Yun Liao

Yun Liao, Seyyed Ali Hashemi, Hengjie Yang et al.

While constructing polar codes for successive-cancellation decoding can be implemented efficiently by sorting the bit-channels, finding optimal polar codes for cyclic-redundancy-check-aided successive-cancellation list (CA-SCL) decoding in an efficient and scalable manner still awaits investigation. This paper first maps a polar code to a unique heterogeneous graph called the polar-code-construction message-passing (PCCMP) graph. Next, a heterogeneous graph-neural-network-based iterative message-passing (IMP) algorithm is proposed which aims to find a PCCMP graph that corresponds to the polar code with minimum frame error rate under CA-SCL decoding. This new IMP algorithm's major advantage lies in its scalability power. That is, the model complexity is independent of the blocklength and code rate, and a trained IMP model over a short polar code can be readily applied to a long polar code's construction. Numerical experiments show that IMP-based polar-code constructions outperform classical constructions under CA-SCL decoding. In addition, when an IMP model trained on a length-128 polar code directly applies to the construction of polar codes with different code rates and blocklengths, simulations show that these polar code constructions deliver comparable performance to the 5G polar codes.

Zeyu Gan, Yun Liao, Yong Liu

Test-time scaling, which is also often referred to as slow-thinking, has been demonstrated to enhance multi-step reasoning in large language models (LLMs). However, despite its widespread utilization, the mechanisms underlying slow-thinking methods remain poorly understood. This paper explores the mechanisms of external slow-thinking from a theoretical standpoint. We begin by examining the snowball error effect within the LLM reasoning process and connect it to the likelihood of correct reasoning using information theory. Building on this, we show that external slow-thinking methods can be interpreted as strategies to mitigate the error probability. We further provide a comparative analysis of popular external slow-thinking approaches, ranging from simple to complex, highlighting their differences and interrelationships. Our findings suggest that the efficacy of these methods is not primarily determined by the specific framework employed, and that expanding the search scope or the model's internal reasoning capacity may yield more sustained improvements in the long term. We open-source our code at https://github.com/ZyGan1999/Snowball-Errors-and-Probability.

Yide Di, Yun Liao, Hao Zhou et al.

Image feature matching, a foundational task in computer vision, remains challenging for multimodal image applications, often necessitating intricate training on specific datasets. In this paper, we introduce a Unified Feature Matching pre-trained model (UFM) designed to address feature matching challenges across a wide spectrum of modal images. We present Multimodal Image Assistant (MIA) transformers, finely tunable structures adept at handling diverse feature matching problems. UFM exhibits versatility in addressing both feature matching tasks within the same modal and those across different modals. Additionally, we propose a data augmentation algorithm and a staged pre-training strategy to effectively tackle challenges arising from sparse data in specific modals and imbalanced modal datasets. Experimental results demonstrate that UFM excels in generalization and performance across various feature matching tasks. The code will be released at:https://github.com/LiaoYun0x0/UFM.

Lingjie Kong, Yun Liao

Graph neural networks (GNN) extends deep learning to graph-structure dataset. Similar to Convolutional Neural Networks (CNN) using on image prediction, convolutional and pooling layers are the foundation to success for GNN on graph prediction tasks. In the initial PAN paper, it uses a path integral based graph neural networks for graph prediction. Specifically, it uses a convolution operation that involves every path linking the message sender and receiver with learnable weights depending on the path length, which corresponds to the maximal entropy random walk. It further generalizes such convolution operation to a new transition matrix called maximal entropy transition (MET). Because the diagonal entries of the MET matrix is directly related to the subgraph centrality, it provide a trial mechanism for pooling based on centrality score. While the initial PAN paper only considers node features. We further extends its capability to handle complex heterogeneous graph including both node and edge features.

Yun Liao, Junfan Li, Shizhong Liao et al.

In this paper, we study the mistake bound of online kernel learning on a budget. We propose a new budgeted online kernel learning model, called Ahpatron, which significantly improves the mistake bound of previous work and resolves the open problem posed by Dekel, Shalev-Shwartz, and Singer (2005). We first present an aggressive variant of Perceptron, named AVP, a model without budget, which uses an active updating rule. Then we design a new budget maintenance mechanism, which removes a half of examples,and projects the removed examples onto a hypothesis space spanned by the remaining examples. Ahpatron adopts the above mechanism to approximate AVP. Theoretical analyses prove that Ahpatron has tighter mistake bounds, and experimental results show that Ahpatron outperforms the state-of-the-art algorithms on the same or a smaller budget.

Xinhao Yao, Ruifeng Ren, Yun Liao et al.

The integration of explicit Chain-of-Thought (CoT) reasoning into training large language models (LLMs) has advanced their reasoning capabilities, yet the mechanisms by which CoT enhances generalization remain poorly understood. This work investigates (1) \textit{how} CoT training reshapes internal model representations and (2) \textit{why} it improves both in-distribution (ID) and out-of-distribution (OOD) reasoning generalization. Through controlled experiments and theoretical analysis, we derive the following key insights. \textbf{1)} Structural Advantage: CoT training internalizes reasoning into a two-stage generalizing circuit, where the number of stages corresponds to the explicit reasoning steps during training. Notably, CoT-trained models resolve intermediate results at shallower layers compared to non-CoT counterparts, freeing up deeper layers to specialize in subsequent reasoning steps. \textbf{2)} Theoretical Analysis: the information-theoretic generalization bounds via distributional divergence can be decomposed into ID and OOD components. While ID error diminishes with sufficient training regardless of CoT, OOD error critically depends on CoT: Non-CoT training fails to generalize to OOD samples due to unseen reasoning patterns, whereas CoT training achieves near-perfect OOD generalization by mastering subtasks and reasoning compositions during training. The identified mechanisms explain our experimental results: CoT training accelerates convergence and enhances generalization from ID to both ID and OOD scenarios while maintaining robust performance even with tolerable noise. These findings are further validated on complex real-world datasets. This paper offers valuable insights for designing CoT strategies to enhance LLM reasoning robustness.

Yun Liao, Seyyed Ali Hashemi, John Cioffi et al.

This paper formulates the polar-code construction problem for the successive-cancellation list (SCL) decoder as a maze-traversing game, which can be solved by reinforcement learning techniques. The proposed method provides a novel technique for polar-code construction that no longer depends on sorting and selecting bit-channels by reliability. Instead, this technique decides whether the input bits should be frozen in a purely sequential manner. The equivalence of optimizing the polar-code construction for the SCL decoder under this technique and maximizing the expected reward of traversing a maze is drawn. Simulation results show that the standard polar-code constructions that are designed for the successive-cancellation decoder are no longer optimal for the SCL decoder with respect to the frame error rate. In contrast, the simulations show that, with a reasonable amount of training, the game-based construction method finds code constructions that have lower frame-error rate for various code lengths and decoders compared to standard constructions.

Yun Liao, Nariman Farsad, Nir Shlezinger et al.

This paper proposes to use a deep neural network (DNN)-based symbol detector for mmWave systems such that CSI acquisition can be bypassed. In particular, we consider a sliding bidirectional recurrent neural network (BRNN) architecture that is suitable for the long memory length of typical mmWave channels. The performance of the DNN detector is evaluated in comparison to that of the Viterbi detector. The results show that the performance of the DNN detector is close to that of the optimal Viterbi detector with perfect CSI, and that it outperforms the Viterbi algorithm with CSI estimation error. Further experiments show that the DNN detector is robust to a wide range of noise levels and varying channel conditions, and that a pretrained detector can be reliably applied to different mmWave channel realizations with minimal overhead.