Constant bit-size Transformers are known to be Turing complete, but existing constructions require $Ω(s(n))$ chain-of-thought (CoT) steps per simulated Turing machine (TM) step, leading to impractical reasoning lengths. In this paper, we significantly reduce this efficiency gap by proving that any $(t(n),s(n))$-bounded multi-tape TM can be simulated by a constant bit-size Transformer with an optimal $O(s(n))$-long context window and only $O(s(n)^c)$ CoT steps per TM step, where $c>0$ can be made arbitrarily small by letting the Transformers' head-layer product sufficiently large. In addition, our construction shows that sparse attention with fixed geometric offsets suffices for efficient universal computation. Our proof leverages multi-queue TMs as a bridge. The main technical novelty is a more efficient simulation of multi-tape TMs by synchronous multi-queue TMs, improving both time and space complexity under stricter model assumptions.

In massive multiple-input multiple-output (MIMO) systems, how to reliably acquire downlink channel state information (CSI) with low overhead is challenging. In this work, by integrating the generative pre-trained Transformer (GPT) with federated-tuning, we propose a CSI-GPT approach to realize efficient downlink CSI acquisition. Specifically, we first propose a Swin Transformer-based channel acquisition network (SWTCAN) to acquire downlink CSI, where pilot signals, downlink channel estimation, and uplink CSI feedback are jointly designed. Furthermore, to solve the problem of insufficient training data, we propose a variational auto-encoder-based channel sample generator (VAE-CSG), which can generate sufficient CSI samples based on a limited number of high-quality CSI data obtained from the current cell. The CSI dataset generated from VAE-CSG will be used for pre-training SWTCAN. To fine-tune the pre-trained SWTCAN for improved performance, we propose an online federated-tuning method, where only a small amount of SWTCAN parameters are unfrozen and updated using over-the-air computation, avoiding the high communication overhead caused by aggregating the complete CSI samples from user equipment (UEs) to the BS for centralized fine-tuning. Simulation results verify the advantages of the proposed SWTCAN and the communication efficiency of the proposed federated-tuning method. Our code is publicly available at https://github.com/BIT-ZY/CSI-GPT

Programmatic reinforcement learning (PRL) has been explored for representing policies through programs as a means to achieve interpretability and generalization. Despite promising outcomes, current state-of-the-art PRL methods are hindered by sample inefficiency, necessitating tens of millions of program-environment interactions. To tackle this challenge, we introduce a novel LLM-guided search framework (LLM-GS). Our key insight is to leverage the programming expertise and common sense reasoning of LLMs to enhance the efficiency of assumption-free, random-guessing search methods. We address the challenge of LLMs' inability to generate precise and grammatically correct programs in domain-specific languages (DSLs) by proposing a Pythonic-DSL strategy - an LLM is instructed to initially generate Python codes and then convert them into DSL programs. To further optimize the LLM-generated programs, we develop a search algorithm named Scheduled Hill Climbing, designed to efficiently explore the programmatic search space to consistently improve the programs. Experimental results in the Karel domain demonstrate the superior effectiveness and efficiency of our LLM-GS framework. Extensive ablation studies further verify the critical role of our Pythonic-DSL strategy and Scheduled Hill Climbing algorithm.

This paper presents a novel approach to modeling the dynamics of human movements with a grid-based representation.For each grid cell, we formulate the local dynamics using a variant of the left-to-right HMM, and thus explicitly model the exiting direction from the current cell. The dependency of this process on the entry direction is captured by employing the Input-Output HMM (IOHMM). On a higher level, we introduce the place where the whole trajectory originated into the IOHMM framework forming a hierarchical input structure. Therefore, we manage to capture both local spatial-temporal correlations and the long-term dependency on faraway initiating events, thus enabling the developed model to incorporate more information and to generate more informative predictions of future trajectories.The experimental results in an office corridor environment verify the capabilities of our method.

Moving-target search, where a hunter has to catch a moving target, is an important problem for video game developers. In our case, the hunter repeatedly moves towards the target and thus has to solve similar search problems repeatedly. We develop Incremental ARA* (I-ARA*) for this purpose, the first incremental anytime search algorithm for moving-target search in known terrain. We provide an error bound on the lengths of the paths found by I-ARA* and show experimentally in known four-neighbor gridworlds that I-ARA* can be used with smaller time limits between moves of the hunter than competing state-of-the-art moving-target search algorithms, namely repeated A*, G-FRA*, FRA*, and sometimes repeated ARA*. The hunter tends to make more moves with I-ARA* than repeated A*, G-FRA* or FRA*, which find shortest paths for the hunter, but fewer moves with I-ARA* than repeated ARA*, which finds suboptimal paths for the hunter like I-ARA*. Also, the error bounds on the lengths of the paths of the hunter tend to be smaller with I-ARA* than repeated ARA*.

Incremental search algorithms reuse information from previous searches to speed up the current search and are thus often able to find shortest paths for series of similar search problems faster than by solving each search problem independently from scratch. However, they do poorly on moving target search problems, where both the start and goal cells change over time. In this paper, we thus develop Fringe-Retrieving A* (FRA*), an incremental version of A* that repeatedly finds shortest paths for moving target search in known gridworlds. We demonstrate experimentally that it runs up to one order of magnitude faster than a variety of state-of-the-art incremental search algorithms applied to moving target search in known gridworlds.