arXiv subjects

Huibo Xu

Publications and source records attributed to Huibo Xu.

6 recordsLinked to original sources

arXiv2026

Restricted Eigenvalues Beyond Gaussian Width: Threshold Occupancy under Heavy Tails

Restricted eigenvalue (RE) bounds govern stable recovery by norm-regularized estimators. For isotropic sub-Gaussian measurements, the benchmark sample size is $1+w(A)^2$, where $w(A)$ is the Gaussian width of the normalized descent cone. The COLT 2015 open-problem note (Banerjee et al., 2015) asked whether the same law follows for heavy-tailed designs from a uniform small-ball condition alone. We give an explicit and systematic negative answer to the general question as formulated there: the proposed law fails in its full dimension-free, arbitrary-set form, and the missing obstruction is simultaneous threshold occupancy. A constant-width polyhedral descent cone with fixed small-ball constants has zero empirical RE on every sample path up to half the ambient dimension. More generally, every finite range space admits exact threshold encoding in an arbitrarily narrow spherical cap and a lift to a full polyhedral descent-cone section. For every fixed threshold VC dimension $d$, as $\beta\downarrow0$, the sharp worst-case sample complexity is $\Theta(\beta^{-1}[d\log(1/\beta)+\log(1/\delta)])$. The separation persists under exact isotropy and all finite moments: on the same constant-width cone, Gaussian measurements succeed with $O(1+\log(1/\delta))$ samples, whereas an isotropic heavy-tailed design fails pathwise for $n\lesssim\sqrt{p/\log p}$. Gaussian smoothing yields an everywhere-positive $C^\infty$ density while retaining arbitrarily poor RE. Under isotropy, a distribution-free fallback governed by affine dimension times squared enclosing radius is sharp on this family.

cs.LG↗

arXiv2026

Synchronization Strings over the Optimal Alphabet

Synchronization strings provide deterministic position labels for recovering coordinates after insertions and deletions. Haeupler and Shahrasbi introduced these objects, and subsequent work proved that four symbols suffice for some fixed parameter epsilon < 1, whereas two symbols cannot support arbitrarily long synchronization strings. We resolve the remaining ternary case: every length admits a ternary 2001/2002-synchronization string. Thus three is the exact minimum constant alphabet size. A computer-assisted refinement based on a larger 54-uniform family yields ternary epsilon-synchronization strings for every epsilon > 215/216. The previous four-symbol construction uses a ternary square-free backbone to exclude short repetitions and a fourth symbol to carry long-range synchronization marks. Our main technical contribution is a local-entropy transfer theorem: every square-free block-local source with a positive interval conditional min-entropy rate supports synchronization strings with a fixed gap. We instantiate this theorem using occurrence-wise branching in a Brinkhuis family. Every outcome remains ternary and square-free, while every long interval retains linear conditional min-entropy after all choices outside it are exposed. A deletion-ball estimate converts this entropy into an exponentially small probability of a near-complete common subsequence between adjacent intervals, and an asymmetric Lovasz Local Lemma enforces all interval constraints simultaneously. The same framework also yields exponentially many valid words, synchronization circles, and synchronization within a class of extremal square-free words. Adding constraints on distant intervals gives a Las Vegas construction in expected O(n^2 log^3(n+2)) time.

cs.IT↗

arXiv2026

Feature Priming in Online Linear Regression: Sparse-Regret Lower Bounds and Tight Coordinatewise Rates

In high-dimensional online prediction, sparse comparators motivate regret bounds that depend on sparsity rather than ambient dimension. Feature priming seeks such adaptation by reweighting features using past data and refitting a minimum-norm predictor. At COLT 2023, Warmuth and Amid posed the open problem of whether the univariate, Pearson, or multivariate priming rules admit competitive online regret guarantees. Under the natural past-only Moore--Penrose protocol, we establish sparse-regret lower bounds that refute the corresponding sparse-logarithmic guarantee. The key obstruction is cheap nuisance interpolation, which permits exact interpolation of the history while assigning insufficient weight to the truly predictive coordinate. An exact target-mass identity and a two-sign argument convert this obstruction into clipped prediction loss. Hadamard constructions yield $\Omega(\min\{T,\sqrt d\})$ clipped regret for each of the three unit-power rules against a zero-loss one-sparse comparator. For every fixed power $\alpha\ge1$, one shared paired construction further yields linear regret simultaneously for all three powered rules and selectors among them in sufficiently high dimension. A rank upper bound is tight for powered univariate priming, even with Euclidean-unit inputs, and for unit-power Pearson priming with coordinatewise bounded inputs and target-preserving totalization. A separate algebraic construction gives $\Omega(\min\{T,d^{1/4}\})$ regret for unit-power multivariate priming under Euclidean-unit inputs. The univariate lower bound persists under any nonnegative second-stage ridge schedule, while a paired ridge construction yields linear lower bounds for all three powered rules. Exploratory diagnostics on frozen language-model activations are consistent with the same qualitative mechanism. The exact multivariate frontier remains open.

