Looped transformers with recall and outer normalization produce reachable, input-dependent fixed points with stable gradients, enabling generalization, while those without recall cannot; a new internal recall variant performs competitively or better.
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Hierarchical Reasoning Model
Canonical reference. 71% of citing Pith papers cite this work as background.
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abstract
Reasoning, the process of devising and executing complex goal-oriented action sequences, remains a critical challenge in AI. Current large language models (LLMs) primarily employ Chain-of-Thought (CoT) techniques, which suffer from brittle task decomposition, extensive data requirements, and high latency. Inspired by the hierarchical and multi-timescale processing in the human brain, we propose the Hierarchical Reasoning Model (HRM), a novel recurrent architecture that attains significant computational depth while maintaining both training stability and efficiency. HRM executes sequential reasoning tasks in a single forward pass without explicit supervision of the intermediate process, through two interdependent recurrent modules: a high-level module responsible for slow, abstract planning, and a low-level module handling rapid, detailed computations. With only 27 million parameters, HRM achieves exceptional performance on complex reasoning tasks using only 1000 training samples. The model operates without pre-training or CoT data, yet achieves nearly perfect performance on challenging tasks including complex Sudoku puzzles and optimal path finding in large mazes. Furthermore, HRM outperforms much larger models with significantly longer context windows on the Abstraction and Reasoning Corpus (ARC), a key benchmark for measuring artificial general intelligence capabilities. These results underscore HRM's potential as a transformative advancement toward universal computation and general-purpose reasoning systems.
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representative citing papers
CanViT is the first task- and policy-agnostic AVFM pretrained via passive-to-active dense latent distillation on 13.2M scenes and 1B random glimpses, achieving 38.5% ADE20K mIoU in one glimpse and 84.5% ImageNet-1k top-1 after fine-tuning.
Recursive Masked Diffusion Models add recursive depth via repeated application of the same transformer to improve parameter efficiency and reduce inference steps in masked diffusion models.
Sheaf-ADMM trains multi-agent systems by unrolling ADMM with sheaf-specified constraints, yielding improved MNIST robustness to shifts and higher Sudoku solve rates than MPNN baselines.
RiM trains LLMs to perform latent reasoning via fixed memory blocks processed in one forward pass using a two-stage curriculum, matching or exceeding prior latent methods on benchmarks.
Interaction locality is introduced as a task-geometry-aware measurement framework showing that high-level states in recursive models write locally while recursive updates build broader structures on maze, Sudoku, ARC-AGI, and 3D grounding tasks.
LoopUS converts pretrained LLMs into looped latent refinement models via block decomposition, selective gating, random deep supervision, and confidence-based early exiting to improve reasoning performance.
Bifurcation models represent set-valued solution maps via weight-tied equilibrium dynamics whose attractors encode multiple solutions, with a proof that broad locally Lipschitz set-valued maps admit regular dynamical representations and experiments showing label-free discovery of multiple equilibria
Looped LLMs converge to distinct cyclic fixed points per layer, repeating feedforward-style inference stages across recurrences.
TRM with 7M parameters achieves 45% accuracy on ARC-AGI-1 and 8% on ARC-AGI-2, surpassing most LLMs with under 0.01% of their parameters.
SFT supplies entangled compositional traces of atomic skills and routing modules; RL identifies those modules and enables recombination on novel compositions outside the SFT support.
G-RRM neural guidance reduces median conflicts to zero and delivers speedups up to 33.3x on 9x9 Sudoku for backtracking solvers when search spaces are large and solvers can overwrite imperfect hints.
Stochastic loop counts during training of looped transformers reduce OOD variance on binary addition, Dyck-1, Unique Set and Copy tasks, with learned RL-Halting further improving the accuracy-stability trade-off.
DiARC improves LLM performance on ARC-like benchmarks by constructing and training on preference pairs from three types of negative samples while keeping demonstrations fixed.
Aggressive compression of recursive reasoners keeps local predictions intact but destroys global reasoning accuracy, recoverable with calibrated INT4 and detectable via carry-trajectory fidelity.
FPRM is a Transformer-based model using fixed-point convergence for adaptive halting in looped architectures, claimed effective on Sudoku, Maze, state-tracking, and ARC-AGI benchmarks.
Re-applying a frozen LLM's top layers at high-entropy tokens creates a deterministic rollout-diversity axis complementary to temperature, raising the joint oracle on MATH-500 from 83.4% to 91.6% for one 3B model.
DSSA decouples per-frame appearance from temporal identity in slot attention mechanisms to reduce slot swapping and improve temporal consistency in video object segmentation.
