# Controlled Text Generation as Continuous Optimization with Multiple Constraints

arXiv: https://arxiv.org/abs/2108.01850 · HTML: https://mlsanity.com/paper/2108.01850/

## Key facts

- Cited by 70 papers in the map (data through 14 Oct 2026).
- Builds on 59 of its 85 references that are in the map.
- First posted on arXiv 4 Aug 2021.

## Builds on (most cited first, 30 of 59)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [Sentence-BERT: Sentence Embeddings using Siamese BERT-Networks](https://mlsanity.com/paper/1908.10084/) (2019)
- [BERTScore: Evaluating Text Generation with BERT](https://mlsanity.com/paper/1904.09675/) (2019)
- [Prefix-Tuning: Optimizing Continuous Prompts for Generation](https://mlsanity.com/paper/2101.00190/) (2021)
- [A Broad-Coverage Challenge Corpus for Sentence Understanding through Inference](https://mlsanity.com/paper/1704.05426/) (2017)
- [HuggingFace's Transformers: State-of-the-art Natural Language Processing](https://mlsanity.com/paper/1910.03771/) (2019)
- [Fine-Tuning Language Models from Human Preferences](https://mlsanity.com/paper/1909.08593/) (2019)
- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [Google's Neural Machine Translation System: Bridging the Gap between Human and Machine Translation](https://mlsanity.com/paper/1609.08144/) (2016)
- [Multi-Task Learning Using Uncertainty to Weigh Losses for Scene Geometry and Semantics](https://mlsanity.com/paper/1705.07115/) (2017)
- [RealToxicityPrompts: Evaluating Neural Toxic Degeneration in Language Models](https://mlsanity.com/paper/2009.11462/) (2020)
- [SemEval-2017 Task 1: Semantic Textual Similarity - Multilingual and Cross-lingual Focused Evaluation](https://mlsanity.com/paper/1708.00055/) (2017)
- [Neural Network Acceptability Judgments](https://mlsanity.com/paper/1805.12471/) (2018)
- [GradNorm: Gradient Normalization for Adaptive Loss Balancing in Deep Multitask Networks](https://mlsanity.com/paper/1711.02257/) (2017)
- [Multi-Task Learning as Multi-Objective Optimization](https://mlsanity.com/paper/1810.04650/) (2018)
- [Plug and Play Language Models: A Simple Approach to Controlled Text Generation](https://mlsanity.com/paper/1912.02164/) (2019)
- [CTRL: A Conditional Transformer Language Model for Controllable Generation](https://mlsanity.com/paper/1909.05858/) (2019)
- [Universal Adversarial Triggers for Attacking and Analyzing NLP](https://mlsanity.com/paper/1908.07125/) (2019)
- [Making Monolingual Sentence Embeddings Multilingual using Knowledge Distillation](https://mlsanity.com/paper/2004.09813/) (2020)
- [Defending Against Neural Fake News](https://mlsanity.com/paper/1905.12616/) (2019)
- [Neural Text Generation with Unlikelihood Training](https://mlsanity.com/paper/1908.04319/) (2019)
- [Non-Autoregressive Neural Machine Translation](https://mlsanity.com/paper/1711.02281/) (2017)
- [DExperts: Decoding-Time Controlled Text Generation with Experts and Anti-Experts](https://mlsanity.com/paper/2105.03023/) (2021)
- [GeDi: Generative Discriminator Guided Sequence Generation](https://mlsanity.com/paper/2009.06367/) (2020)
- [SeqGAN: Sequence Generative Adversarial Nets with Policy Gradient](https://mlsanity.com/paper/1609.05473/) (2016)
- [FUDGE: Controlled Text Generation With Future Discriminators](https://mlsanity.com/paper/2104.05218/) (2021)

