Completion (2023.eacl-main)
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| Challenge: | Existing methods for knowledge graph completion use a dual-encoding framework with a bottleneck that allows for fast approximate search over a vast collection of candidates. |
| Approach: | They propose to use a dual-encoder framework to find more informative negatives by searching for candidates with high lexical overlaps. |
| Outcome: | The proposed methods improve on the large-scale Wikidata5M dataset and combine different kinds of strategies to achieve state-of-the-art performance. |
Memory-efficient Temporal Moment Localization in Long Videos (2023.eacl-main)
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| Challenge: | Temporal Moment Localization is a multi-modal task that requires understanding the temporal relationships in the entire input video. |
| Approach: | They propose a stochastic sampling module that can process long videos at a constant memory footprint. |
| Outcome: | The proposed model can process videos as long as 18 minutes at a constant memory footprint and achieves faster and faster results than competing models. |
SPUQ: Perturbation-Based Uncertainty Quantification for Large Language Models (2024.eacl-long)
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| Challenge: | Large language models have a tendency to make confidently wrong predictions, highlighting the need for uncertainty quantification (UQ) . previous studies focused on aleatoric uncertainty, but the full spectrum of uncertainties, including epistemic, remains inadequately explored. |
| Approach: | They propose a method to quantify uncertainty in large language models (LLMs) they use a set of perturbations and an aggregation module to generalize the method. |
| Outcome: | The proposed method improves model uncertainty calibration and reduces expected calibration error by 50% on average. |
You should evaluate your language model on marginal likelihood over tokenisations (2021.emnlp-main)
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| Challenge: | Neural language models typically tokenise input text into sub-word units to achieve an open vocabulary. |
| Approach: | They propose that language models should be evaluated on their marginal likelihood over tokenisations instead. |
| Outcome: | The proposed approach is unsatisfactory and may bottleneck model out-of-domain performance. |
Automatic Detection of Generated Text is Easiest when Humans are Fooled (2020.acl-main)
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| Challenge: | Recent advances in neural language modelling make it possible to rapidly generate vast amounts of human-sounding text. |
| Approach: | They compare decoding methods with popular sampling-based decoding strategies . they show that multi-sentence excerpts can fool expert human raters over 30% of the time . |
| Outcome: | The proposed methods improve with longer excerpt length, but multi-sentence excerpts fool human raters over 30% of the time. |
Reasoning Aware Self-Consistency: Leveraging Reasoning Paths for Efficient LLM Sampling (2025.naacl-long)
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| Challenge: | Large Language Models (LLMs) generate reasoning paths before answers, but lack a systematic approach to determine optimal number of samples or select the most faithful rationale. |
| Approach: | They propose a framework that evaluates the quality of reasoning and consistency of answers for each generated sample and uses criteria-based stopping and weighted majority voting to guide early stopping decisions and rationale selection. |
| Outcome: | The proposed framework outperforms existing methods while maintaining accuracy. |
The Good, The Bad, and The Greedy: Evaluation of LLMs Should Not Ignore Non-Determinism (2025.naacl-long)
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| Challenge: | Current evaluations of large language models (LLMs) focus on a single output per example, which limits our understanding of LLM performance variability in real-world applications. |
| Approach: | They explore the performance differences between greedy decoding and sampling and identify benchmarks’ consistency regarding non-determinism and examine unique model behaviors. |
| Outcome: | The proposed model outperforms sampling methods and greedy decoding outperformed other models. |
Beyond Sampling: Self-Sorting for Long-Context Ranking (2026.findings-eacl)
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| Challenge: | Large language models (LLMs) remain unstable on long-context ranking. |
| Approach: | They propose a method that fuses explicit within-list positions with implicit cross-list preferences to score entities and return a top-k set. |
| Outcome: | Experimental results show that large language models remain unstable on long-context ranking . |
Waste Not, Want Not; Recycled Gumbel Noise Improves Consistency in Natural Language Generation (2025.naacl-long)
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| Challenge: | Consistency in the output of language models can vary significantly in style, factual accuracy, and tone, even for similar inputs. |
| Approach: | They propose a decoding algorithm that enhances response consistency across different prompts with no degradation in response quality. |
