# It's All Connected: A Journey Through Test-Time Memorization, Attentional Bias, Retention, and Online Optimization

arXiv: https://arxiv.org/abs/2504.13173 · HTML: https://mlsanity.com/paper/2504.13173/

## Key facts

- Cited by 66 papers in the map (data through 14 Oct 2026).
- Builds on 69 of its 95 references that are in the map.
- First posted on arXiv 17 Apr 2025.

## Builds on (most cited first, 30 of 69)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Lost in the Middle: How Language Models Use Long Contexts](https://mlsanity.com/paper/2307.03172/) (2023)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [BoolQ: Exploring the Surprising Difficulty of Natural Yes/No Questions](https://mlsanity.com/paper/1905.10044/) (2019)
- [Transformers are RNNs: Fast Autoregressive Transformers with Linear Attention](https://mlsanity.com/paper/2006.16236/) (2020)
- [Root Mean Square Layer Normalization](https://mlsanity.com/paper/1910.07467/) (2019)
- [RULER: What's the Real Context Size of Your Long-Context Language Models?](https://mlsanity.com/paper/2404.06654/) (2024)
- [Transformers are SSMs: Generalized Models and Efficient Algorithms Through Structured State Space Duality](https://mlsanity.com/paper/2405.21060/) (2024)
- [The FineWeb Datasets: Decanting the Web for the Finest Text Data at Scale](https://mlsanity.com/paper/2406.17557/) (2024)
- [The LAMBADA dataset: Word prediction requiring a broad discourse context](https://mlsanity.com/paper/1606.06031/) (2016)
- [RWKV: Reinventing RNNs for the Transformer Era](https://mlsanity.com/paper/2305.13048/) (2023)
- [Introduction to Online Convex Optimization](https://mlsanity.com/paper/1909.05207/) (2019)
- [Simplified State Space Layers for Sequence Modeling](https://mlsanity.com/paper/2208.04933/) (2022)
- [Retentive Network: A Successor to Transformer for Large Language Models](https://mlsanity.com/paper/2307.08621/) (2023)
- [Gated Delta Networks: Improving Mamba2 with Delta Rule](https://mlsanity.com/paper/2412.06464/) (2024)
- [Gated Linear Attention Transformers with Hardware-Efficient Training](https://mlsanity.com/paper/2312.06635/) (2023)
- [Linear Transformers Are Secretly Fast Weight Programmers](https://mlsanity.com/paper/2102.11174/) (2021)
- [Hopfield Networks is All You Need](https://mlsanity.com/paper/2008.02217/) (2020)
- [Resurrecting Recurrent Neural Networks for Long Sequences](https://mlsanity.com/paper/2303.06349/) (2023)

