arXiv:2607. 20586v1 Announce Type: new Abstract: We study vector-valued affine refinement operators of the form [ (W\gamma)(t)=\sum_{j\in\mathbb{Z}} A_j\gamma(Mt-j)+B(t), ] with finitely supported matrix mask and compactly supported continuous piecewise linear input and forcing data.
By Boldsaikhan Bolorkhuu, Tsogtgerel Gantumur
arXiv:2608. 02624v1 Announce Type: cross Abstract: Refinement operators generate many functions used in wavelet constructions, subdivision schemes, and geometric modeling.
By Tsogtgerel Gantumur
The paper proposes a fixed‑width recurrent feedback scheme for Recurrent Tsetlin Machines (RTMs) by folding clause activations with XOR, retaining the folded bits at two time scales, and thresholding them back to binary. This compression reduces 480 clause activations to 96 recurrent bits while achieving comparable accuracy (61.47 ± 6.74% and 62.94 ± 9.92%) on a reproducible Boolean finite‑state‑machine benchmark across 144 runs. The study shows that raw clause feedback offers only marginal accuracy gains but increases recurrent width and execution time significantly, and highlights the importance of no‑feedback controls in sequence model benchmarking.
By Ankit Kumar, Utkarsh Raj, Rishad Shafik, Sudip Roy
arXiv:2606. 07574v1 Announce Type: cross Abstract: Manifold-constrained hyper-connections (mHCs) have recently been proposed as a principled extension of hyper-connections, where the residual mixing matrices are constrained to be doubly stochastic via projection onto the Birkhoff polytope.
By Chenrui Wang, Yixuan Qiu
arXiv:2607. 20519v1 Announce Type: new Abstract: Looped Transformers increase test-time computation by repeatedly applying a shared recurrent block.
By Andrei Cristian Popescu, Haitz S\'aez de Oc\'ariz Borde, Pietro Li\`o
The paper introduces Gated Recurrent Transformers, a depth‑sharing architecture that brackets a single shared core with fixed prelude and coda blocks and uses a lightweight projection and element‑wise update gate to modulate recurrent updates. This design allows functional specialization across recurrences while reducing memory footprint. Experiments show that, under equal FLOPs or parameter budgets, the recurrent model matches or surpasses deeper GPT‑2 Small baselines, achieving similar or better accuracy with fewer parameters and lower peak decoding memory.
By Amr Hegazy, Amr Alanwar, Mostafa Elhoushi