| Outcome: | The proposed method outperforms standard sampling methods by 10% across semantic and stylistic consistency benchmarks. |
Learning to Sample Replacements for ELECTRA Pre-Training (2021.findings-acl)
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| Challenge: | Experimental results show that ELECTRA pretrains a discriminator to detect replaced tokens . despite compelling performance, there is no direct feedback loop from discriminator and generator to generator, making replacements biased to correct tokens. |
| Approach: | They propose to augment sampling with a hardness prediction mechanism to encourage the discriminator to learn what it has not acquired. |
| Outcome: | The proposed method improves ELECTRA pre-training on various downstream tasks. |
Limitations of Autoregressive Models and Their Alternatives (2021.naacl-main)
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| Challenge: | Standard autoregressive language models only perform polynomial-time computation to compute probability of next symbol. |
| Approach: | authors propose alternative to standard autoregressive language models that use polynomial-time computation to compute probability of next symbol. |
| Outcome: | a large model size can grow superpolynomially in length, allowing it to store precomputed results and verify solutions. |
Consistency of a Recurrent Language Model With Respect to Incomplete Decoding (2020.emnlp-main)
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| Challenge: | Neural sequence models trained with maximum likelihood have been shown to exhibit issues such as length bias and degenerate repetition. |
| Approach: | They propose to use a recurrent language model to address inconsistency in decoding algorithms that are inconsistent despite the fact that recursive language models are trained to produce sequences of finite length. |
| Outcome: | The proposed methods prevent inconsistency in the proposed models. |
Prosody-TTS: Improving Prosody with Masked Autoencoder and Conditional Diffusion Model For Expressive Text-to-Speech (2023.findings-acl)
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| Challenge: | Expressive text-to-speech aims to generate high-quality samples with rich prosody . prosodic attributes in highly dynamic voices are difficult to capture and model without intonation . |
| Approach: | They propose a pipeline that enhances prosody modeling and sampling by introducing a self-supervised masked autoencoder and a diffusion model to sample diverse prosodic patterns within the latent space. |
| Outcome: | The proposed pipeline achieves new state-of-the-art in text-to-speech with natural and expressive synthesis. |
Doubling Your Data in Minutes: Ultra-fast Tabular Data Generation via LLM-Induced Dependency Graphs (2025.emnlp-main)
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| Challenge: | Tabular data is critical across diverse domains, yet high-quality tabular datasets remain scarce due to privacy concerns and the cost of collection. |
| Approach: | They propose a lightweight generative framework that captures sparse dependencies via an LLM-induced graph. |
| Outcome: | The proposed framework reduces constraint violations by 4% and accelerates generation by nearly 9,500 over diffusion-based methods. |
From Evidence to Belief: A Bayesian Epistemology Approach to Language Models (2025.naacl-long)
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| Challenge: | Existing studies on language models have focused on factual correctness and justification, but prior research has focused on the factual truth condition and justifier. |
| Approach: | They analyze language models’ responses and confidence using verbalized confidence, token probability, and sampling to examine their knowledge of Bayesian epistemology. |
| Outcome: | The language models that follow the Bayesian confirmation assumption with true evidence show varying performance depending on the degree of irrelevance, indicating they deviate from Bayes' assumptions. |
Mitigating Tail Narrowing in LLM Self-Improvement via Socratic-Guided Sampling (2025.naacl-long)
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Yiwen Ding, Zhiheng Xi, Wei He, Lizhuoyuan Lizhuoyuan, Yitao Zhai, Shi Xiaowei, Xunliang Cai, Tao Gui, Qi Zhang, Xuanjing Huang
| Challenge: | Large language models (LLMs) generate solutions themselves and iteratively train on filtered, high-quality rationales, but performance reaches a ceiling after a few iterations. |
| Approach: | They propose a strategy to improve the efficiency of sampling heavy-tailed data by using Socratic-style guidance signals to help LLMs reasoning with complex queries. |
| Outcome: | The proposed approach is effective on difficult queries and on held-out tasks, while requiring human supervision. |
Explicit over Implict: Explicit Diversity Conditions for Effective Question Answer Generation (2024.lrec-main)
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| Challenge: | Recent pretrained and large language model-based QAG methods suffer from redundant generation of QA pairs, affecting downstream QA systems. |
