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Ziwei Hong

Publications and source records attributed to Ziwei Hong.

13 recordsLinked to original sources

A secondary term in the first moment of primitive cubic Dirichlet L-functions

P. Gao and L. Zhao obtained an asymptotic formula for the smoothed first moment of primitive cubic Dirichlet $L$-functions over $Q$ with conductors coprime to $3$, with a main term of order $Q$ and error \(O\left(Q^{\frac{7}{8}+\eps}\right)\) under the generalized Lindelöf hypothesis. Building on their double Dirichlet series, we assume the generalized Riemann hypothesis and separate an explicit secondary term of order $Q^{\frac{5}{6}}$, with error $O\left(Q^{\frac{23}{28}+\eps}\right)$.

math.NT↗

Improved first moments of primitive quartic and sextic Dirichlet $L$-functions

We study the smoothed first moments of primitive quartic and sextic Dirichlet $L$-functions for which every nontrivial power of the character remains primitive. Assuming the generalized Riemann hypothesis for the Dirichlet and finite order Hecke $L$-functions occurring in the proof, we obtain asymptotic formulas with errors $O(Q^{\frac{49}{58}+\eps})$ and $O(Q^{\frac{23}{26}+\eps})$, respectively. We follow the double Dirichlet series approach of Gao and Zhao. The main ingredient is a joint estimate for the two sums arising from the removal of rational prime divisors, with the Möbius coefficients retained. This gives a quotient of Dirichlet $L$-functions. Under GRH, we bound both the Dirichlet $L$-functions and their reciprocals. Combining the joint estimate with estimates for the generating series of Gauss sums gives larger regions of meromorphic continuation. These regions do not separate the possible secondary terms.

math.NT↗

The first moment of primitive quartic \(L\)-functions with a secondary term

Let $q\equiv3\pmod4$ be a fixed odd prime power. We study the first moment of central values of primitive quartic Dirichlet $L$-functions over $\F_q[T]$, with fixed genus $g$ and with $χ^2$ primitive. We obtain a main term $C_q q^{2g/3}$ and a secondary term $(α_r g+β_r)q^{g/2}$, with error $O_{q,\eps}(q^{(16/33+\eps)g})$, where $r\equiv g/3+1\pmod4$. The constants are explicit, with $C_q>0$ and $α_r<0$ for every $r$. We use a double Dirichlet series and the functional equation of the quartic Gauss sum generating series to compute the residues and obtain the continuation needed to separate both terms.

math.NT↗

Non-vanishing of primitive cubic, quartic and sextic L-functions

We establish lower bounds for the non-vanishing proportions of primitive cubic, quartic and sextic Dirichlet $L$-functions over $\F_q[T]$ in the non-Kummer setting. Adapting truncated-exponential techniques for shifted moments, we improve the cubic lower bound of David, Florea and Lalín and obtain positive lower bounds for quartic and sextic families. For each family, the lower limit of the non-vanishing proportion exceeds $e^{-e^{53}}$ as the conductor degree tends to infinity with $q$ fixed. We use a common choice of truncation parameters and explicitly control the exceptional sets. The cubic argument uses the published twisted first moment. We also establish uniform twisted first moments in the quartic and sextic cases, yielding an asymptotic formula for the sextic first moment.

math.NT↗

A secondary term in the first moment of cubic $L$-functions over function fields

Let $q$ be a fixed odd prime power with $q\equiv2\pmod3$. We study the first moment of primitive cubic Dirichlet $L$-functions over $\Fq(T)$, ordered by their genus. By averaging the rational sieve variable in the double Dirichlet series of Hong and Fang, we obtain meromorphic continuation beyond the secondary polar divisor. Combining this continuation with the cubic Gauss-sum residues computed by David, Florea and Lalín gives an explicit term of order $q^{5g/6}$, with a real coefficient depending on $g$ modulo $6$, and an error $O_{q,\eps}(q^{(23/28+\eps)g})$. The periodic coefficient is not identically zero. The proof uses an exact first difference supplied by the functional equation, an Euler product for the sieve average, and Bochner's tube theorem in the Dirichlet variables.

math.NT↗

The first moment of central value of primitive quartic $L$-functions with fixed genus

We investigate the mean value of the first moment of primitive quartic $L$-functions over $\mathbb{F}_q(T)$ in the non-Kummer setting. Specifically, we study the sum \begin{equation*} \sum_{\substack{χ primitive\ quartic\\ χ^2 primitive\\ genus(χ)=g}}L_q(\frac{1}{2}, χ), \end{equation*} where $L_q(s,χ)$ denotes the $L$-function associated with primitive quartic character $χ$. Using double Dirichlet series, we derive an error term of size $q^{(\frac{3}{5}+\varepsilon)g}$.

