arXiv subjects

Hanxu Hou

Publications and source records attributed to Hanxu Hou.

At least 19 recordsLinked to original sources

arXiv2026

Optimal Exponent of the Single-Error Correction Threshold with Fixed Redundancy for Analog Error-Correcting Codes

Analog error-correcting codes (Analog ECCs), introduced by Roth [1], address errors in vector-matrix multiplication arising from analog noise and sparse outliers in in-memory computing. A fundamental open problem concerns the lower bound on the single-error correction threshold $\Gamma_2(\mathcal C)$ for real $[n,k]$ linear codes with fixed redundancy $r=n-k\geq 2$. Li et al. [2] recently established that for redundancy $r=2$, every real $[n,n-2]$ linear code $\mathcal{C}$ satisfies $\Gamma_2(\mathcal C)\geq \csc^2(\frac{\pi}{2n})$, resolving an open problem in [1], and showed that, for every fixed $r \geq 2$, there exists a class of $[n,k]$ linear code $\mathcal{C}$ over $\mathbb{R}$ such that $\Gamma_2(\mathcal{C}) \leq O(n^{1+\frac{1}{r-1}})$. This paper proves the matching converse in [2]. For every $[n,k]$ linear code $\mathcal{C}\subseteq \mathbb R^n$ with fixed redundancy $2\leq r<n$, we show that \[ \Gamma_2(\mathcal C)\ge \frac{a_r}{\sqrt{r}\,\beta_{r-1}\,2^{\frac{1}{r-1}}}\cdot n^{1+\frac{1}{r-1}}, \] where $a_r =\frac{\Gamma(\frac{r}{2})}{\sqrt{\pi}\,\Gamma(\frac{r+1}{2})}$ and $\beta_d = \left(\frac{d\pi^{d-1}|\mathbb S^d|}{|\mathbb S^{d-1}|}\right)^{\frac{1}{d}}$ for positive integer $d$. Here $\mathbb S^d$ denotes the unit sphere in $\mathbb R^{d+1}$, $|\mathbb S^d|$ its surface area, and $\Gamma(\cdot)$ the Gamma function. In particular, we further show that $\Gamma_2(\mathcal C)\geq \frac{1}{4\pi\sqrt{3}r}\cdot n^{1+\frac{1}{r-1}}$. Together with the upper bound in [2], this confirms that the exponent $n^{1+\frac{1}{r-1}}$ is optimal, completing the asymptotic characterization of the single-error correction threshold for Analog ECCs.

cs.IT↗

arXiv2026

DemoPSD: Disagreement-Modulated Policy Self-Distillation

On-policy self-distillation (OPSD) has emerged as a practical method for training large language models (LLMs) to reason, where a single model acts as both the teacher and the student with different levels of information access. However, recent studies have found that the teacher's dense token-level supervision, conditioned on privileged information, can lead to overfitting to in-domain patterns, suppress exploration, and hurt cross-domain generalization, while also introducing a more fundamental issue: *privileged information leakage*, where the student encodes answer-dependent shortcuts that are unavailable at test time. We introduce **DemoPSD**, a novel framework that resolves such problems through the idea of *selective adoption of teacher guidance*. Instead of fitting the full teacher distribution, DemoPSD steers the student toward a *reverse-KL barycenter target*, a weighted geometric combination of the teacher and student distributions, that naturally balances learning from the teacher with preserving the student's own reasoning capacity. We measure the difference between their distributions and use such a discrepancy to adaptively control the blending at each token position. We provably show that DemoPSD achieves **(1)** *leakage attenuation*, i.e., effective mitigation of privileged information leakage; and **(2)** *exploration preservation*, i.e., preservation of exploration capacity under dense token-level distillation. Extensive experiments on SciKnowEval across four scientific fields show that DemoPSD outperforms both GRPO and SDPO while maintaining higher training entropy and robustly generalizing to out-of-distribution GPQA benchmarks.

cs.LG↗

arXiv2026

Asymptotically Optimal Codes for Correcting Burst Deletions and Insertions in Labeled DNA Sequences

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}

cs.IT↗

arXiv2026

ReasonAlloc: Hierarchical Decoding-Time KV Cache Budget Allocation for Reasoning Models