| Approach: | They propose to use explicit diversity conditions to generate diverse question-answer synthetic data by focusing on spatial aspects, question types, and entities. |
| Outcome: | The proposed diversity conditions significantly increase diversity in QA generation over existing diversity techniques. |
Few-Shot Multimodal Named Entity Recognition Based on Mutlimodal Causal Intervention Graph (2024.lrec-main)
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| Challenge: | Existing methods for multimodal named entity recognition are limited due to limited resources. |
| Approach: | They propose a Few-shot Multimodal Named Entity Recognition task to address these relation types by constructing a multimodal graph and a new multimodal causal intervention strategy. |
| Outcome: | The proposed model improves on two multimodal named entity recognition datasets. |
Contrastive Decoding: Open-ended Text Generation as Optimization (2023.acl-long)
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Xiang Lisa Li, Ari Holtzman, Daniel Fried, Percy Liang, Jason Eisner, Tatsunori Hashimoto, Luke Zettlemoyer, Mike Lewis
| Challenge: | Using a language model, maximum probability is a poor decoding objective because it produces short and repetitive text. |
| Approach: | They propose a reliable decoding approach that optimizes a contrastive objective subject to a plausibility constraint. |
| Outcome: | The proposed approach outperforms four strong decoding algorithms in automatic and human evaluations across wikipedia, news and story domains. |
Student Guides Teacher: Weak-to-Strong Inference via Spectral Orthogonal Exploration (2026.acl-long)
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| Challenge: | Existing Large Language Models suffer from "Reasoning Collapse" on mathematical reasoning tasks where stochastic sampling produces lexical variations of the same erroneous logic rather than genuine semantic exploration. |
| Approach: | They propose a geometric inference framework that uses a spectral orthogonal probe to introduce semantically heterogeneous reasoning signals into the teacher's orthogonale complement of its dominant subspace. |
| Outcome: | The proposed framework improves accuracy and sampling efficiency over baseline methods on logic and code generation benchmarks. |
SPILL: Domain-Adaptive Intent Clustering based on Selection and Pooling with Large Language Models (2025.findings-acl)
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| Challenge: | Existing methods for intent clustering rely on labeled examples or unsupervised fine-tuning to optimize results for each new dataset. |
| Approach: | They propose a method that uses an embedder to derive an embedding for each utterance and then pool them with the seed to improve the embeddable results. |
| Outcome: | The proposed method outperforms embedding methods and is comparable to state-of-the-art methods. |
A Probability–Quality Trade-off in Aligned Language Models and its Relation to Sampling Adaptors (2024.emnlp-main)
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| Challenge: | a relationship exists between the quality of a string and its probability, p(y), under a language model, and the quality and quality of the string. |
| Approach: | They examine the probability-quality relationship in language models aligned to human preferences through reinforcement learning through human feedback. |
| Outcome: | The proposed method improves the quality of text sampled from a language model by skewing the model towards high-probability strings. |
Can LLMs simulate the same correct solutions to free-response math problems as real students? (2025.emnlp-main)
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| Challenge: | Existing studies have explored modeling student mistakes, but lack of understanding of how they generate correct solutions. |
| Approach: | They compare distribution of correct solutions produced by four large language models with students' responses to free-response problems. |
| Outcome: | The proposed model can generate correct solutions that represent student responses to free-response problems. |
To Revise or Not to Revise: Learning to Detect Improvable Claims for Argumentative Writing Support (2023.acl-long)
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| Challenge: | assessing whether and how different claims in a text need to be revised is a hard task, especially for novice writers. |
| Approach: | They propose a sampling strategy based on revision distance to capture differences between versions of the same text. |
| Outcome: | The proposed sampling strategy can be done without additional annotations and judgments. |
Reverse Preference Optimization for Complex Instruction Following (2025.findings-acl)
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| Challenge: | Existing methods for identifying and evaluating preference pairs with multiple constraints are noisy. |
| Approach: | They propose a method that dynamically reverses constraints to ensure the chosen response is perfect. |
| Outcome: | The proposed method reduces noise in preference pairs by reversing constraints to ensure the chosen response is perfect. |
SpecHub: Provable Acceleration to Multi-Draft Speculative Decoding (2024.emnlp-main)
