# To be Continuous, or to be Discrete, Those are Bits of Questions

arXiv: https://arxiv.org/abs/2406.07812 · HTML: https://mlsanity.com/paper/2406.07812/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 47 of its 77 references that are in the map.
- First posted on arXiv 12 Jun 2024.

## Builds on (most cited first, 30 of 47)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [BART: Denoising Sequence-to-Sequence Pre-training for Natural Language Generation, Translation, and Comprehension](https://mlsanity.com/paper/1910.13461/) (2019)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [Efficient Estimation of Word Representations in Vector Space](https://mlsanity.com/paper/1301.3781/) (2013)
- [Distributed Representations of Words and Phrases and their Compositionality](https://mlsanity.com/paper/1310.4546/) (2013)
- [Neural Machine Translation of Rare Words with Subword Units](https://mlsanity.com/paper/1508.07909/) (2015)
- [XLNet: Generalized Autoregressive Pretraining for Language Understanding](https://mlsanity.com/paper/1906.08237/) (2019)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [Deep contextualized word representations](https://mlsanity.com/paper/1802.05365/) (2018)
- [SimCSE: Simple Contrastive Learning of Sentence Embeddings](https://mlsanity.com/paper/2104.08821/) (2021)
- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [BioBERT: a pre-trained biomedical language representation model for biomedical text mining](https://mlsanity.com/paper/1901.08746/) (2019)
- [Generating Diverse High-Fidelity Images with VQ-VAE-2](https://mlsanity.com/paper/1906.00446/) (2019)
- [The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables](https://mlsanity.com/paper/1611.00712/) (2016)
- [Subword Regularization: Improving Neural Network Translation Models with Multiple Subword Candidates](https://mlsanity.com/paper/1804.10959/) (2018)
- [Understanding Straight-Through Estimator in Training Activation Quantized Neural Nets](https://mlsanity.com/paper/1903.05662/) (2019)
- [Constituency Parsing with a Self-Attentive Encoder](https://mlsanity.com/paper/1805.01052/) (2018)
- [A* Sampling](https://mlsanity.com/paper/1411.0030/) (2014)
- [Named Entity Recognition as Dependency Parsing](https://mlsanity.com/paper/2005.07150/) (2020)
- [Neural Variational Inference and Learning in Belief Networks](https://mlsanity.com/paper/1402.0030/) (2014)
- [Multilingual Constituency Parsing with Self-Attention and Pre-Training](https://mlsanity.com/paper/1812.11760/) (2018)
- [Structured Attention Networks](https://mlsanity.com/paper/1702.00887/) (2017)
- [Variational inference for Monte Carlo objectives](https://mlsanity.com/paper/1602.06725/) (2016)
- [Locate and Label: A Two-stage Identifier for Nested Named Entity Recognition](https://mlsanity.com/paper/2105.06804/) (2021)
- [A Minimal Span-Based Neural Constituency Parser](https://mlsanity.com/paper/1705.03919/) (2017)

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

- [Dual Latent Memory for Visual Multi-agent System](https://mlsanity.com/paper/2602.00471/) (2026)
- [On Eliciting Syntax from Language Models via Hashing](https://mlsanity.com/paper/2410.04074/) (2024)

## Abstract (arXiv)

Recently, binary representation has been proposed as a novel representation that lies between continuous and discrete representations. It exhibits considerable information-preserving capability when being used to replace continuous input vectors. In this paper, we investigate the feasibility of further introducing it to the output side, aiming to allow models to output binary labels instead. To preserve the structural information on the output side along with label information, we extend the previous contrastive hashing method as structured contrastive hashing. More specifically, we upgrade CKY from label-level to bit-level, define a new similarity function with span marginal probabilities, and introduce a novel contrastive loss function with a carefully designed instance selection strategy. Our model achieves competitive performance on various structured prediction tasks, and demonstrates that binary representation can be considered a novel representation that further bridges the gap between the continuous nature of deep learning and the discrete intrinsic property of natural languages.