# State Stream Transformer (SST) V2: Parallel Training of Nonlinear Recurrence for Latent Space Reasoning

arXiv: https://arxiv.org/abs/2605.00206 · HTML: https://mlsanity.com/paper/2605.00206/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 33 of its 42 references that are in the map.
- First posted on arXiv 30 Apr 2026.

## Builds on (most cited first, 30 of 33)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [Gemma 3 Technical Report](https://mlsanity.com/paper/2503.19786/) (2025)
- [Root Mean Square Layer Normalization](https://mlsanity.com/paper/1910.07467/) (2019)
- [Training Large Language Models to Reason in a Continuous Latent Space](https://mlsanity.com/paper/2412.06769/) (2024)
- [Simplified State Space Layers for Sequence Modeling](https://mlsanity.com/paper/2208.04933/) (2022)
- [Universal Transformers](https://mlsanity.com/paper/1807.03819/) (2018)
- [Deep Equilibrium Models](https://mlsanity.com/paper/1909.01377/) (2019)
- [Sequence Level Training with Recurrent Neural Networks](https://mlsanity.com/paper/1511.06732/) (2015)
- [Executable Code Actions Elicit Better LLM Agents](https://mlsanity.com/paper/2402.01030/) (2024)
- [Adaptive Computation Time for Recurrent Neural Networks](https://mlsanity.com/paper/1603.08983/) (2016)
- [Scaling up Test-Time Compute with Latent Reasoning: A Recurrent Depth Approach](https://mlsanity.com/paper/2502.05171/) (2025)
- [Looped Transformers as Programmable Computers](https://mlsanity.com/paper/2301.13196/) (2023)
- [Hierarchical Reasoning Model](https://mlsanity.com/paper/2506.21734/) (2025)
- [Lipschitz Certificates for Layered Network Structures Driven by Averaged Activation Operators](https://mlsanity.com/paper/1903.01014/) (2019)
- [Parallelizing non-linear sequential models over the sequence length](https://mlsanity.com/paper/2309.12252/) (2023)
- [When More Thinking Hurts: Overthinking in LLM Test-Time Compute Scaling](https://mlsanity.com/paper/2604.10739/) (2026)

## Abstract (arXiv)

Current transformers discard their rich latent residual stream between positions, reconstructing latent reasoning context at each new position and leaving potential reasoning capacity untapped. The State Stream Transformer (SST) V2 enables parameter-efficient reasoning in continuous latent space through an FFN-driven nonlinear recurrence at each decoder layer, where latent states are streamed horizontally across the full sequence via a learned blend. This same mechanism supports continuous latent deliberation per position at inference time, dedicating additional FLOPs to exploring abstract reasoning before committing to a token. A two-pass parallel training procedure approximates the sequential recurrence, making co-training computationally practical. Hidden state analysis shows that the state stream facilitates reasoning through sharp, content-dependent reorganisations in continuous latent space; the LM head exposes the resulting latent belief states through the output distribution, while the state stream carries them forward to influence future positions. A learned probe shows that at the first generated token, the latent state already predicts whether the eventual answer will survive or break under additional latent computation for every subsequent position. Co-trained into an existing 27B backbone using only a small dataset of GSM8K examples and evaluated using an oracle to route each question to a depth of one to four recurrent forward passes per token, the SST achieves an architectural capacity bound of 61.11% on out-of-distribution GPQA-Diamond, a +15.15 point gain over a fine-tuning-matched baseline, and cuts that same baseline's remaining GSM8K errors by 46%. Together, these results provide a method for efficiently training a nonlinear recurrence and show that the state stream provides additional reasoning capacity beyond that of an otherwise training-matched transformer.