arXiv subjects
Publications and source records attributed to Kai Liang.
We find some significant special cases of subtraction games with infinite subtraction sets, whose outcome sequences are periodic, but whose SG value sequences are bounded and aperiodic.
This study applies finite automata to the automatic solving of a variety of combinatorial games. For games whose positions and moves can be represented as regular languages and their operations, we design a two-stage automatic solving algorithm: first, construct a candidate finite automaton to determine the $\mathcal{P}$- and $\mathcal{N}$-positions, and then perform rigorous formal verification on this automaton; once verified, a complete solution of the game is obtained. For partizan octal games, we introduce a generalized mis\`ere quotient, overcoming the limitation that traditional theory applies only to impartial games. Using the above algorithm, we successfully solve the majority of two-digit partizan octal games, and based on these results, we propose a partizan version of Guy's conjecture. We also successfully solve a considerable number of partizan octal games under mis\`ere play, and give a conjecture on the structure of those games exhibiting ``algebraic periodicity'' among them. For Kotzig's nim, we resolve the most important related conjecture: we prove that the outcomes and SG values are periodic under both normal and mis\`ere play (including their partizan versions). Our algorithm successfully solves several small-scale cases, including mis\`ere play and partizan versions. This study pioneers a new theoretical tool and algorithmic paradigm for the automatic solving of combinatorial games, and has broad prospects for further extension and application in the field of combinatorial game theory.
We give a weak solution for an impartial game we called ``Inverse Treblecross''. We have determined which of its starting positions are $\mathscr{P}$-position and give a reasonable strategy.
We introduce Step 3.5 Flash, a sparse Mixture-of-Experts (MoE) model that bridges frontier-level agentic intelligence and computational efficiency. We focus on what matters most when building agents: sharp reasoning and fast, reliable execution. Step 3.5 Flash pairs a 196B-parameter foundation with 11B active parameters for efficient inference. It is optimized with interleaved 3:1 sliding-window/full attention and Multi-Token Prediction (MTP-3) to reduce the latency and cost of multi-round agentic interactions. To reach frontier-level intelligence, we design a scalable reinforcement learning framework that combines verifiable signals with preference feedback, while remaining stable under large-scale off-policy training, enabling consistent self-improvement across mathematics, code, and tool use. Step 3.5 Flash demonstrates strong performance across agent, coding, and math tasks, achieving 85.4% on IMO-AnswerBench, 86.4% on LiveCodeBench-v6 (2024.08-2025.05), 88.2% on tau2-Bench, 69.0% on BrowseComp (with context management), and 51.0% on Terminal-Bench 2.0, comparable to frontier models such as GPT-5.2 xHigh and Gemini 3.0 Pro. By redefining the efficiency frontier, Step 3.5 Flash provides a high-density foundation for deploying sophisticated agents in real-world industrial environments.
We introduce LongCat-Flash, a 560-billion-parameter Mixture-of-Experts (MoE) language model designed for both computational efficiency and advanced agentic capabilities. Stemming from the need for scalable efficiency, LongCat-Flash adopts two novel designs: (a) Zero-computation Experts, which enables dynamic computational budget allocation and activates 18.6B-31.3B (27B on average) per token depending on contextual demands, optimizing resource usage. (b) Shortcut-connected MoE, which enlarges the computation-communication overlap window, demonstrating notable gains in inference efficiency and throughput compared to models of a comparable scale. We develop a comprehensive scaling framework for large models that combines hyperparameter transfer, model-growth initialization, a multi-pronged stability suite, and deterministic computation to achieve stable and reproducible training. Notably, leveraging the synergy among scalable architectural design and infrastructure efforts, we complete model training on more than 20 trillion tokens within 30 days, while achieving over 100 tokens per second (TPS) for inference at a cost of \$0.70 per million output tokens. To cultivate LongCat-Flash towards agentic intelligence, we conduct a large-scale pre-training on optimized mixtures, followed by targeted mid- and post-training on reasoning, code, and instructions, with further augmentation from synthetic data and tool use tasks. Comprehensive evaluations demonstrate that, as a non-thinking foundation model, LongCat-Flash delivers highly competitive performance among other leading models, with exceptional strengths in agentic tasks. The model checkpoint of LongCat-Flash is open-sourced to foster community research. LongCat Chat: https://longcat.ai Hugging Face: https://huggingface.co/meituan-longcat GitHub: https://github.com/meituan-longcat
We applied tensor network contraction algorithms to compute the hard-core lattice gas model, i.e., the enumeration of independent sets on grid graphs. We observed the influence of surface effect and parity effect on the enumeration (and entropy), and derived upper and lower bounds for both the combinatorics entropy and the coefficients of surface effect by numerical analysis. Additionally, we conducted corresponding calculations and analyses for triangular grid graphs, king graph, and cylindrical grid graph. We computed and analyzed their associated constants and compared how different adjacency and boundary conditions affect these constants. Our computational results have contributed substantial new terms to the OEIS sequence A089980, A027740, A219741, A226444, A245013 and A286513. In addition, we have provided fairly accurate estimates of the relevant constants through numerical analysis of the obtained results. Among them, our valuation of the hard square entropy constant is more accurate than existing results. And we conject that the surface effect of the periodic boundary of the cylindrical grid graph is $0$--its estimated value of coefficients is very close to $0$.