Loop-OWM uses color-prototype slots, demonstration-conditioned task summaries, and looped transitions to model ARC rules as visual-symbolic state changes and outperforms baselines on ARC-1 and ARC-2.
LARM enables test-time compute scaling in non-autoregressive ASR via depth-conditioned looping with CTC checkpoints, supervision embeddings, FiLM conditioning, and posterior feedback, yielding lower WER on LibriSpeech with more loops.
Confidence-based decoding and training in masked diffusion models shortcut long-range dependencies in reasoning, producing errors on complex inputs that random masking avoids.
WaveLiT combines wavelet tokenization, linear attention, and multiscale pyramids to produce parameter-efficient neural PDE solvers that match much larger models on TheWell benchmarks.
Learned Relay Representations add a differentiable per-token channel to masked diffusion models so they can propagate latent information across iterative denoising steps, yielding better coding performance and up to 32% lower latency on Fast-dLLM v2 than standard supervised finetuning.
WONN is a new oscillatory neural network based on generalized Winfree dynamics that scales competitively to ImageNet-1K and reaches 80.1% accuracy on Maze-hard with 1% of prior model parameters.
citing papers explorer
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Stability and Generalization in Looped Transformers
Looped transformers with recall and outer normalization produce reachable, input-dependent fixed points with stable gradients, enabling generalization, while those without recall cannot; a new internal recall variant performs competitively or better.
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CanViT: Toward Active-Vision Foundation Models
CanViT is the first task- and policy-agnostic AVFM pretrained via passive-to-active dense latent distillation on 13.2M scenes and 1B random glimpses, achieving 38.5% ADE20K mIoU in one glimpse and 84.5% ImageNet-1k top-1 after fine-tuning.
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Recursive Scaling in Masked Diffusion Models
Recursive Masked Diffusion Models add recursive depth via repeated application of the same transformer to improve parameter efficiency and reduce inference steps in masked diffusion models.
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Learning Multi-Agent Coordination via Sheaf-ADMM
Sheaf-ADMM trains multi-agent systems by unrolling ADMM with sheaf-specified constraints, yielding improved MNIST robustness to shifts and higher Sudoku solve rates than MPNN baselines.
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Unlocking the Working Memory of Large Language Models for Latent Reasoning
RiM trains LLMs to perform latent reasoning via fixed memory blocks processed in one forward pass using a two-stage curriculum, matching or exceeding prior latent methods on benchmarks.
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Interaction Locality in Hierarchical Recursive Reasoning
Interaction locality is introduced as a task-geometry-aware measurement framework showing that high-level states in recursive models write locally while recursive updates build broader structures on maze, Sudoku, ARC-AGI, and 3D grounding tasks.
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LoopUS: Recasting Pretrained LLMs into Looped Latent Refinement Models
LoopUS converts pretrained LLMs into looped latent refinement models via block decomposition, selective gating, random deep supervision, and confidence-based early exiting to improve reasoning performance.
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Bifurcation Models: Learning Set-Valued Solution Maps with Weight-Tied Dynamics
Bifurcation models represent set-valued solution maps via weight-tied equilibrium dynamics whose attractors encode multiple solutions, with a proof that broad locally Lipschitz set-valued maps admit regular dynamical representations and experiments showing label-free discovery of multiple equilibria
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A Mechanistic Analysis of Looped Reasoning Language Models
Looped LLMs converge to distinct cyclic fixed points per layer, repeating feedforward-style inference stages across recurrences.
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Less is More: Recursive Reasoning with Tiny Networks
TRM with 7M parameters achieves 45% accuracy on ARC-AGI-1 and 8% on ARC-AGI-2, surpassing most LLMs with under 0.01% of their parameters.
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From Reasoning Traces to Reusable Modules: Understanding Compositional Generalization in Language Model Reasoning
SFT supplies entangled compositional traces of atomic skills and routing modules; RL identifies those modules and enables recombination on novel compositions outside the SFT support.
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G-RRM: Guiding Symbolic Solvers with Recurrent Reasoning Models
G-RRM neural guidance reduces median conflicts to zero and delivers speedups up to 33.3x on 9x9 Sudoku for backtracking solvers when search spaces are large and solvers can overwrite imperfect hints.
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Stabilizing Extrapolation in Looped Transformers via Learned Stochastic Stopping
Stochastic loop counts during training of looped transformers reduce OOD variance on binary addition, Dyck-1, Unique Set and Copy tasks, with learned RL-Halting further improving the accuracy-stability trade-off.
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DiARC: Distinguishing Positive and Negative Samples Helps Improving ARC-like Reasoning Ability of Large Language Models
DiARC improves LLM performance on ARC-like benchmarks by constructing and training on preference pairs from three types of negative samples while keeping demonstrations fixed.
