# DCER: Dual-Stage Compression and Energy-Based Reconstruction

arXiv: https://arxiv.org/abs/2602.04904 · HTML: https://mlsanity.com/paper/2602.04904/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 29 references that are in the map.
- First posted on arXiv 3 Feb 2026.

## Builds on (most cited first, 15 of 15)

- [FEDformer: Frequency Enhanced Decomposed Transformer for Long-term Series Forecasting](https://mlsanity.com/paper/2201.12740/) (2022)
- [Perceiver: General Perception with Iterative Attention](https://mlsanity.com/paper/2103.03206/) (2021)
- [Deep Variational Information Bottleneck](https://mlsanity.com/paper/1612.00410/) (2016)
- [Multimodal Transformer for Unaligned Multimodal Language Sequences](https://mlsanity.com/paper/1906.00295/) (2019)
- [Tensor Fusion Network for Multimodal Sentiment Analysis](https://mlsanity.com/paper/1707.07250/) (2017)
- [VLMo: Unified Vision-Language Pre-Training with Mixture-of-Modality-Experts](https://mlsanity.com/paper/2111.02358/) (2021)
- [Multimodal Learning with Transformers: A Survey](https://mlsanity.com/paper/2206.06488/) (2022)
- [FNet: Mixing Tokens with Fourier Transforms](https://mlsanity.com/paper/2105.03824/) (2021)
- [Learning in the Frequency Domain](https://mlsanity.com/paper/2002.12416/) (2020)
- [Learning Modality-Specific Representations with Self-Supervised Multi-Task Learning for Multimodal Sentiment Analysis](https://mlsanity.com/paper/2102.04830/) (2021)
- [LEAF: A Learnable Frontend for Audio Classification](https://mlsanity.com/paper/2101.08596/) (2021)
- [Structured Prediction Energy Networks](https://mlsanity.com/paper/1511.06350/) (2015)
- [Towards Robust Multimodal Sentiment Analysis with Incomplete Data](https://mlsanity.com/paper/2409.20012/) (2024)
- [Multimodal Prompt Learning with Missing Modalities for Sentiment Analysis and Emotion Recognition](https://mlsanity.com/paper/2407.05374/) (2024)
- [Efficient Multimodal Transformer with Dual-Level Feature Restoration for Robust Multimodal Sentiment Analysis](https://mlsanity.com/paper/2208.07589/) (2022)

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

- [SAS-Net: Cross-Domain Image Registration as Inverse Rendering via Structure-Appearance Factorization](https://mlsanity.com/paper/2602.09050/) (2026)
- [Deformation-Free Cross-Domain Image Registration via Position-Encoded Temporal Attention](https://mlsanity.com/paper/2602.15959/) (2026)

## Abstract (arXiv)

Multimodal fusion faces two robustness challenges: noisy inputs degrade representation quality, and missing modalities cause prediction failures. We propose DCER, a unified framework addressing both challenges through dual-stage compression and energy-based reconstruction. The compression stage operates at two levels: within-modality frequency transforms (wavelet for audio, DCT for video) remove noise while preserving task-relevant patterns, and cross-modality bottleneck tokens force genuine integration rather than modality-specific shortcuts. For missing modalities, energy-based reconstruction recovers representations via gradient descent on a learned energy function, with the final energy providing intrinsic uncertainty quantification (rho > 0.72 correlation with prediction error). Experiments on CMU-MOSI, CMU-MOSEI, and CH-SIMS demonstrate state-of-the-art performance across all benchmarks, with a U-shaped robustness pattern favoring multimodal fusion at both complete and high-missing conditions. The code will be available on Github.