Hanxu Hou

Zhengyi Jiang, Wenhao Liu, Zhongyi Huang et al.

Analog error-correcting codes (Analog ECCs) for approximate vector-matrix multiplication have been extensively studied as means to achieve fault-tolerant in-memory computation. The theoretical foundations for such coding schemes, particularly the characterization of their correction capabilities via the height profile, have been well established in recent literature. In this paper, we focus on the case of single-error detection Analog ECCs. Among several open problems related to this case proposed by Ron M. Roth in [1], Problem 1 asks: "Identify the values of $k$ and $n$ for which every linear $[n, k]$ code $\mathcal{C}$ over $\mathbb{R}$ satisfies: $$\mathsf{h}_1(\mathcal{C}):=\max_{\boldsymbol{c}\in \mathcal{C}\setminus{\{\boldsymbol{0}\}}}\mathsf{h}_1(\boldsymbol{c})\geq \Big\lceil \frac{k}{n-k} \Big\rceil.\text{"}$$ Here, for any $\boldsymbol{x}\in\mathbb{R}^n$, $\mathsf{h}_1(\boldsymbol{x})$ represents the ratio between the largest and second largest absolute values of $\boldsymbol{x}$'s entries. As the simplest special case of Problem 1 (with $n-k=2$), the following problem was posed as Problem 2 in [1]: "Must every $(n-2)$-dimensional subspace of $\mathbb{R}^n$, $n$ even, contain a nonzero vector in which the ratio between the largest and second largest absolute values of its entries is at least $(n/2)-1$?" These problems directly pertain to the lower bounds on the single-error detection threshold for Analog ECCs: Problem 1 corresponds to arbitrary $n-k$ and Problem 2 corresponds to $n-k=2$. In this paper, we provide an affirmative answer to Problem 2 and a rigorous proof using theories related to convex optimization. Furthermore, we extend our analytical method to show that the lower bound in Problem 1 is tight for the case where $n-k$ divides $k$. Our results fill the gap in the lower bound theory of thresholds for single-error detection in Analog ECCs.

Yunhe Li, Hao Shi, Bowen Deng et al.

Although most of the automated theorem-proving approaches depend on formal proof systems, informal theorem proving can align better with large language models' (LLMs) strength in natural language processing. In this work, we identify a primary bottleneck in informal theorem proving as a lack of insight, namely the difficulty of recognizing the core techniques required to solve complex problems. To address this, we propose a novel framework designed to cultivate this essential reasoning skill and enable LLMs to perform insightful reasoning. We propose $\mathtt{DeepInsightTheorem}$, a hierarchical dataset that structures informal proofs by explicitly extracting core techniques and proof sketches alongside the final proof. To fully exploit this dataset, we design a Progressive Multi-Stage SFT strategy that mimics the human learning process, guiding the model from basic proof writing to insightful thinking. Our experiments on challenging mathematical benchmarks demonstrate that this insight-aware generation strategy significantly outperforms baselines. These results demonstrate that teaching models to identify and apply core techniques can substantially improve their mathematical reasoning.

Hao Shi, Zhengyi Jiang, Gefeng Deng et al.

Efficient node repair is a central requirement in distributed storage systems, particularly in high-rate erasure-coded deployments where repair traffic directly affects network overhead and recovery cost. Piggybacking codes reduce the repair bandwidth of MDS array codes while keeping the sub-packetization level small. However, existing piggybacking constructions often rely on restrictive piggyback-function designs to preserve the MDS property over small fields, which limits their repair-bandwidth reduction. We propose {\em conjugate-piggybacking} codes, a new class of MDS array codes that jointly design piggyback functions and conjugate transformations under small sub-packetization. The proposed construction improves repair efficiency while preserving the MDS property over moderate field sizes. In particular, it enables some parity nodes to achieve optimal repair bandwidth and reduces the overall repair bandwidth compared with existing piggybacking-based designs. We analyze the MDS property and repair bandwidth of the proposed codes and evaluate them against existing piggybacking codes under high-code-rate settings over $\mathbb{F}_{2^8}$. We further conduct a repair-traffic simulation under uniform single-node failures to quantify the expected traffic reduction in storage-oriented settings. The results show that our construction consistently achieves lower repair bandwidth than related piggybacking codes and reduces expected repair traffic compared with conventional RS repair. These gains are obtained at the cost of a slightly larger field size, revealing a practical trade-off between repair efficiency and field-size overhead for high-rate distributed storage.

Jian Xu, Sichun Luo, Xiangyu Chen et al.

