arXiv subjects

Yunjiang Jiang

Publications and source records attributed to Yunjiang Jiang.

At least 19 recordsLinked to original sources

arXiv2026

Cutoff and a Gaussian-shift profile for the Rudvalis shuffle

The Rudvalis shuffle removes the top card and reinserts it uniformly at random in one of the bottom two positions. Hildebrand proved the classical upper bound $O(n^3\log n)$, and Wilson later proved the sharp lower coefficient $1/(8π^2)$, establishing the correct order but leaving the leading upper constant, cutoff, and the cutoff profile open. We prove that the full labelled shuffle has total-variation cutoff at \[ \frac{n^3\log n}{8π^2} \] with a window of order $n^3$. The upper bound is obtained by writing one deterministic rotation of the shuffle as a nonnormal sweep of adjacent averaging projections, comparing that sweep to a weighted interchange generator, and controlling the entire regular-representation heat trace. The key sharp-window ingredients are heat-kernel smoothing through the Octopus Inequality, zero extension of deletion-harmonic ordered-tuple functions, a representation-theoretic multiplicity payment, and a sectorwise entrance estimate that disposes of all large Young-diagram deficits. For the profile, an exact complex one-card eigenfunction yields a deck statistic whose surviving first Fourier mode converges to a Gaussian shift. A matching full-deck $L^2$ bound then shows that this one-dimensional Gaussian likelihood ratio asymptotically exhausts all remaining information, giving the exact total-variation profile.

math.PR↗

arXiv2026

Adhesive riffle shuffles: one-parameter models and mixing bounds

We compare four simple shuffles with one adhesion parameter $p$: a card-weighted sticky riffle, a block-weighted riffle, a midpoint-interpolation shuffle, and a correlated-label inverse riffle. Independent surviving contacts create contiguous blocks; no force or energy constants are fitted. We give polynomial upper bounds with explicit dependence on $p$, common adjacency-survival lower bounds, and a sharper information lower bound for interpolation. For fixed deck size $n\ge4$, the mixing time diverges as $Θ((1-p)^{-1})$ for the three cut-first models, but as $Θ((1-p)^{-2})$ for the correlated-label model. The latter distinction comes from whether one or two additional contact breaks are needed to escape cyclic rotations. For even $n$, unglued interpolation retains the lower bound $Ω(\sqrt n\log n)$ and upper bound $O(n^{5/2}\log n)$. We distinguish proved bounds from conjectured scales, recover classical riffle cutoff under sufficiently small perturbations, and explain precisely where established results on clumpy shuffles apply. The fixed-parameter asymptotic orders of the new cut-first families and their possible cutoff remain unresolved.

math.PR↗

arXiv2026

LIME: Link-based User-item Interaction Modeling with Decoupled XOR Attention for Efficient Test Time Scaling

Scaling large recommendation systems requires advancing three major frontiers: processing longer user histories, expanding candidate sets, and increasing model capacity. While promising, transformers' computational cost scales quadratically with the user sequence length and linearly with the number of candidates. This trade-off makes it prohibitively expensive to expand candidate sets or increase sequence length at inference, despite the significant performance improvements. We introduce \textbf{LIME}, a novel architecture that resolves this trade-off. Through two key innovations, LIME fundamentally reduces computational complexity. First, low-rank ``link embeddings" enable pre-computation of attention weights by decoupling user and candidate interactions, making the inference cost nearly independent of candidate set size. Second, a linear attention mechanism, \textbf{LIME-XOR}, reduces the complexity with respect to user sequence length from quadratic ($O(N^2)$) to linear ($O(N)$). Experiments on public and industrial datasets show LIME achieves near-parity with state-of-the-art transformers but with a 10$\times$ inference speedup on large candidate sets or long sequence lengths. When tested on a major recommendation platform, LIME improved user engagement while maintaining minimal inference costs with respect to candidate set size and user history length, establishing a new paradigm for efficient and expressive recommendation systems.