Long chain-of-thought (CoT) trajectories in large language model (LLM) reasoning cause severe inference bottlenecks due to rapid key-value (KV) cache growth. Current decoding-time compression methods mitigate this issue via token eviction, but typically assume a uniform budget distribution across all layers and heads. In contrast, existing non-uniform budget allocation methods are predominantly designed for the static prompt prefill phase, and they do not capture the stepwise context demands of autoregressive reasoning. To bridge this gap, we propose ReasonAlloc, a training-free framework that recasts decoding-time KV compression as a hierarchical budget allocation problem. ReasonAlloc operates at two complementary levels: an offline layer-wise preallocation strategy captures an architecture-driven demand pattern which we call ``\textit{Reasoning Wave}'', while an online head-wise strategy reallocates resources during decoding to information-rich heads based on real-time utility. Evaluations on mathematical reasoning benchmarks (MATH-500, AIME~2024) using DeepSeek-R1-Distill-Llama-8B, DeepSeek-R1-Distill-Qwen-14B, and AceReason-14B show that ReasonAlloc outperforms uniform-budget R-KV, SnapKV, and Pyramid-RKV (a baseline enforcing a static, monotonically decreasing layer budget), with the largest gains at small budgets (128-512 tokens). ReasonAlloc is plug-and-play with existing token-eviction policies and introduces negligible inference-time overhead.

cs.AI↗

arXiv2026

Tight Lower Bounds on The Single-Error Detection Threshold for Analog Error-Correcting Codes

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.

cs.IT↗

arXiv2026

Joint Design of Piggyback and Conjugate Transformation Functions for Repair Bandwidth Reduction in Piggybacking Codes

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.

cs.IT↗

arXiv2026

Learning to Reason with Insight for Informal Theorem Proving

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 $\texttt{DeepInsight}$, a unified training framework designed to cultivate this essential reasoning skill and enable LLMs to perform insightful reasoning. Our framework consists of three components: (1) $\texttt{DeepInsightTheorem}$, a hierarchical dataset that structures informal proofs by explicitly extracting core techniques and proof sketches alongside the final proof; (2) a Progressive Multi-Stage SFT strategy that mimics the human learning process, teaching the model proof writing, planning, and insight identification; and (3) $\texttt{InsightPO}$, a policy optimization method that assigns structured rewards over this insight hierarchy. 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.

cs.AI↗

arXiv2026

Redundancy-Optimal Constructions of $(1,1)$-Criss-Cross Deletion Correcting Codes with Efficient Encoding/Decoding Algorithms

Two-dimensional error-correcting codes, where codewords are represented as $n \times n$ arrays over a $q$-ary alphabet, find important applications in areas such as QR codes, DNA-based storage, and racetrack memories. Among the possible error patterns, $(t_r,t_c)$-criss-cross deletions-where $t_r$ rows and $t_c$ columns are simultaneously deleted-are of particular significance. In this paper, we focus on $q$-ary $(1,1)$-criss-cross deletion correcting codes. We present a novel code construction and develop complete encoding, decoding, and data recovery algorithms for parameters $n \ge 11$ and $q \ge 3$. The complexity of the proposed encoding, decoding, and data recovery algorithms is $\mathcal{O}(n^2)$. Furthermore, we show that for $n \ge 11$ and $q = \Omega(n)$ (i.e., there exists a constant $c>0$ such that $q \ge cn$), both the code redundancy and the encoder redundancy of the constructed codes are $2n + 2\log_q n + \mathcal{O}(1)$, which attain the lower bound ($2n + 2\log_q n - 3$) within an $\mathcal{O}(1)$ gap. To the best of our knowledge, this is the first construction that can achieve the optimal redundancy with only an $\mathcal{O}(1)$ gap, while simultaneously featuring explicit encoding and decoding algorithms.

cs.IT↗

arXiv2025

Grid-like Error-Correcting Codes for Matrix Multiplication with Better Correcting Capability