In this paper, we investigate the transmission latency of the secure aggregation problem in a \emph{wireless} federated learning system with multiple curious servers. We propose a privacy-preserving coded aggregation scheme where the servers can not infer any information about the distributed users' local gradients, nor the aggregation value. In our scheme, each user encodes its local gradient into $\sK$ confidential messages intended exclusively for different servers using a multi-secret sharing method, and each server forwards the summation of the received confidential messages, while the users sequentially employ artificial noise alignment techniques to facilitate secure transmission. Through these summations, the user can recover the aggregation of all local gradients. We prove the privacy guarantee in the information-theoretic sense and characterize the uplink and downlink communication latency measured by \emph{normalized delivery time} (NDT), both of which decrease monotonically with the number of servers $\sK$ while increasing over most of the range of the number of users $\sM$. Finally, we establish a lower bound on the NDT of the considered system and theoretically prove that the scheme achieves the optimal uplink and downlink NDT under the conditions $\sK \gg \sM \gg 0$ and $\sK \gg \sM$, respectively. For arbitrary $\sK$ and $\sM$, the proposed scheme achieves the optimal uplink NDT within a multiplicative gap of $4$.
This paper discusses the enumeration of independent sets in king graphs of size $m \times n$, based on the tensor network contractions algorithm given in reference~\cite{tilEnum}. We transform the problem into Wang tiling enumeration within an $(m+1) \times (n+1)$ rectangle and compute the results for all cases where $m + n \leq 79$ using tensor network contraction algorithm, and provided an approximation for larger $m, n$. Using the same algorithm, we also enumerated independent sets with vertex number restrictions. Based on the results, we analyzed the vertex number that maximize the enumeration for each pair $(m, n)$. Additionally, we compute the corresponding weighted enumeration, where each independent set is weighted by the number of its vertices (i.e., the total sum of vertices over all independent sets). The approximations for larger $m, n$ are given as well. Our results have added thousands of new items to the OEIS sequences A089980 and A193580. In addition, the combinatorial problems above are closely related to the hard-core model in physics. We estimate some important constants based on the existing results, and the relative error between our estimation of the entropy constant and the existing results is less than $10^{-9}$.
This paper presents an algorithm for computing the contraction of two-dimensional tensor networks on a square lattice; and we combine it with solving congruence equations to compute the exact enumeration (including weighted enumeration) of Wang tilings. Based on this, the paper demonstrates how to transform other tiling enumeration problems (such as those of polyominoes) into Wang tiling enumeration problems, thereby solving them using this algorithm. Our algorithm extends the sequence length records for dozens of sequences defined by polyomino tiling enumeration on chessboards on the OEIS website, covering numerous of different polyomino sets, including I-polyominoes, tetrominoes, pentominoes, etc. This demonstrates the high efficiency and strong universality of the algorithm for solving exact tiling enumeration problems. In addition, the theory and techniques used in the algorithm establish a bridge between tensor network contractions and tiling enumeration, where the former provides a theoretical foundation for solving problems in the latter, while the latter offers an intuitive combinatorial interpretation of the former.