cs.IR↗

arXiv2026

MARS: Multi-resolution Adaptive Routing for Sequential Recommendation

Long-history recommenders often compress each user's history into a compact, candidate-independent memory that is cached and reused to score large candidate pools. We show that real user histories exhibit multi-scale semantic structure, with short-lived intent, medium-term interests, and long-term preferences coexisting in one sequence, and that monolithic cached memories preserve these scales unevenly: linear probes recover recent and mid-range content far worse than long-range content. We call this failure mode \textit{temporal aliasing}. We propose \textbf{MARS}, a multi-resolution user memory that writes the full history into recurrent state tracks anchored to different half-lives, and a sparse routing reader that materializes compact seed memories by selecting the relevant temporal resolutions for each seed, preserving fixed-size candidate scoring. MARS outperforms strong baselines on three public datasets, with gains that grow with history length. Component-matched ablations with paired tests show that temporal diversity and selective routing each contribute beyond what hard-window memories or added capacity provide. The advantage of MARS over its interface-matched baseline also widens after within-user behavioral shifts, at about $1.02\times$ that baseline's warm-cache serving latency for $1{,}000$ candidates per user.

cs.AI↗

arXiv2026

A subquadratic upper bound for the mixing time of the Thorp shuffle

Let $n=2^d$. We prove that the worst-start total-variation mixing time of the full labelled Thorp shuffle satisfies, for every fixed $0<\varepsilon<1$, \[ t_{\mathrm{mix}}(\varepsilon) \le C_* d^{5/3}+O_\varepsilon\!\left(d^{4/3}\log(d+2)\right), \qquad C_*=5.1536951454\ldots . \] Time is measured in ordinary Thorp shuffles. This improves the previously published full-deck upper bound $O(d^3)$ of Morris. The geometric starting point is elementary: label the $n=2^d$ positions by binary strings. One physical Thorp shuffle is a random swap layer on one coordinate matching of the $d$-dimensional cube, followed by a deterministic cyclic rotation of the coordinates. In a rotating frame that deterministic rotation disappears, so $d$ successive physical shuffles become one \emph{sweep}: one independent random swap layer in each coordinate direction. The proof then combines five ingredients. First, a collision-graph representation and negative dependence give pointwise smoothing for ordered marked cards. Second, an entropy argument is sharpened by moving an endpoint moment up to the critical exponent $β_c=\log_2(3/2)$, yielding an entropy-preparation clock $s^2/(2\log(3/2))+O(s\log s)$. Third, exact multiplicities in the ordered $h$-tuple permutation representation amplify marked-card bounds into Fourier operator and energy estimates on low representation levels. Fourth, entropy truncation produces a positive mixture whose regular component retains the marked-card budget. Finally, only two long blocks need this entropy regularization: a shorter third block is used solely for additional low-level smoothing. Optimizing the three block lengths gives the constant above.

math.PR↗

arXiv2026

Cutoff for the Overhand Shuffle

We study the overhand shuffle with a fixed cut probability $p\in(0,1)$. In the packet-reversal convention, each gap is cut independently with probability $p$, and each resulting packet is reversed in place. We prove total-variation cutoff at \[ \frac{p^2}{2(1-p)π^2}\,n^2\log n. \] The lower bound uses an exact finite-deck cosine eigenfunction and a uniform conditional-variance estimate. For the upper bound, a coalescing coupling reduces a transposition discrepancy to a symmetric killed two-card chain. Its principal decay rate is $(1-p)π^2/(p^2n^2)+o(n^{-2})$. A boundary-flux identity bounds the sum of adjacent discrepancy probabilities without a factor equal to the deck size. The remaining ingredient is a two-sided $L^1$ inequality on permutations, with constant at most $\sqrt n\exp\{O(\sqrt{\log n\log\log(n+2)})\}$. Its proof decomposes a fixed block-table fiber into assignment words and independent smaller permutations, and closes a recursion using a multivariate hypergeometric inequality and an explicit routing comparison. We also prove relative-entropy cutoff with an $O_p(n^2)$ window about the intrinsic entropy transition time. Its leading coefficient lies between the total-variation coefficient and twice that value; a sharp entropy location is not obtained. The proof states the normalization and hypotheses of its established functional-inequality inputs. An appendix proves the intermediate static bounds and explains the change from one-scale averaging to recursive fibers.

math.PR↗

arXiv2026

Entropy bounds and global couplings for union-closed families

We give a computer-assisted proof that every finite union-closed family containing a nonempty set has an element in at least 0.38288525 of its members. The argument combines independent sampling with conditionally independent sampling and an explicit product lower bound for a binary-entropy kernel. We identify the limiting constant of this pointwise method through a one-variable stationary equation. We also construct a global coupling by balancing inverse union multiplicities and prove a strictly positive, quantitative entropy gain over independent sampling. Combining the two arguments gives an additional frequency bound depending on the size of the family.

