# Mutual Equilibrium: Multimodal Representation Learning through Reciprocal Feedback

arXiv: https://arxiv.org/abs/2609.39456 · HTML: https://mlsanity.com/paper/2609.39456/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 31 of its 42 references that are in the map.
- First posted on arXiv 30 Sep 2026.

## Builds on (most cited first, 30 of 31)

- [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)
- [Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization](https://mlsanity.com/paper/1610.02391/) (2016)
- [Bootstrap your own latent: A new approach to self-supervised Learning](https://mlsanity.com/paper/2006.07733/) (2020)
- [Exploring Simple Siamese Representation Learning](https://mlsanity.com/paper/2011.10566/) (2020)
- [Making the V in VQA Matter: Elevating the Role of Image Understanding in Visual Question Answering](https://mlsanity.com/paper/1612.00837/) (2016)
- [Improving Factuality and Reasoning in Language Models through Multiagent Debate](https://mlsanity.com/paper/2305.14325/) (2023)
- [LXMERT: Learning Cross-Modality Encoder Representations from Transformers](https://mlsanity.com/paper/1908.07490/) (2019)
- [Multimodal Machine Learning: A Survey and Taxonomy](https://mlsanity.com/paper/1705.09406/) (2017)
- [Multimodal Transformer for Unaligned Multimodal Language Sequences](https://mlsanity.com/paper/1906.00295/) (2019)
- [Deep Equilibrium Models](https://mlsanity.com/paper/1909.01377/) (2019)
- [From Recognition to Cognition: Visual Commonsense Reasoning](https://mlsanity.com/paper/1811.10830/) (2018)
- [The Hateful Memes Challenge: Detecting Hate Speech in Multimodal Memes](https://mlsanity.com/paper/2005.04790/) (2020)
- [Mixture-of-Agents Enhances Large Language Model Capabilities](https://mlsanity.com/paper/2406.04692/) (2024)
- [Tensor Fusion Network for Multimodal Sentiment Analysis](https://mlsanity.com/paper/1707.07250/) (2017)
- [Multimodal Learning with Transformers: A Survey](https://mlsanity.com/paper/2206.06488/) (2022)
- [Pay Attention to MLPs](https://mlsanity.com/paper/2105.08050/) (2021)
- [Deep Modular Co-Attention Networks for Visual Question Answering](https://mlsanity.com/paper/1906.10770/) (2019)
- [Efficient Low-rank Multimodal Fusion with Modality-Specific Factors](https://mlsanity.com/paper/1806.00064/) (2018)
- [Visual Entailment: A Novel Task for Fine-Grained Image Understanding](https://mlsanity.com/paper/1901.06706/) (2019)
- [Multimodal Compact Bilinear Pooling for Visual Question Answering and Visual Grounding](https://mlsanity.com/paper/1606.01847/) (2016)
- [Sorting out Lipschitz function approximation](https://mlsanity.com/paper/1811.05381/) (2018)
- [Multiscale Deep Equilibrium Models](https://mlsanity.com/paper/2006.08656/) (2020)
- [On Training Implicit Models](https://mlsanity.com/paper/2111.05177/) (2021)
- [Stabilizing Equilibrium Models by Jacobian Regularization](https://mlsanity.com/paper/2106.14342/) (2021)
- [I2MoE: Interpretable Multimodal Interaction-aware Mixture-of-Experts](https://mlsanity.com/paper/2505.19190/) (2025)
- [Approximating Lipschitz continuous functions with GroupSort neural networks](https://mlsanity.com/paper/2006.05254/) (2020)
- [Multimodality Representation Learning: A Survey on Evolution, Pretraining and Its Applications](https://mlsanity.com/paper/2302.00389/) (2023)
- [On the explainable properties of 1-Lipschitz Neural Networks: An Optimal Transport Perspective](https://mlsanity.com/paper/2206.06854/) (2022)
- [Deep Equilibrium Multimodal Fusion](https://mlsanity.com/paper/2306.16645/) (2023)

## Abstract (arXiv)

This work proposes a mutual feedback architecture, MEQ, that refines the two inputs, of possibly different modalities, into a pair of coupled embeddings such that each embedding reflects the information of the other. The core idea is to incorporate continuous interchange of information between the two inputs. This idea leads to a mutual feedback architecture consisting of two components whose outputs are fed back into the other. The final output of this model is defined as the fixed point of this interaction. We provide theoretical analysis that offers interpretation of this model as well as design choices to prevent failure cases. We show the benefits of MEQ through classification and visual grounding tasks spanning various datasets. Quantitatively, our model outperforms or shows competitive performance on concatenation-based multimodal classification problems. Qualitatively, the proposed interactive mechanism allows the model to progressively refine the visual grounding when paired with complementary modality, thus demonstrating the power of mutual feedback under such settings.