Face anonymization aims to conceal the visual identity of a face to safeguard the individual's privacy. Traditional methods like blurring and pixelation can largely remove identifying features, but these techniques significantly degrade image quality and are vulnerable to deep reconstruction attacks. Generative models have emerged as a promising solution for anonymizing faces while preserving a natural appearance. However, many still face limitations in visual quality and often overlook the potential to recover the original face from the anonymized version, which can be valuable in specific contexts such as image forensics. This paper proposes a novel framework named iFADIT, an acronym for Invertible Face Anonymization via Disentangled Identity Transform. The framework features a disentanglement architecture coupled with a secure flow-based model: the former decouples identity information from non-identifying attributes, while the latter transforms the decoupled identity into an anonymized version in an invertible manner controlled by a secret key. The anonymized face can then be reconstructed based on a pre-trained StyleGAN that ensures high image quality and realistic facial details. Recovery of the original face (aka de-anonymization) is possible upon the availability of the matching secret, by inverting the anonymization process based on the same set of model parameters. Furthermore, a dedicated secret-key mechanism along with a dual-phase training strategy is devised to ensure the desired properties of face anonymization. Qualitative and quantitative experiments demonstrate the superiority of the proposed approach in anonymity, reversibility, security, diversity, and interpretability over competing methods.
This paper investigates the optimization of the long-standing probabilistically robust transmit beamforming problem with channel uncertainties in the multiuser multiple-input single-output (MISO) downlink transmission. This problem poses significant analytical and computational challenges. Currently, the state-of-the-art optimization method relies on convex restrictions as tractable approximations to ensure robustness against Gaussian channel uncertainties. However, this method not only exhibits high computational complexity and suffers from the rank relaxation issue but also yields conservative solutions. In this paper, we propose an unsupervised deep learning-based approach that incorporates the sampling of channel uncertainties in the training process to optimize the probabilistic system performance. We introduce a model-driven learning approach that defines a new beamforming structure with trainable parameters to account for channel uncertainties. Additionally, we employ a graph neural network to efficiently infer the key beamforming parameters. We successfully apply this approach to the minimum rate quantile maximization problem subject to outage and total power constraints. Furthermore, we propose a bisection search method to address the more challenging power minimization problem with probabilistic rate constraints by leveraging the aforementioned approach. Numerical results confirm that our approach achieves non-conservative robust performance, higher data rates, greater power efficiency, and faster execution compared to state-of-the-art optimization methods.
Anticipating lane change intentions of surrounding vehicles is crucial for efficient and safe driving decision making in an autonomous driving system. Previous works often adopt physical variables such as driving speed, acceleration and so forth for lane change classification. However, physical variables do not contain semantic information. Although 3D CNNs have been developing rapidly, the number of methods utilising action recognition models and appearance feature for lane change recognition is low, and they all require additional information to pre-process data. In this work, we propose an end-to-end framework including two action recognition methods for lane change recognition, using video data collected by cameras. Our method achieves the best lane change classification results using only the RGB video data of the PREVENTION dataset. Class activation maps demonstrate that action recognition models can efficiently extract lane change motions. A method to better extract motion clues is also proposed in this paper.
This paper proposes a novel paradigm for facial privacy protection that unifies multiple characteristics including anonymity, diversity, reversibility and security within a single lightweight framework. We name it PRO-Face S, short for Privacy-preserving Reversible Obfuscation of Face images via Secure flow-based model. In the framework, an Invertible Neural Network (INN) is utilized to process the input image along with its pre-obfuscated form, and generate the privacy protected image that visually approximates to the pre-obfuscated one, thus ensuring privacy. The pre-obfuscation applied can be in diversified form with different strengths and styles specified by users. Along protection, a secret key is injected into the network such that the original image can only be recovered from the protection image via the same model given the correct key provided. Two modes of image recovery are devised to deal with malicious recovery attempts in different scenarios. Finally, extensive experiments conducted on three public image datasets demonstrate the superiority of the proposed framework over multiple state-of-the-art approaches.