math.CO↗

arXiv2026

A 0.41275 lower bound for the three-dimensional Blaschke-Lebesgue problem

We prove that every convex body $K\subset\mathbb{R}^3$ of constant width $w>0$ satisfies \[ \operatorname{Vol}(K)\ge \frac{1651}{4000}w^3=0.41275\,w^3. \] This improves the certified lower bound $0.411040473721188\ldots\,w^3$ announced by Hyra and the earlier spectral bound $4πw^3/33$ of Nishioka. The main new ingredient is a contact-tetrahedron estimate near equality in Jung's circumradius inequality. Four balanced contacts of a minimum circumscribed ball form a near-regular tetrahedron; constant width then forces, beyond the tetrahedron itself, spherical regions over its faces, spindle sectors along its edges, and additional face-edge sectors. These regions can be selected with pairwise disjoint interiors and quantified by the total squared-edge deficit. A sharp convexity argument relates that deficit to the circumradius, and a symmetrization argument controls the four face contributions with only quadratic loss. This gives the analytic bound $\operatorname{Vol}(K)>0.41275318$ near the Jung endpoint. For the complementary circumradius range we use Hyra's radial transport/tangent-majorant mechanism together with closed-form contact and antipodal profiles. The antipodal contribution has an elementary primitive. For the contact contribution, a second-order concavity estimate converts the angular Jacobian into an explicit rational lower density; that density is monotone in the circumradius. The whole intermediate range therefore reduces to a single endpoint calculation, giving $\operatorname{Vol}(K)>0.41275168$. For smaller circumradius the tangent-majorant inequality with its nonnegative gap discarded already gives $\operatorname{Vol}(K)>0.41308109$. The proof is entirely analytic and requires no computer-assisted certificate.

math.MG↗

arXiv2026

Resolvent characteristics and quadratic mixing of Kac's walk on $SO(n)$

We study the coordinate-plane Kac walk on $\mathrm{SO}(n)$ with independent uniform rotation angles. For the unnormalized Hilbert-Schmidt Riemannian distance, we prove that the Wasserstein-$2$ Lipschitz coefficient of a block of $2\binom n2$ steps is at most $2n^{-1/200}$ for sufficiently large $n$. This gives a fixed-accuracy $O(n^2)$ Wasserstein mixing bound and inverse-polynomial accuracy in a constant number of blocks. We also obtain an $O(n^2)$ total-variation upper bound. The coupling averages each component of a regularized-inverse angle correction over its own angle, so its exact flow preserves the joint angle law. A deterministic decreasing regularization parameter cancels the main scalar and matrix-valued resolvent drifts. Its stability factor is polynomial in the inverse regularization, and the matrix estimates close on two partial traces. The same scalar estimate bounds the fraction of deficient covariance directions; independent cores and a cutoff integration-by-parts argument give the total-variation transfer. We provide the parameter estimates, conditioning arguments, and finite-time singular-mass treatment explicitly. The results imply total-variation pre-cutoff on the quadratic scale, but do not establish either the presence or the absence of cutoff.

math.PR↗

arXiv2026

Massive Memorization with Hundreds of Trillions of Parameters for Sequential Transducer Generative Recommenders

Modern large-scale recommendation systems rely heavily on user interaction history sequences to enhance the model performance. The advent of large language models and sequential modeling techniques, particularly transformer-like architectures, has led to significant advancements recently (e.g., HSTU, SIM, and TWIN models). While scaling to ultra-long user histories (10k to 100k items) generally improves model performance, it also creates significant challenges on latency, queries per second (QPS) and GPU cost in industry-scale recommendation systems. Existing models do not adequately address these industrial scalability issues. In this paper, we propose a novel two-stage modeling framework, namely VIrtual Sequential Target Attention (VISTA), which decomposes traditional target attention from a candidate item to user history items into two distinct stages: (1) user history summarization into a few hundred tokens; followed by (2) candidate item attention to those tokens. These summarization token embeddings are then cached in storage system and then utilized as sequence features for downstream model training and inference. This novel design for scalability enables VISTA to scale to lifelong user histories (up to one million items) while keeping downstream training and inference costs fixed, which is essential in industry. Our approach achieves significant improvements in offline and online metrics and has been successfully deployed on an industry leading recommendation platform serving billions of users.

