# C-voting: Confidence-Based Test-Time Voting without Explicit Energy Functions

arXiv: https://arxiv.org/abs/2604.13521 · HTML: https://mlsanity.com/paper/2604.13521/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 35 references that are in the map.
- First posted on arXiv 15 Apr 2026.

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

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [GLU Variants Improve Transformer](https://mlsanity.com/paper/2002.05202/) (2020)
- [Root Mean Square Layer Normalization](https://mlsanity.com/paper/1910.07467/) (2019)
- [RePaint: Inpainting using Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2201.09865/) (2022)
- [Context Encoders: Feature Learning by Inpainting](https://mlsanity.com/paper/1604.07379/) (2016)
- [Least-to-Most Prompting Enables Complex Reasoning in Large Language Models](https://mlsanity.com/paper/2205.10625/) (2022)
- [Perceiver: General Perception with Iterative Attention](https://mlsanity.com/paper/2103.03206/) (2021)
- [Diffusion-LM Improves Controllable Text Generation](https://mlsanity.com/paper/2205.14217/) (2022)
- [SpanBERT: Improving Pre-training by Representing and Predicting Spans](https://mlsanity.com/paper/1907.10529/) (2019)
- [Universal Transformers](https://mlsanity.com/paper/1807.03819/) (2018)
- [Deep Equilibrium Models](https://mlsanity.com/paper/1909.01377/) (2019)
- [Scaling up Test-Time Compute with Latent Reasoning: A Recurrent Depth Approach](https://mlsanity.com/paper/2502.05171/) (2025)
- [Analyzing and Improving the Training Dynamics of Diffusion Models](https://mlsanity.com/paper/2312.02696/) (2023)
- [Reasoning with Latent Thoughts: On the Power of Looped Transformers](https://mlsanity.com/paper/2502.17416/) (2025)
- [ARC-AGI-2: A New Challenge for Frontier AI Reasoning Systems](https://mlsanity.com/paper/2505.11831/) (2025)
- [Hierarchical Reasoning Model](https://mlsanity.com/paper/2506.21734/) (2025)
- [SATNet: Bridging deep learning and logical reasoning using a differentiable satisfiability solver](https://mlsanity.com/paper/1905.12149/) (2019)
- [GTA: A Geometry-Aware Attention Mechanism for Multi-View Transformers](https://mlsanity.com/paper/2310.10375/) (2023)
- [Scaling Exponents Across Parameterizations and Optimizers](https://mlsanity.com/paper/2407.05872/) (2024)
- [Recurrent Relational Networks](https://mlsanity.com/paper/1711.08028/) (2017)
- [Slow and Steady Wins the Race: Maintaining Plasticity with Hare and Tortoise Networks](https://mlsanity.com/paper/2406.02596/) (2024)
- [Path Independent Equilibrium Models Can Better Exploit Test-Time Computation](https://mlsanity.com/paper/2211.09961/) (2022)
- [Artificial Kuramoto Oscillatory Neurons](https://mlsanity.com/paper/2410.13821/) (2024)
- [Continuous Thought Machines](https://mlsanity.com/paper/2505.05522/) (2025)
- [Switch EMA: A Free Lunch for Better Flatness and Sharpness](https://mlsanity.com/paper/2402.09240/) (2024)
- [Hyper-SET: Designing Transformers via Hyperspherical Energy Minimization](https://mlsanity.com/paper/2502.11646/) (2025)

## Built on by (most cited first, 1 of 1)

- [Steering Recurrent Reasoners at Inference Time with Readout Feedback](https://mlsanity.com/paper/2608.24136/) (2026)

## Abstract (arXiv)

Neural network models with latent recurrent processing, where identical layers are recursively applied to the latent state, have gained attention as promising models for performing reasoning tasks. A strength of such models is that they enable test-time scaling, where the models can enhance their performance in the test phase without additional training. Models such as the Hierarchical Reasoning Model (HRM) and Artificial Kuramoto Oscillatory Neurons (AKOrN) can facilitate deeper reasoning by increasing the number of recurrent steps, thereby enabling the completion of challenging tasks, including Sudoku, Maze solving, and AGI benchmarks. In this work, we introduce confidence-based voting (C-voting), a test-time scaling strategy designed for recurrent models with multiple latent candidate trajectories. Initializing the latent state with multiple candidates using random variables, C-voting selects the one maximizing the average of top-1 probabilities of the predictions, reflecting the model's confidence. Additionally, it yields 4.9% higher accuracy on Sudoku-hard than the energy-based voting strategy, which is specific to models with explicit energy functions. An essential advantage of C-voting is its applicability: it can be applied to recurrent models without requiring an explicit energy function. Finally, we introduce a simple attention-based recurrent model with randomized initial values named ItrSA++, and demonstrate that when combined with C-voting, it outperforms HRM on Sudoku-extreme (95.2% vs. 55.0%) and Maze (78.6% vs. 74.5%) tasks.