# Second-Order Multi-Level Variance Correction for Modality Competition in Multimodal Models

arXiv: https://arxiv.org/abs/2605.16165 · HTML: https://mlsanity.com/paper/2605.16165/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 26 references that are in the map.
- First posted on arXiv 15 May 2026.

## Builds on (most cited first, 22 of 22)

- [Visual Instruction Tuning](https://mlsanity.com/paper/2304.08485/) (2023)
- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [Sigmoid Loss for Language Image Pre-Training](https://mlsanity.com/paper/2303.15343/) (2023)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [InstructBLIP: Towards General-purpose Vision-Language Models with Instruction Tuning](https://mlsanity.com/paper/2305.06500/) (2023)
- [Qwen-VL: A Versatile Vision-Language Model for Understanding, Localization, Text Reading, and Beyond](https://mlsanity.com/paper/2308.12966/) (2023)
- [Gradient Surgery for Multi-Task Learning](https://mlsanity.com/paper/2001.06782/) (2020)
- [Chameleon: Mixed-Modal Early-Fusion Foundation Models](https://mlsanity.com/paper/2405.09818/) (2024)
- [GradNorm: Gradient Normalization for Adaptive Loss Balancing in Deep Multitask Networks](https://mlsanity.com/paper/1711.02257/) (2017)
- [Optimizing Neural Networks with Kronecker-factored Approximate Curvature](https://mlsanity.com/paper/1503.05671/) (2015)
- [Mind the Gap: Understanding the Modality Gap in Multi-modal Contrastive Representation Learning](https://mlsanity.com/paper/2203.02053/) (2022)
- [Janus: Decoupling Visual Encoding for Unified Multimodal Understanding and Generation](https://mlsanity.com/paper/2410.13848/) (2024)
- [Balanced Multimodal Learning via On-the-fly Gradient Modulation](https://mlsanity.com/paper/2203.15332/) (2022)
- [The Marginal Value of Adaptive Gradient Methods in Machine Learning](https://mlsanity.com/paper/1705.08292/) (2017)
- [LLaVA-Plus: Learning to Use Tools for Creating Multimodal Agents](https://mlsanity.com/paper/2311.05437/) (2023)
- [SOAP: Improving and Stabilizing Shampoo using Adam](https://mlsanity.com/paper/2409.11321/) (2024)
- [Revisiting Natural Gradient for Deep Networks](https://mlsanity.com/paper/1301.3584/) (2013)
- [A Distributed Data-Parallel PyTorch Implementation of the Distributed Shampoo Optimizer for Training Neural Networks At-Scale](https://mlsanity.com/paper/2309.06497/) (2023)
- [Improving Multimodal Learning with Multi-Loss Gradient Modulation](https://mlsanity.com/paper/2405.07930/) (2024)
- [The Potential of Second-Order Optimization for LLMs: A Study with Full Gauss-Newton](https://mlsanity.com/paper/2510.09378/) (2025)
- [DynCIM: Dynamic Curriculum for Imbalanced Multimodal Learning](https://mlsanity.com/paper/2503.06456/) (2025)
- [Beyond the Mean: Fisher-Orthogonal Projection for Natural Gradient Descent in Large Batch Training](https://mlsanity.com/paper/2508.13898/) (2025)

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

- [Does Gradient Conflict Predict the Understanding--Generation Trade-off? A Controlled Audit of Conflict-Metric Validity in Unified Multimodal Models](https://mlsanity.com/paper/2609.38465/) (2026)
- [Beyond Layers: Position-Resolved Gradient Conflict and Position-Aware Modulation for Unified Multimodal Models](https://mlsanity.com/paper/2609.38485/) (2026)

## Abstract (arXiv)

Autoregressive next-token training offers a unified formulation for image generation and text understanding, but it also creates strong modality competition that destabilizes optimization and limits large-batch scaling. We show that first-order optimizers such as AdamW are vulnerable to cross-modality gradient heterogeneity, while second-order preconditioning, particularly SOAP, provides a more stable basis for multimodal alignment. Building on this insight, we propose ML-FOP-SOAP, a second-order optimization framework with Multi-Level Variance Correction. Our Fisher-Orthogonal Projection suppresses variance-induced modality conflicts, reducing the trade-off between visual generation and textual understanding. To make this practical under large gradient accumulation, we introduce a hierarchical folding strategy that captures fine-grained variance with low micro-step overhead. Experiments on Janus and Emu3 show consistent gains across both modalities and stable training at batch size 8192. Compared with AdamW, our method improves sample efficiency by up to 1.4× and accelerates wall-clock training by up to 1.5×, offering a robust optimizer for scaling multimodal foundation models.