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| Challenge: | Large Language Models (LLMs) have limited inference speed due to sequential token generation . Spechub is a novel, efficient sampling-verification method for MDSD that improves acceptance rates with only linear computational overhead. |
| Approach: | They propose a method that uses a smaller draft model to generate multiple token sequences . Spechub generates 0.05-0.27 and 0.02-0.16 more tokens per step than RRS and RRS without replacement . |
| Outcome: | The proposed method improves acceptance rates with only linear computational overhead. |
Preference-Guided Reflective Sampling for Aligning Language Models (2024.emnlp-main)
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| Challenge: | Repeated random sampling is a widely used method that independently queries the model multiple times to generate outputs. |
| Approach: | They propose a more efficient method for iterative data generation and model re-training that leverages tree-based tree-derived generation framework to enable more efficient sampling. |
| Outcome: | The proposed method significantly outperforms repeated random sampling in best-of-N sampling on AlpacaEval and Arena-Hard. |
TSPO: Breaking the Double Homogenization Dilemma in Multi-turn Search Policy Optimization (2026.findings-acl)
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Shichao Ma, Zhiyuan Ma, Ming Yang, Xiaofan Li, Xing Wu, Jintao Du, Yu Cheng, Weiqiang Wang, Qiliang Liu, Zhengyang Zhou, Yang Wang
| Challenge: | Large Language Models (LLMs) can solve complex tasks through iterative information retrieval. |
| Approach: | They propose a turn-level stage-aware policy optimization approach to solve this problem . they introduce a first-occurrence latent reward mechanism to allocate partial rewards . |
| Outcome: | Experiments show that TSPO outperforms state-of-the-art models on Qwen2.5-3B and 7B models. |
Subtle Errors in Reasoning: Preference Learning via Error-injected Self-editing (2025.acl-long)
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Kaishuai Xu, Tiezheng Yu, Wenjun Hou, Yi Cheng, Chak Tou Leong, Liangyou Li, Xin Jiang, Lifeng Shang, Qun Liu, Wenjie Li
| Challenge: | Existing studies to improve mathematical ability typically involve applying preference learning to step-wise solution pairs, but they overlook critical subtle errors. |
| Approach: | They propose a preference learning framework that injects predefined subtle errors into pivotal tokens to construct hard pairs for error mitigation. |
| Outcome: | Extensive experiments show that the proposed framework improves on Qwen2-7B-Instruct and MATH with 4.5K training samples. |
Self-Consistency from Only Two Samples: CoT–PoT Ensembling for Efficient LLM Reasoning (2026.findings-acl)
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| Challenge: | Self-consistency (SC) is a popular technique for improving the reasoning accuracy of large language models but it comes at a high computational cost due to extensive sampling. |
| Approach: | They propose a hybrid ensembling approach that leverages the complementary strengths of Chain-of-Thought and Program-of -Thus . they propose encapsulating two different modes of reasoning to create a single output and a final answer is selected as the most frequently occurring one among these outputs. |
| Outcome: | The proposed approach reduces the number of samples required for SC by 9.3x . the majority of tasks can be addressed with only two samples, which has not been possible with prior methods. |
D-RAG: Differentiable Retrieval-Augmented Generation for Knowledge Graph Question Answering (2025.emnlp-main)
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Guangze Gao, Zixuan Li, Chunfeng Yuan, Jiawei Li, Wu Jianzhuo, Yuehao Zhang, Xiaolong Jin, Bing Li, Weiming Hu
| Challenge: | Existing approaches to Knowledge Graph Question Answering (KGQA) use Retrieval-Augmented Generation (RAG) but subgraph selection process is non-differentiable, preventing end-to-end training of the retriever and the generator. |
| Approach: | They propose a Differentiable RAG approach that optimizes the retriever and the generator for KGQA. |
| Outcome: | The proposed approach outperforms state-of-the-art approaches on WebQSP and CWQ. |
Universally Empowering Zeroth-Order Optimization via Adaptive Layer-wise Sampling (2026.findings-acl)
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| Challenge: | Existing methods for fine-tuning Large Language Models are slow and lack of performance. |
| Approach: | They propose a Zeroth-Order optimization framework that uses forward passes to fine-tune Large Language Models. |
| Outcome: | The proposed framework achieves 1.7 to 3.0 wall-clock acceleration on LLaMA and OPT models. |
Parallel Test-Time Scaling for Latent Reasoning Models (2026.acl-long)
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| Challenge: | Parallel test-time scaling is a pivotal approach for enhancing large language models. |
| Approach: | They propose two uncertainty-inspired stochastic strategies for parallel test-time scaling for latent reasoning models and a Latent Reward Model for aggregation. |
| Outcome: | The proposed model scales well with compute and enables effective trajectory selection. |