Large Language Models (LLMs) have been integrated into recommendation systems to enhance user behavior comprehension. The Retrieval Augmented Generation (RAG) technique is further incorporated into these systems to retrieve more relevant items and improve system performance. However, existing RAG methods rely primarily on textual semantics and often fail to incorporate the most relevant items, limiting the effectiveness of the systems. In this paper, we propose Representation learning for retrieval-Augmented Large Language model Recommendation (RALLRec). Specifically, we enhance textual semantics by prompting LLMs to generate more detailed item descriptions, followed by joint representation learning of textual and collaborative semantics, which are extracted by the LLM and recommendation models, respectively. Considering the potential time-varying characteristics of user interest, a simple yet effective reranking method is further introduced to capture the dynamics of user preference. We conducted extensive experiments on three real-world datasets, and the evaluation results validated the effectiveness of our method. Code is made public at https://github.com/JianXu95/RALLRec.

Yuxuan Yao, Han Wu, Zhijiang Guo et al.

Large language models (LLMs) have demonstrated outstanding performance across various tasks, yet they still exhibit limitations such as hallucination, unfaithful reasoning, and toxic content. One potential approach to mitigate these issues is learning from human or external feedback (e.g. tools). In this paper, we introduce an intrinsic self-correct reasoning framework for LLMs that eliminates the need for human feedback, external tools, and handcraft prompts. The proposed framework, based on a multi-step reasoning paradigm \textbf{Le}arning from \textbf{Co}rrectness (\textsc{LeCo}), improves reasoning performance without needing to learn from errors. This paradigm prioritizes learning from correct reasoning steps, and a unique method to measure confidence for each reasoning step based on generation logits. Experimental results across various multi-step reasoning tasks demonstrate the effectiveness of the framework in improving reasoning performance with reduced token consumption.

Wenhao Liu, Zhengyi Jiang, Zhongyi Huang et al.

Fluorescent labeling is a cornerstone of DNA visualization and a key enabler of random access in DNA-based data storage. However, the stochastic nature of biochemical processes, including synthesis, hybridization, and optical readout, induces \emph{burst} synchronization errors within the resulting labeling sequences. To address this critical challenge, we formally introduce \emph{burst $t$-deletion/insertion $\mathcal{A}$-labeling codes,} designed to correct a single burst of $t$ deletions or insertions in the label domain. Our contributions are threefold. \begin{itemize} \item \textbf{Fundamental limit.} We establish an information-theoretic lower bound of $\log_4 n + \mathcal{O}(1)$ on the redundancy of any such code for all $t \ge 1$ with $t \mid n$. To the best of our knowledge, this resolves the first information-theoretic lower bound even for the single-error case \(t=1\). \item \textbf{Explicit construction.} For $t \ge 2$, $t \mid n$, and $n \ge 7t + 3$, we propose explicit encoding and decoding algorithms, both running in $\mathcal{O}(n^2)$ time. A novel generalized Run-Length Limited (RLL) constraint is introduced to bridge the structural mismatch between the DNA encoding domain and the label error domain. \item \textbf{Asymptotic optimality.} The proposed scheme achieves redundancy $\log_4 n + (t-1)\log_4 \log_{8/3} n + \mathcal{O}(1)$, matching the dominant term of the lower bound up to a small $\mathcal{O}(\log\log n)$ overhead, rendering the construction asymptotically optimal for fixed $t$. \end{itemize}

Guangfeng Yan, Tan Li, Yuanzhang Xiao et al.

Gradient compression has surfaced as a key technique to address the challenge of communication efficiency in distributed learning. In distributed deep learning, however, it is observed that gradient distributions are heavy-tailed, with outliers significantly influencing the design of compression strategies. Existing parameter quantization methods experience performance degradation when this heavy-tailed feature is ignored. In this paper, we introduce a novel compression scheme specifically engineered for heavy-tailed gradients, which effectively combines gradient truncation with quantization. This scheme is adeptly implemented within a communication-limited distributed Stochastic Gradient Descent (SGD) framework. We consider a general family of heavy-tail gradients that follow a power-law distribution, we aim to minimize the error resulting from quantization, thereby determining optimal values for two critical parameters: the truncation threshold and the quantization density. We provide a theoretical analysis on the convergence error bound under both uniform and non-uniform quantization scenarios. Comparative experiments with other benchmarks demonstrate the effectiveness of our proposed method in managing the heavy-tailed gradients in a distributed learning environment.

Sichun Luo, Wei Shao, Yuxuan Yao et al.

Nowadays, large language models (LLMs) have been integrated with conventional recommendation models to improve recommendation performance. However, while most of the existing works have focused on improving the model performance, the privacy issue has only received comparatively less attention. In this paper, we review recent advancements in privacy within LLM-based recommendation, categorizing them into privacy attacks and protection mechanisms. Additionally, we highlight several challenges and propose future directions for the community to address these critical problems.