cs.IR↗

arXiv2025

pEBR: A Probabilistic Approach to Embedding Based Retrieval

Embedding-based retrieval aims to learn a shared semantic representation space for both queries and items, enabling efficient and effective item retrieval through approximate nearest neighbor (ANN) algorithms. In current industrial practice, retrieval systems typically retrieve a fixed number of items for each query. However, this fixed-size retrieval often results in insufficient recall for head queries and low precision for tail queries. This limitation largely stems from the dominance of frequentist approaches in loss function design, which fail to address this challenge in industry. In this paper, we propose a novel \textbf{p}robabilistic \textbf{E}mbedding-\textbf{B}ased \textbf{R}etrieval (\textbf{pEBR}) framework. Our method models the item distribution conditioned on each query, enabling the use of a dynamic cosine similarity threshold derived from the cumulative distribution function (CDF) of the probabilistic model. Experimental results demonstrate that pEBR significantly improves both retrieval precision and recall. Furthermore, ablation studies reveal that the probabilistic formulation effectively captures the inherent differences between head-to-tail queries.

cs.IR↗

arXiv2023

Differentiable Retrieval Augmentation via Generative Language Modeling for E-commerce Query Intent Classification

Retrieval augmentation, which enhances downstream models by a knowledge retriever and an external corpus instead of by merely increasing the number of model parameters, has been successfully applied to many natural language processing (NLP) tasks such as text classification, question answering and so on. However, existing methods that separately or asynchronously train the retriever and downstream model mainly due to the non-differentiability between the two parts, usually lead to degraded performance compared to end-to-end joint training. In this paper, we propose Differentiable Retrieval Augmentation via Generative lANguage modeling(Dragan), to address this problem by a novel differentiable reformulation. We demonstrate the effectiveness of our proposed method on a challenging NLP task in e-commerce search, namely query intent classification. Both the experimental results and ablation study show that the proposed method significantly and reasonably improves the state-of-the-art baselines on both offline evaluation and online A/B test.

cs.IR↗

arXiv2023

Attention Weighted Mixture of Experts with Contrastive Learning for Personalized Ranking in E-commerce

Ranking model plays an essential role in e-commerce search and recommendation. An effective ranking model should give a personalized ranking list for each user according to the user preference. Existing algorithms usually extract a user representation vector from the user behavior sequence, then feed the vector into a feed-forward network (FFN) together with other features for feature interactions, and finally produce a personalized ranking score. Despite tremendous progress in the past, there is still room for improvement. Firstly, the personalized patterns of feature interactions for different users are not explicitly modeled. Secondly, most of existing algorithms have poor personalized ranking results for long-tail users with few historical behaviors due to the data sparsity. To overcome the two challenges, we propose Attention Weighted Mixture of Experts (AW-MoE) with contrastive learning for personalized ranking. Firstly, AW-MoE leverages the MoE framework to capture personalized feature interactions for different users. To model the user preference, the user behavior sequence is simultaneously fed into expert networks and the gate network. Within the gate network, one gate unit and one activation unit are designed to adaptively learn the fine-grained activation vector for experts using an attention mechanism. Secondly, a random masking strategy is applied to the user behavior sequence to simulate long-tail users, and an auxiliary contrastive loss is imposed to the output of the gate network to improve the model generalization for these users. This is validated by a higher performance gain on the long-tail user test set. Experiment results on a JD real production dataset and a public dataset demonstrate the effectiveness of AW-MoE, which significantly outperforms state-of-art methods. Notably, AW-MoE has been successfully deployed in the JD e-commerce search engine, ...

cs.IR↗

arXiv2022

Givens Coordinate Descent Methods for Rotation Matrix Learning in Trainable Embedding Indexes

Product quantization (PQ) coupled with a space rotation, is widely used in modern approximate nearest neighbor (ANN) search systems to significantly compress the disk storage for embeddings and speed up the inner product computation. Existing rotation learning methods, however, minimize quantization distortion for fixed embeddings, which are not applicable to an end-to-end training scenario where embeddings are updated constantly. In this paper, based on geometric intuitions from Lie group theory, in particular the special orthogonal group $SO(n)$, we propose a family of block Givens coordinate descent algorithms to learn rotation matrix that are provably convergent on any convex objectives. Compared to the state-of-the-art SVD method, the Givens algorithms are much more parallelizable, reducing runtime by orders of magnitude on modern GPUs, and converge more stably according to experimental studies. They further improve upon vanilla product quantization significantly in an end-to-end training scenario.

