The paper investigates how neural networks can learn to execute the insertion‑sort algorithm faithfully. Analysis of the CLRS30 baseline reveals that the model often learns shortcuts, producing correct final outputs without following the intended intermediate steps. To address this, the authors propose Discrete Neural Insertion Sort, which represents the sequence as a chain, separates exchanges from control transitions, and discretizes node states after each step. Trained on sequences of length 16, the model attains perfect accuracy on lengths 64 and 128, but ablation studies show that discretization and graph structure alone are insufficient without additional supervision of the global inner‑loop state.
arXiv:2606. 06574v1 Announce Type: new Abstract: Large language models (LLMs) perform inference by following a fixed depth and order, non-recurrent execution of all layers.
arXiv:2607. 26504v1 Announce Type: new Abstract: Many discrete reasoning tasks, such as code generation, are inherently non-causal: programmers move between high-level structure and local details, a process we call any-order inference.
Many discrete reasoning tasks, such as code generation, are inherently non-causal: programmers move between high-level structure and local details, a process we call any-order inference. For autoregressive language models, which lack a native any-order interface, non-causal abilities such as infilling and next-edit prediction require hand-designed mechanisms.
arXiv:2606. 21497v2 Announce Type: replace-cross Abstract: Modern deep neural networks are trained using error backpropagation, which requires sequential forward and backward computations across network layers.
arXiv:2511. 08577v3 Announce Type: replace-cross Abstract: Improving the reasoning abilities of Large Language Models (LLMs), especially under parameter constraints, is crucial for real-world applications.
The paper investigates how temporal recurrence affects the required depth of neural networks in streaming tasks. By treating depth, expert width, and parallel experts as a compute‑allocation problem, the authors compare recurrent and non‑recurrent models across various compute budgets. Experiments on Sokoban and FineWeb language modeling show that recurrence shifts the optimal compute allocation toward fewer layers while maintaining or improving performance.
arXiv:2603.21676v2 Announce Type: replace-cross Abstract: Standard Transformers have a fixed computational depth, limiting their ability to generalize to tasks that require variable-depth reasoning....
arXiv:2511.08577v4 Announce Type: replace-cross Abstract: Improving the reasoning abilities of Large Language Models (LLMs), especially under parameter constraints, is crucial for real-world applicat...
arXiv:2606. 02133v1 Announce Type: cross Abstract: Non-monotonic sequence generation methods, such as masked diffusion models, provide a flexible alternative to left-to-right autoregressive modeling by allowing tokens to be generated in non-fixed and prescribed orders.
arXiv:2608. 09031v1 Announce Type: new Abstract: Graph neural networks typically propagate information through repeated message-passing layers, coupling the distance over which information travels with the number of nonlinear transformations applied.
The paper introduces CHASE, a cache‑hole‑adapted skip‑exit mechanism for looped state‑space language models, specifically Looped Mamba and Looped Hybrid Mamba‑Transformer. It shows that looping these architectures improves performance on controlled reasoning tasks and remains competitive in pre‑training benchmarks while using fewer distinct parameters. The cache‑hole adaptation allows selective skipping of recurrent steps during inference, maintaining perplexity close to full computation and achieving significant speedups.
arXiv:2605. 08696v4 Announce Type: replace-cross Abstract: Over the last two decades, language modeling has experienced a shift from the use of predominantly recurrent architectures that process tokens sequentially during training and inference to non-recurrent models that process sequence elements in parallel during training, which results in greater training efficiency and stability at the expense of lower inference throughput.