## Built on by (most cited first, 30 of 66)

- [Test-Time Training Done Right](https://mlsanity.com/paper/2505.23884/) (2025)
- [TTT3R: 3D Reconstruction as Test-Time Training](https://mlsanity.com/paper/2509.26645/) (2025)
- [Cartridges: Lightweight and general-purpose long context representations via self-study](https://mlsanity.com/paper/2506.06266/) (2025)
- [A Survey on Latent Reasoning](https://mlsanity.com/paper/2507.06203/) (2025)
- [Nested Learning: The Illusion of Deep Learning Architectures](https://mlsanity.com/paper/2512.24695/) (2025)
- [ATLAS: Learning to Optimally Memorize the Context at Test Time](https://mlsanity.com/paper/2505.23735/) (2025)
- [Understanding Transformer from the Perspective of Associative Memory](https://mlsanity.com/paper/2505.19488/) (2025)
- [Scal3R: Scalable Test-Time Training for Large-Scale 3D Reconstruction](https://mlsanity.com/paper/2604.08542/) (2026)
- [In-Place Test-Time Training](https://mlsanity.com/paper/2604.06169/) (2026)
- [RoboTTT: Context Scaling for Robot Policies](https://mlsanity.com/paper/2607.15275/) (2026)
- [Speed Always Wins: A Survey on Efficient Architectures for Large Language Models](https://mlsanity.com/paper/2508.09834/) (2025)
- [Comba: Improving Bilinear RNNs with Closed-loop Control](https://mlsanity.com/paper/2506.02475/) (2025)
- [Position: Agentic Evolution is the Path to Evolving LLMs](https://mlsanity.com/paper/2602.00359/) (2026)
- [Memory Caching: RNNs with Growing Memory](https://mlsanity.com/paper/2602.24281/) (2026)
- [Scaling Linear Attention with Sparse State Expansion](https://mlsanity.com/paper/2507.16577/) (2025)
- [Fast-weight Product Key Memory](https://mlsanity.com/paper/2601.00671/) (2026)
- [Test-Time Training with KV Binding Is Secretly Linear Attention](https://mlsanity.com/paper/2602.21204/) (2026)
- [TNT: Improving Chunkwise Training for Test-Time Memorization](https://mlsanity.com/paper/2511.07343/) (2025)
- [SplatPainter: Interactive Authoring of 3D Gaussians from 2D Edits via Test-Time Training](https://mlsanity.com/paper/2512.05354/) (2025)
- [Beyond the Black Box: A Survey on the Theory and Mechanism of Large Language Models](https://mlsanity.com/paper/2601.02907/) (2026)
- [Memento 2: Learning by Stateful Reflective Memory](https://mlsanity.com/paper/2512.22716/) (2025)
- [MSA: Memory Sparse Attention for Efficient End-to-End Memory Model Scaling to 100M Tokens](https://mlsanity.com/paper/2603.23516/) (2026)
- [Mem3R: Streaming 3D Reconstruction with Hybrid Memory via Test-Time Training](https://mlsanity.com/paper/2604.07279/) (2026)
- [Trellis: Learning to Compress Key-Value Memory in Attention Models](https://mlsanity.com/paper/2512.23852/) (2025)
- [A Neuropsychologically Grounded Evaluation of LLM Cognitive Abilities](https://mlsanity.com/paper/2603.02540/) (2026)
- [Local Linear Attention: An Optimal Interpolation of Linear and Softmax Attention For Test-Time Regression](https://mlsanity.com/paper/2510.01450/) (2025)
- [Transformers as Intrinsic Optimizers: Forward Inference through the Energy Principle](https://mlsanity.com/paper/2511.00907/) (2025)
- [OpenSage: Self-programming Agent Generation Engine](https://mlsanity.com/paper/2602.16891/) (2026)
- [Fast Spatial Memory with Elastic Test-Time Training](https://mlsanity.com/paper/2604.07350/) (2026)
- [MuonSSM: Orthogonalizing State Space Models for Sequence Modeling](https://mlsanity.com/paper/2606.30461/) (2026)

## Abstract (arXiv)

Designing efficient and effective architectural backbones has been in the core of research efforts to enhance the capability of foundation models. Inspired by the human cognitive phenomenon of attentional bias-the natural tendency to prioritize certain events or stimuli-we reconceptualize neural architectures, including Transformers, Titans, and modern linear recurrent neural networks as associative memory modules that learn a mapping of keys and values using an internal objective, referred to as attentional bias. Surprisingly, we observed that most existing sequence models leverage either (1) dot-product similarity, or (2) L2 regression objectives as their attentional bias. Going beyond these objectives, we present a set of alternative attentional bias configurations along with their effective approximations to stabilize their training procedure. We then reinterpret forgetting mechanisms in modern deep learning architectures as a form of retention regularization, providing a novel set of forget gates for sequence models. Building upon these insights, we present Miras, a general framework to design deep learning architectures based on four choices of: (i) associative memory architecture, (ii) attentional bias objective, (iii) retention gate, and (iv) memory learning algorithm. We present three novel sequence models-Moneta, Yaad, and Memora-that go beyond the power of existing linear RNNs while maintaining a fast parallelizable training process. Our experiments show different design choices in Miras yield models with varying strengths. For example, certain instances of Miras achieve exceptional performance in special tasks such as language modeling, commonsense reasoning, and recall intensive tasks, even outperforming Transformers and other modern linear recurrent models.