# Simple Projection Variants Improve ColBERT Performance

arXiv: https://arxiv.org/abs/2510.12327 · HTML: https://mlsanity.com/paper/2510.12327/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 53 of its 69 references that are in the map.
- First posted on arXiv 14 Oct 2025.

## Builds on (most cited first, 30 of 53)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [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)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [GLU Variants Improve Transformer](https://mlsanity.com/paper/2002.05202/) (2020)
- [MS MARCO: A Human Generated MAchine Reading COmprehension Dataset](https://mlsanity.com/paper/1611.09268/) (2016)
- [MiniLM: Deep Self-Attention Distillation for Task-Agnostic Compression of Pre-Trained Transformers](https://mlsanity.com/paper/2002.10957/) (2020)
- [Transformer Feed-Forward Layers Are Key-Value Memories](https://mlsanity.com/paper/2012.14913/) (2020)
- [Text Embeddings by Weakly-Supervised Contrastive Pre-training](https://mlsanity.com/paper/2212.03533/) (2022)
- [BEIR: A Heterogenous Benchmark for Zero-shot Evaluation of Information Retrieval Models](https://mlsanity.com/paper/2104.08663/) (2021)
- [ColBERT: Efficient and Effective Passage Search via Contextualized Late Interaction over BERT](https://mlsanity.com/paper/2004.12832/) (2020)
- [Sigmoid-Weighted Linear Units for Neural Network Function Approximation in Reinforcement Learning](https://mlsanity.com/paper/1702.03118/) (2017)
- [Language Modeling with Gated Convolutional Networks](https://mlsanity.com/paper/1612.08083/) (2016)
- [PaliGemma: A versatile 3B VLM for transfer](https://mlsanity.com/paper/2407.07726/) (2024)
- [MTEB: Massive Text Embedding Benchmark](https://mlsanity.com/paper/2210.07316/) (2022)
- [Fact or Fiction: Verifying Scientific Claims](https://mlsanity.com/paper/2004.14974/) (2020)
- [Smarter, Better, Faster, Longer: A Modern Bidirectional Encoder for Fast, Memory Efficient, and Long Context Finetuning and Inference](https://mlsanity.com/paper/2412.13663/) (2024)
- [Empirical Evaluation of Rectified Activations in Convolutional Network](https://mlsanity.com/paper/1505.00853/) (2015)
- [ColBERTv2: Effective and Efficient Retrieval via Lightweight Late Interaction](https://mlsanity.com/paper/2112.01488/) (2021)
- [SPLADE: Sparse Lexical and Expansion Model for First Stage Ranking](https://mlsanity.com/paper/2107.05720/) (2021)
- [Pretrained Transformers for Text Ranking: BERT and Beyond](https://mlsanity.com/paper/2010.06467/) (2020)
- [Do Wide and Deep Networks Learn the Same Things? Uncovering How Neural Network Representations Vary with Width and Depth](https://mlsanity.com/paper/2010.15327/) (2020)
- [ColPali: Efficient Document Retrieval with Vision Language Models](https://mlsanity.com/paper/2407.01449/) (2024)
- [RocketQAv2: A Joint Training Method for Dense Passage Retrieval and Passage Re-ranking](https://mlsanity.com/paper/2110.07367/) (2021)
- [Show Your Work: Improved Reporting of Experimental Results](https://mlsanity.com/paper/1909.03004/) (2019)
- [Activation Functions in Deep Learning: A Comprehensive Survey and Benchmark](https://mlsanity.com/paper/2109.14545/) (2021)
- [PLAID: An Efficient Engine for Late Interaction Retrieval](https://mlsanity.com/paper/2205.09707/) (2022)
- [SPLADE-v3: New baselines for SPLADE](https://mlsanity.com/paper/2403.06789/) (2024)
- [MetaEmbed: Scaling Multimodal Retrieval at Test-Time with Flexible Late Interaction](https://mlsanity.com/paper/2509.18095/) (2025)

## Built on by (most cited first, 2 of 2)

- [Sculpting the Vector Space: Towards Efficient Multi-Vector Visual Document Retrieval via Prune-then-Merge Framework](https://mlsanity.com/paper/2602.19549/) (2026)
- [EigenLI: Spectral Approximations to Late Interaction](https://mlsanity.com/paper/2609.07561/) (2026)

## Abstract (arXiv)

Multi-vector dense retrieval methods like ColBERT systematically use a single-layer linear projection to reduce the dimensionality of individual vectors. In this study, we explore the implications of the MaxSim operator on the gradient flows of the training of multi-vector models and show that such a simple linear projection has inherent, if non-critical, limitations in this setting. We then discuss the theoretical improvements that could result from replacing this single-layer projection with well-studied alternative feedforward linear networks (FFN), such as deeper, non-linear FFN blocks, GLU blocks, and skip-connections, could alleviate these limitations. Through the design and systematic evaluation of alternate projection blocks, we show that better-designed final projections positively impact the downstream performance of ColBERT models. We highlight that many projection variants outperform the original linear projections, with the best-performing variants increasing average performance on a range of retrieval benchmarks across domains by over 2 NDCG@10 points. We then conduct further exploration on the individual parameters of these projections block in order to understand what drives this empirical performance, highlighting the particular importance of upscaled intermediate projections and residual connections. As part of these ablation studies, we show that numerous suboptimal projection variants still outperform the traditional single-layer projection across multiple benchmarks, confirming our hypothesis. Finally, we observe that this effect is consistent across random seeds, further confirming that replacing the linear layer of ColBERT models is a robust, drop-in upgrade.