stat.ML↗

arXiv2025

From Entity Reliability to Clean Feedback: An Entity-Aware Denoising Framework Beyond Interaction-Level Signals

Implicit feedback is central to modern recommender systems but is inherently noisy, often impairing model training and degrading user experience. At scale, such noise can mislead learning processes, reducing both recommendation accuracy and platform value. Existing denoising strategies typically overlook the entity-specific nature of noise while introducing high computational costs and complex hyperparameter tuning. To address these challenges, we propose \textbf{EARD} (\textbf{E}ntity-\textbf{A}ware \textbf{R}eliability-\textbf{D}riven Denoising), a lightweight framework that shifts the focus from interaction-level signals to entity-level reliability. Motivated by the empirical observation that training loss correlates with noise, EARD quantifies user and item reliability via their average training losses as a proxy for reputation, and integrates these entity-level factors with interaction-level confidence. The framework is \textbf{model-agnostic}, \textbf{computationally efficient}, and requires \textbf{only two intuitive hyperparameters}. Extensive experiments across multiple datasets and backbone models demonstrate that EARD yields substantial improvements over state-of-the-art baselines (e.g., up to 27.01\% gain in NDCG@50), while incurring negligible additional computational cost. Comprehensive ablation studies and mechanism analyses further confirm EARD's robustness to hyperparameter choices and its practical scalability. These results highlight the importance of entity-aware reliability modeling for denoising implicit feedback and pave the way for more robust recommendation research.

cs.IR↗

arXiv2025

NeuTSFlow: Modeling Continuous Functions Behind Time Series Forecasting

Time series forecasting is a fundamental task with broad applications, yet conventional methods often treat data as discrete sequences, overlooking their origin as noisy samples of continuous processes. Crucially, discrete noisy observations cannot uniquely determine a continuous function; instead, they correspond to a family of plausible functions. Mathematically, time series can be viewed as noisy observations of a continuous function family governed by a shared probability measure. Thus, the forecasting task can be framed as learning the transition from the historical function family to the future function family. This reframing introduces two key challenges: (1) How can we leverage discrete historical and future observations to learn the relationships between their underlying continuous functions? (2) How can we model the transition path in function space from the historical function family to the future function family? To address these challenges, we propose NeuTSFlow, a novel framework that leverages Neural Operators to facilitate flow matching for learning path of measure between historical and future function families. By parameterizing the velocity field of the flow in infinite-dimensional function spaces, NeuTSFlow moves beyond traditional methods that focus on dependencies at discrete points, directly modeling function-level features instead. Experiments on diverse forecasting tasks demonstrate NeuTSFlow's superior accuracy and robustness, validating the effectiveness of the function-family perspective.

cs.LG↗

arXiv2025

Bridging the Last Mile of Prediction: Enhancing Time Series Forecasting with Conditional Guided Flow Matching

Existing generative models for time series forecasting often transform simple priors (typically Gaussian) into complex data distributions. However, their sampling initialization, independent of historical data, hinders the capture of temporal dependencies, limiting predictive accuracy. They also treat residuals merely as optimization targets, ignoring that residuals often exhibit meaningful patterns like systematic biases or nontrivial distributional structures. To address these, we propose Conditional Guided Flow Matching (CGFM), a novel model-agnostic framework that extends flow matching by integrating outputs from an auxiliary predictive model. This enables learning from the probabilistic structure of prediction residuals, leveraging the auxiliary model's prediction distribution as a source to reduce learning difficulty and refine forecasts. CGFM incorporates historical data as both conditions and guidance, uses two-sided conditional paths (with source and target conditioned on the same history), and employs affine paths to expand the path space, avoiding path crossing without complex mechanisms, preserving temporal consistency, and strengthening distribution alignment. Experiments across datasets and baselines show CGFM consistently outperforms state-of-the-art models, advancing forecasting.

cs.LG↗