# Prompt Algebra for Task Composition

arXiv: https://arxiv.org/abs/2306.00310 · HTML: https://mlsanity.com/paper/2306.00310/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 46 references that are in the map.
- First posted on arXiv 1 Jun 2023.

## Builds on (most cited first, 29 of 29)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [PaLM: Scaling Language Modeling with Pathways](https://mlsanity.com/paper/2204.02311/) (2022)
- [Flamingo: a Visual Language Model for Few-Shot Learning](https://mlsanity.com/paper/2204.14198/) (2022)
- [Efficient Estimation of Word Representations in Vector Space](https://mlsanity.com/paper/1301.3781/) (2013)
- [Prefix-Tuning: Optimizing Continuous Prompts for Generation](https://mlsanity.com/paper/2101.00190/) (2021)
- [Scaling Up Visual and Vision-Language Representation Learning With Noisy Text Supervision](https://mlsanity.com/paper/2102.05918/) (2021)
- [The Power of Scale for Parameter-Efficient Prompt Tuning](https://mlsanity.com/paper/2104.08691/) (2021)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [iCaRL: Incremental Classifier and Representation Learning](https://mlsanity.com/paper/1611.07725/) (2016)
- [Pre-train, Prompt, and Predict: A Systematic Survey of Prompting Methods in Natural Language Processing](https://mlsanity.com/paper/2107.13586/) (2021)
- [ViLBERT: Pretraining Task-Agnostic Visiolinguistic Representations for Vision-and-Language Tasks](https://mlsanity.com/paper/1908.02265/) (2019)
- [Align before Fuse: Vision and Language Representation Learning with Momentum Distillation](https://mlsanity.com/paper/2107.07651/) (2021)
- [VL-BERT: Pre-training of Generic Visual-Linguistic Representations](https://mlsanity.com/paper/1908.08530/) (2019)
- [Three scenarios for continual learning](https://mlsanity.com/paper/1904.07734/) (2019)
- [DER: Dynamically Expandable Representation for Class Incremental Learning](https://mlsanity.com/paper/2103.16788/) (2021)
- [VL-Adapter: Parameter-Efficient Transfer Learning for Vision-and-Language Tasks](https://mlsanity.com/paper/2112.06825/) (2021)
- [DyTox: Transformers for Continual Learning with DYnamic TOken eXpansion](https://mlsanity.com/paper/2111.11326/) (2021)
- [S-Prompts Learning with Pre-trained Transformers: An Occam's Razor for Domain Incremental Learning](https://mlsanity.com/paper/2207.12819/) (2022)
- [ZeroCap: Zero-Shot Image-to-Text Generation for Visual-Semantic Arithmetic](https://mlsanity.com/paper/2111.14447/) (2021)
- [Task-Driven Modular Networks for Zero-Shot Compositional Learning](https://mlsanity.com/paper/1905.05908/) (2019)
- [Learning Graph Embeddings for Compositional Zero-shot Learning](https://mlsanity.com/paper/2102.01987/) (2021)
- [Learning to Compose Soft Prompts for Compositional Zero-Shot Learning](https://mlsanity.com/paper/2204.03574/) (2022)
- [CLIP model is an Efficient Continual Learner](https://mlsanity.com/paper/2210.03114/) (2022)
- [Independent Prototype Propagation for Zero-Shot Compositionality](https://mlsanity.com/paper/2106.00305/) (2021)

## Built on by (most cited first, 6 of 6)

- [The Linear Representation Hypothesis and the Geometry of Large Language Models](https://mlsanity.com/paper/2311.03658/) (2023)
- [A Second-Order Perspective on Model Compositionality and Incremental Learning](https://mlsanity.com/paper/2405.16350/) (2024)
- [Uncovering Meanings of Embeddings via Partial Orthogonality](https://mlsanity.com/paper/2310.17611/) (2023)
- [Not Only Text: Exploring Compositionality of Visual Representations in Vision-Language Models](https://mlsanity.com/paper/2503.17142/) (2025)
- [PICASO: Permutation-Invariant Context Composition with State Space Models](https://mlsanity.com/paper/2502.17605/) (2025)
- [Experimental Design for Active Transductive Inference in Large Language Models](https://mlsanity.com/paper/2404.08846/) (2024)

## Abstract (arXiv)

We investigate whether prompts learned independently for different tasks can be later combined through prompt algebra to obtain a model that supports composition of tasks. We consider Visual Language Models (VLM) with prompt tuning as our base classifier and formally define the notion of prompt algebra. We propose constrained prompt tuning to improve performance of the composite classifier. In the proposed scheme, prompts are constrained to appear in the lower dimensional subspace spanned by the basis vectors of the pre-trained vocabulary. Further regularization is added to ensure that the learned prompt is grounded correctly to the existing pre-trained vocabulary. We demonstrate the effectiveness of our method on object classification and object-attribute classification datasets. On average, our composite model obtains classification accuracy within 2.5% of the best base model. On UTZappos it improves classification accuracy over the best base model by 8.45% on average.