cs.IR↗

arXiv2022

Sequential Search with Off-Policy Reinforcement Learning

Recent years have seen a significant amount of interests in Sequential Recommendation (SR), which aims to understand and model the sequential user behaviors and the interactions between users and items over time. Surprisingly, despite the huge success Sequential Recommendation has achieved, there is little study on Sequential Search (SS), a twin learning task that takes into account a user's current and past search queries, in addition to behavior on historical query sessions. The SS learning task is even more important than the counterpart SR task for most of E-commence companies due to its much larger online serving demands as well as traffic volume. To this end, we propose a highly scalable hybrid learning model that consists of an RNN learning framework leveraging all features in short-term user-item interactions, and an attention model utilizing selected item-only features from long-term interactions. As a novel optimization step, we fit multiple short user sequences in a single RNN pass within a training batch, by solving a greedy knapsack problem on the fly. Moreover, we explore the use of off-policy reinforcement learning in multi-session personalized search ranking. Specifically, we design a pairwise Deep Deterministic Policy Gradient model that efficiently captures users' long term reward in terms of pairwise classification error. Extensive ablation experiments demonstrate significant improvement each component brings to its state-of-the-art baseline, on a variety of offline and online metrics.

cs.IR↗

arXiv2021

DSGPT: Domain-Specific Generative Pre-Training of Transformers for Text Generation in E-commerce Title and Review Summarization

We propose a novel domain-specific generative pre-training (DS-GPT) method for text generation and apply it to the product titleand review summarization problems on E-commerce mobile display.First, we adopt a decoder-only transformer architecture, which fitswell for fine-tuning tasks by combining input and output all to-gether. Second, we demonstrate utilizing only small amount of pre-training data in related domains is powerful. Pre-training a languagemodel from a general corpus such as Wikipedia or the CommonCrawl requires tremendous time and resource commitment, andcan be wasteful if the downstream tasks are limited in variety. OurDSGPT is pre-trained on a limited dataset, the Chinese short textsummarization dataset (LCSTS). Third, our model does not requireproduct-related human-labeled data. For title summarization task,the state of art explicitly uses additional background knowledgein training and predicting stages. In contrast, our model implic-itly captures this knowledge and achieves significant improvementover other methods, after fine-tuning on the public Taobao.comdataset. For review summarization task, we utilize JD.com in-housedataset, and observe similar improvement over standard machinetranslation methods which lack the flexibility of fine-tuning. Ourproposed work can be simply extended to other domains for a widerange of text generation tasks.

cs.CL↗

arXiv2021

Joint Learning of Deep Retrieval Model and Product Quantization based Embedding Index

Embedding index that enables fast approximate nearest neighbor(ANN) search, serves as an indispensable component for state-of-the-art deep retrieval systems. Traditional approaches, often separating the two steps of embedding learning and index building, incur additional indexing time and decayed retrieval accuracy. In this paper, we propose a novel method called Poeem, which stands for product quantization based embedding index jointly trained with deep retrieval model, to unify the two separate steps within an end-to-end training, by utilizing a few techniques including the gradient straight-through estimator, warm start strategy, optimal space decomposition and Givens rotation. Extensive experimental results show that the proposed method not only improves retrieval accuracy significantly but also reduces the indexing time to almost none. We have open sourced our approach for the sake of comparison and reproducibility.

cs.IR↗

arXiv2021

A unified Neural Network Approach to E-CommerceRelevance Learning

Result relevance scoring is critical to e-commerce search user experience. Traditional information retrieval methods focus on keyword matching and hand-crafted or counting-based numeric features, with limited understanding of item semantic relevance. We describe a highly-scalable feed-forward neural model to provide relevance score for (query, item) pairs, using only user query and item title as features, and both user click feedback as well as limited human ratings as labels. Several general enhancements were applied to further optimize eval/test metrics, including Siamese pairwise architecture, random batch negative co-training, and point-wise fine-tuning. We found significant improvement over GBDT baseline as well as several off-the-shelf deep-learning baselines on an independently constructed ratings dataset. The GBDT model relies on 10 times more features. We also present metrics for select subset combinations of techniques mentioned above.

cs.IR↗