## Built on by (most cited first, 30 of 70)

- [Generating Training Data with Language Models: Towards Zero-Shot Language Understanding](https://mlsanity.com/paper/2202.04538/) (2022)
- [SSD-LM: Semi-autoregressive Simplex-based Diffusion Language Model for Text Generation and Modular Control](https://mlsanity.com/paper/2210.17432/) (2022)
- [Automatically Auditing Large Language Models via Discrete Optimization](https://mlsanity.com/paper/2303.04381/) (2023)
- [COLD Decoding: Energy-based Constrained Text Generation with Langevin Dynamics](https://mlsanity.com/paper/2202.11705/) (2022)
- [Decoding-Time Language Model Alignment with Multiple Objectives](https://mlsanity.com/paper/2406.18853/) (2024)
- [Language Generation Models Can Cause Harm: So What Can We Do About It? An Actionable Survey](https://mlsanity.com/paper/2210.07700/) (2022)
- [Sequential Monte Carlo Steering of Large Language Models using Probabilistic Programs](https://mlsanity.com/paper/2306.03081/) (2023)
- [Word Embeddings Are Steers for Language Models](https://mlsanity.com/paper/2305.12798/) (2023)
- [Mix and Match: Learning-free Controllable Text Generation using Energy Language Models](https://mlsanity.com/paper/2203.13299/) (2022)
- [Prompt Waywardness: The Curious Case of Discretized Interpretation of Continuous Prompts](https://mlsanity.com/paper/2112.08348/) (2021)
- [Gradient-Based Constrained Sampling from Language Models](https://mlsanity.com/paper/2205.12558/) (2022)
- [Controlled Text Generation via Language Model Arithmetic](https://mlsanity.com/paper/2311.14479/) (2023)
- [Syntactic and Semantic Control of Large Language Models via Sequential Monte Carlo](https://mlsanity.com/paper/2504.13139/) (2025)
- [Critic-Guided Decoding for Controlled Text Generation](https://mlsanity.com/paper/2212.10938/) (2022)
- [Plansformer: Generating Symbolic Plans using Transformers](https://mlsanity.com/paper/2212.08681/) (2022)
- [Constrained Decoding for Secure Code Generation](https://mlsanity.com/paper/2405.00218/) (2024)
- [Tuning Language Models as Training Data Generators for Augmentation-Enhanced Few-Shot Learning](https://mlsanity.com/paper/2211.03044/) (2022)
- [A Distributional Lens for Multi-Aspect Controllable Text Generation](https://mlsanity.com/paper/2210.02889/) (2022)
- [Inference-Time Policy Adapters (IPA): Tailoring Extreme-Scale LMs without Fine-tuning](https://mlsanity.com/paper/2305.15065/) (2023)
- [On the Challenges and Opportunities in Generative AI](https://mlsanity.com/paper/2403.00025/) (2024)
- [DisCup: Discriminator Cooperative Unlikelihood Prompt-tuning for Controllable Text Generation](https://mlsanity.com/paper/2210.09551/) (2022)
- [Composable Text Controls in Latent Space with ODEs](https://mlsanity.com/paper/2208.00638/) (2022)
- [Controllable Text Generation via Probability Density Estimation in the Latent Space](https://mlsanity.com/paper/2212.08307/) (2022)
- [BOLT: Fast Energy-based Controlled Text Generation with Tunable Biases](https://mlsanity.com/paper/2305.12018/) (2023)
- [LiSeCo: Linear Semantic Control for Language Generation](https://mlsanity.com/paper/2405.15454/) (2024)
- [ParaGuide: Guided Diffusion Paraphrasers for Plug-and-Play Textual Style Transfer](https://mlsanity.com/paper/2308.15459/) (2023)
- [Socratic Pretraining: Question-Driven Pretraining for Controllable Summarization](https://mlsanity.com/paper/2212.10449/) (2022)
- [TinyStyler: Efficient Few-Shot Text Style Transfer with Authorship Embeddings](https://mlsanity.com/paper/2406.15586/) (2024)
- [Reinforcement Learning with Token-level Feedback for Controllable Text Generation](https://mlsanity.com/paper/2403.11558/) (2024)
- [BioNLI: Generating a Biomedical NLI Dataset Using Lexico-semantic Constraints for Adversarial Examples](https://mlsanity.com/paper/2210.14814/) (2022)

## Abstract (arXiv)

As large-scale language model pretraining pushes the state-of-the-art in text generation, recent work has turned to controlling attributes of the text such models generate. While modifying the pretrained models via fine-tuning remains the popular approach, it incurs a significant computational cost and can be infeasible due to lack of appropriate data. As an alternative, we propose MuCoCO -- a flexible and modular algorithm for controllable inference from pretrained models. We formulate the decoding process as an optimization problem which allows for multiple attributes we aim to control to be easily incorporated as differentiable constraints to the optimization. By relaxing this discrete optimization to a continuous one, we make use of Lagrangian multipliers and gradient-descent based techniques to generate the desired text. We evaluate our approach on controllable machine translation and style transfer with multiple sentence-level attributes and observe significant improvements over baselines.