Matrix multiplication over the real field constitutes a foundational operation in the training of deep learning models, serving as a computational cornerstone for both forward and backward propagation processes. However, the presence of silent data corruption (SDC) in large-scale distributed training environments poses a significant threat to model convergence and predictive accuracy, particularly when such errors manifest during matrix multiplication. Due to their transient and non-intrusive nature, these errors often evade detection, allowing them to propagate and accumulate over time, ultimately leading to substantial degradation in model performance. In this paper, we introduce a novel error-correcting coding framework specifically tailored for matrix multiplication operations. Our proposed framework is designed to detect and correct multiple computational errors that may arise during the execution of matrix products. By leveraging a grid-based structural encoding scheme, our approach enhances error localization and correction capabilities across all participating matrices, thereby significantly improving the fault tolerance of the computation. Experimental results demonstrate that our method achieves deterministic correction of up to two erroneous symbols distributed across three matrices with 100\% reliability, while incurring only a 24\% overhead in computational time on GPU architectures. Furthermore, we provide a rigorous theoretical analysis of the error-correction properties inherent to our coding scheme, establishing its correctness and robustness under well-defined fault models.

cs.IT↗

arXiv2025

Reasoning Meets Personalization: Unleashing the Potential of Large Reasoning Model for Personalized Generation

Personalization is a critical task in modern intelligent systems, with applications spanning diverse domains, including interactions with large language models (LLMs). Recent advances in reasoning capabilities have significantly enhanced LLMs, enabling unprecedented performance in tasks such as mathematics and coding. However, their potential for personalization tasks remains underexplored. In this paper, we present the first systematic evaluation of large reasoning models (LRMs) for personalization tasks. Surprisingly, despite generating more tokens, LRMs do not consistently outperform general-purpose LLMs, especially in retrieval-intensive scenarios where their advantages diminish. Our analysis identifies three key limitations: divergent thinking, misalignment of response formats, and ineffective use of retrieved information. To address these challenges, we propose Reinforced Reasoning for Personalization (\model), a novel framework that incorporates a hierarchical reasoning thought template to guide LRMs in generating structured outputs. Additionally, we introduce a reasoning process intervention method to enforce adherence to designed reasoning patterns, enhancing alignment. We also propose a cross-referencing mechanism to ensure consistency. Extensive experiments demonstrate that our approach significantly outperforms existing techniques.

cs.CL↗

arXiv2025

RALLRec+: Retrieval Augmented Large Language Model Recommendation with Reasoning

Large Language Models (LLMs) have been integrated into recommender 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 have two shortcomings. \textit{(i)} In the \textit{retrieval} stage, they rely primarily on textual semantics and often fail to incorporate the most relevant items, thus constraining system effectiveness. \textit{(ii)} In the \textit{generation} stage, they lack explicit chain-of-thought reasoning, further limiting their potential. In this paper, we propose Representation learning and \textbf{R}easoning empowered retrieval-\textbf{A}ugmented \textbf{L}arge \textbf{L}anguage model \textbf{Rec}ommendation (RALLRec+). Specifically, for the retrieval stage, we prompt LLMs to generate detailed item descriptions and perform joint representation learning, combining textual and collaborative signals extracted from the LLM and recommendation models, respectively. To account for the time-varying nature of user interests, we propose a simple yet effective reranking method to capture preference dynamics. For the generation phase, we first evaluate reasoning LLMs on recommendation tasks, uncovering valuable insights. Then we introduce knowledge-injected prompting and consistency-based merging approach to integrate reasoning LLMs with general-purpose LLMs, enhancing overall performance. Extensive experiments on three real world datasets validate our method's effectiveness.

cs.IR↗

arXiv2025

RALLRec: Improving Retrieval Augmented Large Language Model Recommendation with Representation Learning

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.

cs.IR↗

arXiv2025

Accelerating Data Access for Single Node in Distributed Storage Systems via MDS Codes

Maximum distance separable (MDS) array codes are widely employed in modern distributed storage systems to provide high data reliability with small storage overhead. Compared with the data access latency of the entire file, the data access latency of a single node in a distributed storage system is equally important. In this paper, we propose two algorithms to effectively reduce the data access latency on a single node in different scenarios for MDS codes. We show theoretically that our algorithms have an expected reduction ratio of $\frac{(n-k)(n-k+1)}{n(n+1)}$ and $\frac{n-k}{n}$ for the data access latency of a single node when it obeys uniform distribution and shifted-exponential distribution, respectively, where $n$ and $k$ are the numbers of all nodes and the number of data nodes respectively. In the worst-case analysis, we show that our algorithms have a reduction ratio of more than $60\%$ when $(n,k)=(3,2)$. Furthermore, in simulation experiments, we use the Monte Carlo simulation algorithm to demonstrate less data access latency compared with the baseline algorithm.

