Related papers: Efficient Turing Machine Simulation with Transform…

Universal quantum simulation may provide insights into those many-body systems that cannot be described classically, and that cannot be efficiently simulated with current technology. The Trotter formula, which decomposes a desired unitary…

Large Reasoning Models (LRMs) achieve promising performance but compromise token efficiency due to verbose reasoning processes. Unconscious Thought Theory (UTT) posits that complex problems can be solved more efficiently through…

Alternatives to recurrent neural networks, in particular, architectures based on attention or convolutions, have been gaining momentum for processing input sequences. In spite of their relevance, the computational properties of these…

Transformer has become the dominant architecture for sequence modeling, yet a detailed understanding of how its structural parameters influence expressive power remains limited. In this work, we study the approximation properties of…

Nanomechanical computers promise a greatly improved energetic efficiency compared to their electrical counterparts. However, progress towards this goal is hindered by a lack of modular components, such as logic gates or transistors, and…

Recurrent neural networks (RNNs) with deep test-time memorization modules, such as Titans and TTT, represent a promising, linearly-scaling paradigm distinct from Transformers. While these expressive models do not yet match the peak…

We discuss the following family of problems, parameterized by integers $C\geq 2$ and $D\geq 1$: Does a given one-tape non-deterministic $q$-state Turing machine make at most $Cn+D$ steps on all computations on all inputs of length $n$, for…

For any fixed $k$, a remarkably simple single-tape Turing machine can simulate $k$ independent counters in real time. Informally, a counter is a storage unit that maintains a single integer (initially 0), incrementing it, decrementing it,…

We study learned memory tokens as a computational scratchpad for a single-block Universal Transformer with Adaptive Computation Time (ACT) on Sudoku-Extreme, a combinatorial reasoning benchmark. Memory tokens are empirically necessary: no…

We show how to efficiently simulate continuous-time quantum query algorithms that run in time T in a manner that preserves the query complexity (within a polylogarithmic factor) while also incurring a small overhead cost in the total number…

In this paper we extend the concept of the traditional transactor, which focuses on correct content transfer, to a new timing-coherent transactor that also accurately aligns the timing of each transaction boundary so that designers can…

Simulating quantum systems is one of the most promising avenues to harness the computational power of quantum computers. However, hardware errors in noisy near-term devices remain a major obstacle for applications. Ideas based on the…

Number Theoretic Transform (NTT) is an essential mathematical tool for computing polynomial multiplication in promising lattice-based cryptography. However, costly division operations and complex data dependencies make efficient and…

Large Reasoning Models (LRMs) are criticized for the excessively lengthy Chain-of-Thought (CoT) to derive the final answer, suffering from high first-token and overall latency. Typically, the CoT of LRMs mixes multiple thinking units; each…

We introduce a parallelizable simplification of Neural Turing Machine (NTM), referred to as P-NTM, which redesigns the core operations of the original architecture to enable efficient scan-based parallel execution. We evaluate the proposed…

Neural Turing Machines (NTMs) are an instance of Memory Augmented Neural Networks, a new class of recurrent neural networks which decouple computation from memory by introducing an external memory unit. NTMs have demonstrated superior…

We explore a new form of DFT, which we call the Polynomial Transform. It functions over finite fields, and a size $n$ transform takes $O(n)$ operations. In the multitape Turing machine model, it allows us to multiply two $n$ bit numbers in…

Recent research in the field of machine learning has increasingly focused on the memorization capacity of Transformers, but how efficient they are is not yet well understood. We demonstrate that Transformers can memorize labels with…

Dynamic simulation of materials is a promising application for near-term quantum computers. Current algorithms for Hamiltonian simulation, however, produce circuits that grow in depth with increasing simulation time, limiting feasible…

Length generalization, the ability to solve problems of longer sequences than those observed during training, poses a core challenge of Transformer-based large language models (LLM). Although existing studies have predominantly focused on…