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What Survives When You Compress a Recursive Reasoner for the Edge?
Aggressive compression of recursive reasoners keeps local predictions intact but destroys global reasoning accuracy, recoverable with calibrated INT4 and detectable via carry-trajectory fidelity.
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Fixed-Point Reasoners: Stable and Adaptive Deep Looped Transformers
FPRM is a Transformer-based model using fixed-point convergence for adaptive halting in looped architectures, claimed effective on Sudoku, Maze, state-tracking, and ARC-AGI benchmarks.
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Entropy-Gated Latent Recursion
Re-applying a frozen LLM's top layers at high-entropy tokens creates a deterministic rollout-diversity axis complementary to temperature, raising the joint oracle on MATH-500 from 83.4% to 91.6% for one 3B model.
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Dual-State Slot Attention: Decoupling Appearance and Identity for Video Object-Centric Learning
DSSA decouples per-frame appearance from temporal identity in slot attention mechanisms to reduce slot swapping and improve temporal consistency in video object segmentation.
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Slots, Transitions, Loops: Learning Composable World Models for ARC
Loop-OWM uses color-prototype slots, demonstration-conditioned task summaries, and looped transitions to model ARC rules as visual-symbolic state changes and outperforms baselines on ARC-1 and ARC-2.
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Test-Time Compute Scaling for ASR with Depth-Conditioned Looped Transformers
LARM enables test-time compute scaling in non-autoregressive ASR via depth-conditioned looping with CTC checkpoints, supervision embeddings, FiLM conditioning, and posterior feedback, yielding lower WER on LibriSpeech with more loops.
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The Confidence Shortcut: A Reasoning Failure Mode of Masked Diffusion Models
Confidence-based decoding and training in masked diffusion models shortcut long-range dependencies in reasoning, producing errors on complex inputs that random masking avoids.
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Small Models, Strong Priors: Architectural Inductive Bias for Parameter-Efficient Neural PDE Solvers
WaveLiT combines wavelet tokenization, linear attention, and multiscale pyramids to produce parameter-efficient neural PDE solvers that match much larger models on TheWell benchmarks.
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Learned Relay Representations for Forward-Thinking Discrete Diffusion Models
Learned Relay Representations add a differentiable per-token channel to masked diffusion models so they can propagate latent information across iterative denoising steps, yielding better coding performance and up to 32% lower latency on Fast-dLLM v2 than standard supervised finetuning.
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Winfree Oscillatory Neural Network
WONN is a new oscillatory neural network based on generalized Winfree dynamics that scales competitively to ImageNet-1K and reaches 80.1% accuracy on Maze-hard with 1% of prior model parameters.
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HRM-Text: Efficient Pretraining Beyond Scaling
A 1B-parameter hierarchical recurrent model pretrained on 40B instruction-response tokens achieves 60.7% MMLU and strong results on ARC-C, DROP, GSM8K, and MATH while using 100-900x fewer tokens than standard baselines.
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Generative Recursive Reasoning
GRAM is a latent-variable generative model that performs recursive reasoning via stochastic trajectories, trained with amortized variational inference to support multi-hypothesis reasoning and unconditional generation.
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One Model, Two Roles: Emergent Specialization in a Shared Recurrent Transformer
In a minimal two-state recurrent Transformer, asymmetric input injection induces stable specialization where one state becomes a committed proposal and the other retains shifting uncertainty.
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One Pass Is Not Enough: Recursive Latent Refinement for Generative Models
RTM uses iterative refinement of latent codes in generative models to improve both precision and recall alongside competitive FID scores on CIFAR-10, CelebA-HQ, and few-shot datasets.
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Memory-Efficient Looped Transformer: Decoupling Compute from Memory in Looped Language Models
MELT decouples reasoning depth from memory in looped language models by sharing a single gated KV cache per layer and training it via chunk-wise distillation from Ouro starting models.
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State Stream Transformer (SST) V2: Parallel Training of Nonlinear Recurrence for Latent Space Reasoning
SST V2 introduces parallel-trainable nonlinear recurrence in latent space to let transformers reason continuously across positions, delivering +15 points on GPQA-Diamond and halving remaining GSM8K errors over matched baselines.
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The Thinking Pixel: Recursive Sparse Reasoning in Multimodal Diffusion Latents
A recursive sparse MoE framework integrated into diffusion models iteratively refines visual tokens via gated module selection to improve structured reasoning and image generation performance.
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Universal Transformers Need Memory: Depth-State Trade-offs in Adaptive Recursive Reasoning
Memory tokens are required for non-trivial performance in adaptive Universal Transformers on Sudoku-Extreme, with 8-32 tokens yielding stable 57% exact-match accuracy while trading off against ponder depth.