cs.IT↗

arXiv2024

Error Correction Decoding Algorithms of RS Codes Based on An Earlier Termination Algorithm to Find The Error Locator Polynomial

Reed-Solomon (RS) codes are widely used to correct errors in storage systems. Finding the error locator polynomial is one of the key steps in the error correction procedure of RS codes. Modular Approach (MA) is an effective algorithm for solving the Welch-Berlekamp (WB) key-equation problem to find the error locator polynomial that needs $2t$ steps, where $t$ is the error correction capability. In this paper, we first present a new MA algorithm that only requires $2e$ steps and then propose two fast decoding algorithms for RS codes based on our MA algorithm, where $e$ is the number of errors and $e\leq t$. We propose Improved-Frequency Domain Modular Approach (I-FDMA) algorithm that needs $2e$ steps to solve the error locator polynomial and present our first decoding algorithm based on the I-FDMA algorithm. We show that, compared with the existing methods based on MA algorithms, our I-FDMA algorithm can effectively reduce the decoding complexity of RS codes when $e<t$. Furthermore, we propose the $t_0$-Shortened I-FDMA ($t_0$-SI-FDMA) algorithm ($t_0$ is a predetermined even number less than $2t-1$) based on the new termination mechanism to solve the error number $e$ quickly. We propose our second decoding algorithm based on the SI-FDMA algorithm for RS codes and show that the multiplication complexity of our second decoding algorithm is lower than our first decoding algorithm (the I-FDMA decoding algorithm) when $2e<t_0+1$.

cs.IT↗

arXiv2024

Privacy in LLM-based Recommendation: Recent Advances and Future Directions

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.

cs.CL↗

arXiv2024

Set Transformation: Trade-off Between Repair Bandwidth and Sub-packetization

Maximum distance separable (MDS) codes facilitate the achievement of elevated levels of fault tolerance in storage systems while incurring minimal redundancy overhead. Reed-Solomon (RS) codes are typical MDS codes with the sub-packetization level being one, however, they require large repair bandwidth defined as the total amount of symbols downloaded from other surviving nodes during single-node failure/repair. In this paper, we present the {\em set transformation}, which can transform any MDS code into set transformed code such that (i) the sub-packetization level is flexible and ranges from 2 to $(n-k)^{\lfloor\frac{n}{n-k}\rfloor}$ in which $n$ is the number of nodes and $k$ is the number of data nodes, (ii) the new code is MDS code, (iii) the new code has lower repair bandwidth for any single-node failure. We show that our set transformed codes have both lower repair bandwidth and lower field size than the existing related MDS array codes, such as elastic transformed codes \cite{10228984}. Specifically, our set transformed codes have $2\%-6.6\%$ repair bandwidth reduction compared with elastic transformed codes \cite{10228984} for the evaluated typical parameters.

cs.IT↗

arXiv2024

Reed-Solomon Codes over Cyclic Polynomial Ring with Lower Encoding/Decoding Complexity

Reed-Solomon (RS) codes are constructed over a finite field that have been widely employed in storage and communication systems. Many fast encoding/decoding algorithms such as fast Fourier transform (FFT) and modular approach are designed for RS codes to reduce the encoding/decoding complexity defined as the number of XORs involved in the encoding/decoding procedure. In this paper, we present the construction of RS codes over the cyclic polynomial ring $ \mathbb{F}_2[x]/(1+x+\ldots+x^{p-1})$ and show that our codes are maximum distance separable (MDS) codes. Moreover, we propose the FFT and modular approach over the ring that can be employed in our codes for encoding/decoding complexity reduction. We show that our codes have 17.9\% encoding complexity reduction and 7.5\% decoding complexity reduction compared with RS codes over finite field, for $(n,k)=(2048,1984)$.

cs.IT↗

arXiv2024

Learning From Correctness Without Prompting Makes LLM Efficient Reasoner

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.

cs.CL↗