# Training Deep Nets with Sublinear Memory Cost

arXiv: https://arxiv.org/abs/1604.06174 · HTML: https://mlsanity.com/paper/1604.06174/

## Key facts

- Cited by 848 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Apr 2016.

## Built on by (most cited first, 30 of 848)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Qwen2-VL: Enhancing Vision-Language Model's Perception of the World at Any Resolution](https://mlsanity.com/paper/2409.12191/) (2024)
- [Robust Speech Recognition via Large-Scale Weak Supervision](https://mlsanity.com/paper/2212.04356/) (2022)
- [FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awareness](https://mlsanity.com/paper/2205.14135/) (2022)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [Wan: Open and Advanced Large-Scale Video Generative Models](https://mlsanity.com/paper/2503.20314/) (2025)
- [A Survey of Large Language Models](https://mlsanity.com/paper/2303.18223/) (2023)
- [LlamaFactory: Unified Efficient Fine-Tuning of 100+ Language Models](https://mlsanity.com/paper/2403.13372/) (2024)
- [DINO: DETR with Improved DeNoising Anchor Boxes for End-to-End Object Detection](https://mlsanity.com/paper/2203.03605/) (2022)
- [Swin Transformer V2: Scaling Up Capacity and Resolution](https://mlsanity.com/paper/2111.09883/) (2021)
- [M3-Embedding: Multi-Linguality, Multi-Functionality, Multi-Granularity Text Embeddings Through Self-Knowledge Distillation](https://mlsanity.com/paper/2402.03216/) (2024)
- [One-step Diffusion with Distribution Matching Distillation](https://mlsanity.com/paper/2311.18828/) (2023)
- [BloombergGPT: A Large Language Model for Finance](https://mlsanity.com/paper/2303.17564/) (2023)
- [Cosmos World Foundation Model Platform for Physical AI](https://mlsanity.com/paper/2501.03575/) (2025)
- [EVA-CLIP: Improved Training Techniques for CLIP at Scale](https://mlsanity.com/paper/2303.15389/) (2023)
- [Exploring Plain Vision Transformer Backbones for Object Detection](https://mlsanity.com/paper/2203.16527/) (2022)
- [Towards General Text Embeddings with Multi-stage Contrastive Learning](https://mlsanity.com/paper/2308.03281/) (2023)
- [EVA: Exploring the Limits of Masked Visual Representation Learning at Scale](https://mlsanity.com/paper/2211.07636/) (2022)
- [Efficient Large-Scale Language Model Training on GPU Clusters Using Megatron-LM](https://mlsanity.com/paper/2104.04473/) (2021)
- [FILIP: Fine-grained Interactive Language-Image Pre-Training](https://mlsanity.com/paper/2111.07783/) (2021)
- [XLS-R: Self-supervised Cross-lingual Speech Representation Learning at Scale](https://mlsanity.com/paper/2111.09296/) (2021)
- [LightGlue: Local Feature Matching at Light Speed](https://mlsanity.com/paper/2306.13643/) (2023)
- [A Dataset of Information-Seeking Questions and Answers Anchored in Research Papers](https://mlsanity.com/paper/2105.03011/) (2021)
- [Nystr"omformer: A Nystr"om-Based Algorithm for Approximating Self-Attention](https://mlsanity.com/paper/2102.03902/) (2021)
- [Putting NeRF on a Diet: Semantically Consistent Few-Shot View Synthesis](https://mlsanity.com/paper/2104.00677/) (2021)
- [GaLore: Memory-Efficient LLM Training by Gradient Low-Rank Projection](https://mlsanity.com/paper/2403.03507/) (2024)
- [Ring Attention with Blockwise Transformers for Near-Infinite Context](https://mlsanity.com/paper/2310.01889/) (2023)
- [Directly Fine-Tuning Diffusion Models on Differentiable Rewards](https://mlsanity.com/paper/2309.17400/) (2023)
- [Scaling Speech Technology to 1,000+ Languages](https://mlsanity.com/paper/2305.13516/) (2023)

## Abstract (arXiv)

We propose a systematic approach to reduce the memory consumption of deep neural network training. Specifically, we design an algorithm that costs O(sqrt(n)) memory to train a n layer network, with only the computational cost of an extra forward pass per mini-batch. As many of the state-of-the-art models hit the upper bound of the GPU memory, our algorithm allows deeper and more complex models to be explored, and helps advance the innovations in deep learning research. We focus on reducing the memory cost to store the intermediate feature maps and gradients during training. Computation graph analysis is used for automatic in-place operation and memory sharing optimizations. We show that it is possible to trade computation for memory - giving a more memory efficient training algorithm with a little extra computation cost. In the extreme case, our analysis also shows that the memory consumption can be reduced to O(log n) with as little as O(n log n) extra cost for forward computation. Our experiments show that we can reduce the memory cost of a 1,000-layer deep residual network from 48G to 7G with only 30 percent additional running time cost on ImageNet problems. Similarly, significant memory cost reduction is observed in training complex recurrent neural networks on very long sequences.