# A Multi-Implicit Neural Representation for Fonts

arXiv: https://arxiv.org/abs/2106.06866 · HTML: https://mlsanity.com/paper/2106.06866/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 30 references that are in the map.
- First posted on arXiv 12 Jun 2021.

## Builds on (most cited first, 17 of 17)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018)
- [StarGAN: Unified Generative Adversarial Networks for Multi-Domain Image-to-Image Translation](https://mlsanity.com/paper/1711.09020/) (2017)
- [AtlasNet: A Papier-Mach'e Approach to Learning 3D Surface Generation](https://mlsanity.com/paper/1802.05384/) (2018)
- [Neural Geometric Level of Detail: Real-time Rendering with Implicit 3D Shapes](https://mlsanity.com/paper/2101.10994/) (2021)
- [DeepSVG: A Hierarchical Generative Network for Vector Graphics Animation](https://mlsanity.com/paper/2007.11301/) (2020)
- [STGAN: A Unified Selective Transfer Network for Arbitrary Image Attribute Editing](https://mlsanity.com/paper/1904.09709/) (2019)
- [Im2Vec: Synthesizing Vector Graphics without Vector Supervision](https://mlsanity.com/paper/2102.02798/) (2021)
- [Multi-Content GAN for Few-Shot Font Style Transfer](https://mlsanity.com/paper/1712.00516/) (2017)
- [A Learned Representation for Scalable Vector Graphics](https://mlsanity.com/paper/1904.02632/) (2019)
- [SDF-SRN: Learning Signed Distance 3D Object Reconstruction from Static Images](https://mlsanity.com/paper/2010.10505/) (2020)
- [SurfNet: Generating 3D shape surfaces using deep residual networks](https://mlsanity.com/paper/1703.04079/) (2017)
- [Attribute2Font: Creating Fonts You Want From Attributes](https://mlsanity.com/paper/2005.07865/) (2020)

## Built on by (most cited first, 21 of 21)

- [Towards Layer-wise Image Vectorization](https://mlsanity.com/paper/2206.04655/) (2022)
- [Where Do We Stand with Implicit Neural Representations? A Technical and Performance Survey](https://mlsanity.com/paper/2411.03688/) (2024)
- [Can Large Language Models Understand Symbolic Graphics Programs?](https://mlsanity.com/paper/2408.08313/) (2024)
- [ShapeCoder: Discovering Abstractions for Visual Programs from Unstructured Primitives](https://mlsanity.com/paper/2305.05661/) (2023)
- [NIVeL: Neural Implicit Vector Layers for Text-to-Vector Generation](https://mlsanity.com/paper/2405.15217/) (2024)
- [DualVector: Unsupervised Vector Font Synthesis with Dual-Part Representation](https://mlsanity.com/paper/2305.10462/) (2023)
- [Nonparametric Teaching of Implicit Neural Representations](https://mlsanity.com/paper/2405.10531/) (2024)
- [Regularize implicit neural representation by itself](https://mlsanity.com/paper/2303.15484/) (2023)
- [Segmentation-guided Layer-wise Image Vectorization with Gradient Fills](https://mlsanity.com/paper/2408.15741/) (2024)
- [Kinetic Typography Diffusion Model](https://mlsanity.com/paper/2407.10476/) (2024)
- [Drawing2CAD: Sequence-to-Sequence Learning for CAD Generation from Vector Drawings](https://mlsanity.com/paper/2508.18733/) (2025)
- [Learning Implicit Glyph Shape Representation](https://mlsanity.com/paper/2106.08573/) (2021)
- [VecFontSDF: Learning to Reconstruct and Synthesize High-quality Vector Fonts via Signed Distance Functions](https://mlsanity.com/paper/2303.12675/) (2023)
- [SASNet: Spatially-Adaptive Sinusoidal Networks for INRs](https://mlsanity.com/paper/2503.09750/) (2025)
- [A Simple And Effective Filtering Scheme For Improving Neural Fields](https://mlsanity.com/paper/2201.13013/) (2022)
- [Contour Completion by Transformers and Its Application to Vector Font Data](https://mlsanity.com/paper/2304.13988/) (2023)
- [AmbiGen: Generating Ambigrams from Pre-trained Diffusion Model](https://mlsanity.com/paper/2312.02967/) (2023)
- [2D Neural Fields with Learned Discontinuities](https://mlsanity.com/paper/2408.00771/) (2024)
- [NTK-Guided Implicit Neural Teaching](https://mlsanity.com/paper/2511.15487/) (2025)
- [Regularized interpolation in 4D neural fields enables optimization of 3D printed geometries](https://mlsanity.com/paper/2502.01517/) (2025)
- [Total Disentanglement of Font Images into Style and Character Class Features](https://mlsanity.com/paper/2403.12784/) (2024)

## Abstract (arXiv)

Fonts are ubiquitous across documents and come in a variety of styles. They are either represented in a native vector format or rasterized to produce fixed resolution images. In the first case, the non-standard representation prevents benefiting from latest network architectures for neural representations; while, in the latter case, the rasterized representation, when encoded via networks, results in loss of data fidelity, as font-specific discontinuities like edges and corners are difficult to represent using neural networks. Based on the observation that complex fonts can be represented by a superposition of a set of simpler occupancy functions, we introduce textitmulti-implicits to represent fonts as a permutation-invariant set of learned implict functions, without losing features (e.g., edges and corners). However, while multi-implicits locally preserve font features, obtaining supervision in the form of ground truth multi-channel signals is a problem in itself. Instead, we propose how to train such a representation with only local supervision, while the proposed neural architecture directly finds globally consistent multi-implicits for font families. We extensively evaluate the proposed representation for various tasks including reconstruction, interpolation, and synthesis to demonstrate clear advantages with existing alternatives. Additionally, the representation naturally enables glyph completion, wherein a single characteristic font is used to synthesize a whole font family in the target style.