Internet-of-Things (IoT) networks are expected to support the wireless connection of massive energy limited IoT nodes. The emerging wireless powered backscatter communications (WPBC) enable IoT nodes to harvest energy from the incident radio frequency signals transmitted by a power beacon (PB) to support their circuit operation, but the energy consumption of the PB (a potentially high cost borne by the network operator) has not been sufficiently studied for WPBC. In this paper, we aim to minimize the energy consumption of the PB while satisfying the throughput requirement per IoT node by jointly optimizing the time division multiple access (TDMA) time slot duration and backscatter reflection coefficient of each IoT node and the PB transmit power per time slot. As the formulated joint optimization problem is non-convex, we transform it into a convex problem by using auxiliary variables, then employ the Lagrange dual method to obtain the optimal solutions. To reduce the implementation complexity required for adjusting the PB's transmit power every time slot, we keep the PB transmit power constant in each time block and solve the corresponding PB energy consumption minimization problem by using auxiliary variables, the block coordinated decent method and the successive convex approximation technique. Based on the above solutions, two iterative algorithms are proposed for the dynamic PB transmit power scheme and the static PB transmit power scheme. The simulation results show that the dynamic PB transmit power scheme and the static PB transmit power scheme both achieve a lower PB energy consumption than the benchmark schemes, and the former achieves the lowest PB energy consumption.
In many distributed learning setups such as federated learning (FL), client nodes at the edge use individually collected data to compute local gradients and send them to a central master server. The master server then aggregates the received gradients and broadcasts the aggregation to all clients, with which the clients can update the global model. In this paper, we consider multi-server federated learning with secure aggregation and unreliable communication links. We first define a threat model using Shannon's information-theoretic security framework and propose a novel scheme called Lagrange Coding with Mask (LCM), which divides the servers into groups and uses Coding and Masking techniques. LCM can achieve a trade-off between the uplink and downlink communication loads by adjusting the number of servers in each group. Furthermore, we derive the lower bounds of the uplink and downlink communication loads, respectively, and prove that LCM achieves the optimal uplink communication load, which is unrelated to the number of collusion clients.
Simultaneous wireless information and power transfer (SWIPT) has long been proposed as a key solution for charging and communicating with low-cost and low-power devices. However, the employment of radio frequency (RF) signals for information/power transfer needs to comply with international health and safety regulations. In this paper, we provide a complete framework for the design and analysis of far-field SWIPT under safety constraints. In particular, we deal with two RF exposure regulations, namely, the specific absorption rate (SAR) and the maximum permissible exposure (MPE). The state-of-the-art regarding SAR and MPE is outlined together with a description as to how these can be modeled in the context of communication networks. We propose a deep learning approach for the design of robust beamforming subject to specific information, energy harvesting and SAR constraints. Furthermore, we present a thorough analytical study for the performance of large-scale SWIPT systems, in terms of information and energy coverage under MPE constraints. This work provides insights with regards to the optimal SWIPT design as well as the potentials from the proper development of SWIPT systems under health and safety restrictions.
Due to limited communication resources at the client and a massive number of model parameters, large-scale distributed learning tasks suffer from communication bottleneck. Gradient compression is an effective method to reduce communication load by transmitting compressed gradients. Motivated by the fact that in the scenario of stochastic gradients descent, gradients between adjacent rounds may have a high correlation since they wish to learn the same model, this paper proposes a practical gradient compression scheme for federated learning, which uses historical gradients to compress gradients and is based on Wyner-Ziv coding but without any probabilistic assumption. We also implement our gradient quantization method on the real dataset, and the performance of our method is better than the previous schemes.
In this paper, we consider the distributed mean estimation problem where the server has access to some side information, e.g., its local computed mean estimation or the received information sent by the distributed clients at the previous iterations. We propose a practical and efficient estimator based on an r-bit Wynzer-Ziv estimator proposed by Mayekar et al., which requires no probabilistic assumption on the data. Unlike Mayekar's work which only utilizes side information at the server, our scheme jointly exploits the correlation between clients' data and server' s side information, and also between data of different clients. We derive an upper bound of the estimation error of the proposed estimator. Based on this upper bound, we provide two algorithms on how to choose input parameters for the estimator. Finally, parameter regions in which our estimator is better than the previous one are characterized.