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One Step Forward and K Steps Back: Better Reasoning with Denoising Recursion Models
Denoising Recursion Models train multi-step noise reversal in looped transformers and outperform the prior Tiny Recursion Model on ARC-AGI.
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C-voting: Confidence-Based Test-Time Voting without Explicit Energy Functions
C-voting improves recurrent reasoning models by selecting among multiple latent trajectories the one with highest average top-1 probability, achieving 4.9% better Sudoku-hard accuracy than energy-based voting and outperforming HRM on Sudoku-extreme and Maze when paired with the new ItrSA++ model.
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Parcae: Scaling Laws For Stable Looped Language Models
Parcae stabilizes looped LLMs via spectral norm constraints on injection parameters, enabling power-law scaling for training FLOPs and saturating exponential scaling at test time that improves quality over fixed-depth baselines under fixed parameter budgets.
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Kuramoto Oscillatory Phase Encoding: Neuro-inspired Synchronization for Improved Learning Efficiency
Kuramoto oscillatory phase encoding (KoPE) adds evolving phase states to Vision Transformers and claims better training, parameter, and data efficiency via synchronization-enhanced structure learning.
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When to Think Fast and Slow? AMOR: Adaptive Entropy Gate for Hybrid Models
AMOR uses output entropy to gate attention in recurrent hybrids, matching full attention performance at roughly 22% attention invocations across 180M-1.5B models.
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Language-Guided Abstraction for Visual Reasoning
L-VARC is a LUPI framework that refines crowd-sourced language descriptions with an LLM and uses cross-attention to guide visual ARC models during training only, yielding SOTA results with a lightweight 18M-parameter network.
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Characterize Then Distill: Mechanistic Reasoning in Large Output Spaces
Reasoning in large output spaces proceeds via shortlisting then fine-grained reasoning; this characterization enables a mechanistic distillation strategy that outperforms standard distillation.
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Probabilistic Tiny Recursive Model
PTRM adds stochastic Gaussian noise to Tiny Recursive Model recursion for parallel trajectory exploration and Q-head selection, raising Sudoku-Extreme accuracy from 87.4% to 98.75% and Pencil Puzzle Bench from 62.6% to 91.2% without retraining.
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Graph Hierarchical Recurrence for Long-Range Generalization
GHR uses hierarchical recurrence on pooled graph abstractions to improve long-range dependency capture and out-of-range generalization while using far fewer parameters than existing models.
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bViT: Investigating Single-Block Recurrence in Vision Transformers for Image Recognition
A 12-step single-block recurrent ViT-B reaches accuracy comparable to a standard ViT-B on ImageNet-1K while using an order of magnitude fewer parameters.
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Mela: Test-Time Memory Consolidation based on Transformation Hypothesis
Mela is a Transformer variant with a dual-frequency Hierarchical Memory Module and MemStack that performs test-time memory consolidation, outperforming baselines on long contexts.
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HypEHR: Hyperbolic Modeling of Electronic Health Records for Efficient Question Answering
A 22M-parameter hyperbolic model answers structured EHR questions with accuracy close to LLM-based systems (EHRXQA 89.5%, MIMIC-Instr 76.0%).
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H-Probes: Extracting Hierarchical Structures From Latent Representations of Language Models
H-probes locate low-dimensional subspaces encoding hierarchy in LLM activations for synthetic tree tasks, show causal importance and generalization, and detect weaker signals in mathematical reasoning traces.
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Decidable By Construction: Design-Time Verification for Trustworthy AI
Design-time Hindley-Milner unification over finitely generated abelian groups is claimed to verify AI model reliability properties and to compute a MAP hypothesis under a restricted Solomonoff prior.
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Pretraining Recurrent Networks without Recurrence
SMT trains nonlinear RNNs by imitating one-step memory-transition labels generated by a Transformer, replacing BPTT's unrolled credit assignment with time-parallel supervised learning.
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When to Re-Plan: Subgoal Persistence in Hierarchical Latent Reasoning
Moderate subgoal persistence (P=3-6) in an extended hierarchical latent reasoning model produces lower loss on ARC and ConceptARC than very short or very long persistence periods.
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Reasoning4Sciences: Bridging Reasoning Language Models to All Scientific Branches
A survey of reasoning language model adoption across 28 ERC scientific disciplines finds large maturity gaps, especially when only public resources are counted.
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Hierarchical vs. Flat Iteration in Shared-Weight Transformers
Hierarchical two-speed shared-weight recurrence in Transformers shows a sharp performance gap compared to independent layer stacking in empirical language modeling tests.