math.NT↗

An Explicit Feedback Contract for Iterative ML-Agent Harnesses

Iterative ML agents develop models by editing code, running experiments, reading a validation score, and choosing what to try next. In current harnesses this loop is served by an exact validation score returned after every attempt, which leaves the validation split open to adaptive selection. In this work, we introduce an explicit feedback contract for ML-agent harnesses, which specifies what an agent may observe, when iteration should stop, and when the test split may be touched. The contract releases a validation score only when a submission clears a noise threshold computed from the paired standard error, so no margin has to be tuned. We ran experiments on click-through-rate prediction, learning to rank, and a control task with no signal to find. The control is the sharpest case, because the true gain there is zero by construction: an agent reading exact scores ended by reporting a gain of 0.0157, while under the contract it reported 0.0033. On both real tasks the contract narrows the validation-test gap, and test performance is slightly higher rather than lower. The largest difference is in when the agents stop. Exact feedback used its entire budget of thirty submissions on two of the three tasks, including the one where nothing can be learned, while the contract halted after four to twelve. A run that exhausts its budget is usually read as diligence. It is better read as a symptom: when the feedback channel is unbounded, noise keeps supplying improvements to chase.

cs.LG↗

Conditional Rank Allocation for Taxonomy-Aware Medical Language Model Adaptation

Medical question answering spans specialties and clinical operations that may benefit from different adaptation directions. We propose ARBOR, a parameter-efficient method that selects rank-one components from a shared low-rank basis for each question. An additive gate combines question representations, specialty tags, operation tags, and their interaction; a learned coefficient scales the adapter residual. An illustrative separation under orthogonal, equiprobable subtasks shows how conditional selection can avoid an approximation floor faced by a fixed update with the same active rank. This result motivates the design without asserting a corresponding bound for medical corpora. On Qwen3-8B across CMB, CMExam, MedQA, and MedMCQA, five-seed experiments yield 69.69% mean accuracy across benchmarks, exceeding LoRA r16 and MoELoRA by 1.26 and 1.30 percentage points, respectively. The reported advantage over LoRA r16 increases from 0.08 to 1.94 points as training expands from one to seven specialties. Tag perturbations and atom masking support the usefulness of clinical routing, while atom clusters align with the supplied specialty labels (adjusted Rand index 0.62). Calibration, transfer, and measured costs further characterize the method. These findings support structured conditional adaptation for medical QA, while leaving clinical safety and broader deployment untested.

cs.AI↗

GAUDI: Geometry-Aware Diffusion for Calibrated Air-Quality Time-Series Imputation

Air-quality sensor outages often create contiguous missing blocks, where side information useful for isolated missingness may be less reliable. We study a block-specific, GAUDI-aligned conditional diffusion imputer that retains temporal and feature processing, visible-value and mask conditioning, variable identity, and diffusion-step information, while suppressing absolute time-position side embeddings. On ItalyAir (13 variables, length-32 windows, nominal 50% block missingness; three archived seeds), this feature-side configuration achieves RMSE 0.340, versus 0.355 for full context and 0.355 for local CSDI. The experiment isolates a geometry-aware conditioning effect under block missingness.

cs.LG↗

Dynamic Interaction-Aware and Causality-Disentangled Framework for Multimodal Sentiment Analysis

Although Multimodal Sentiment Analysis (MSA) effectively leverages rich information from language, visual, and acoustic modalities, existing methods still face two core challenges: 1) static conflict suppression mechanisms fail to adapt to dynamic variations across samples, and 2) the inherent sentimental bias within the language modality, which can misguide learning from other modalities, remains entangled. To this end, we propose a Dynamic Multimodal Causal Disentanglement and Adaptive Fusion Framework (MCAF). Its cornerstone is the Multi-Granularity Causal Dynamic Router and a Conditional Diffusion Denoising Module. First, we introduce a causal intervention module based on the information bottleneck principle, which builds a Structural Causal Model to disentangle sentimental bias from language features, yielding a "de-confounded" language representation as a pure guiding signal. Second, we devise a Dynamic Multimodal Router that evaluates the interaction states (complementary, conflicting, or redundant) among visual, acoustic, and de-confounded language signals in real-time across three levels: feature, temporal, and modality, then adaptively allocates weights and routes information flow for fine-grained regulation. Finally, a lightweight Conditional Diffusion Denoising Module performs iterative denoising on the fused joint representation to explicitly filter out residual irrelevant information, generating a robust hyper-modality representation. Extensive experiments on the CMU-MOSI and CMU-MOSEI benchmarks show that MCAF sets new state-of-the-art on key classification metrics, achieving an Acc-2/F1 of 86.52%/86.51% on MOSI and 86.72%/86.65% on MOSEI, while remaining highly competitive on others. Comprehensive analyses and visualizations further validate its efficacy in dynamically perceiving interactions, disentangling bias, and enhancing interpretability.

cs.MM↗

Chain-Aware Encoding for Microservice Trace Anomaly Detection

Microservice traces can be structurally anomalous even when every span returns normally -- a payment flow that silently skips a risk check looks fine to any per-span monitor. Sequence models like DeepLog address this by predicting the next event, but they treat each API endpoint as a context-free token: the same endpoint reached through different invocation chains is mapped to the same vocabulary entry, even when its normal behavior differs across contexts. We propose encoding each event as an (endpoint, root-to-span invocation chain) pair instead. This simple change has two consequences: unseen chains are flagged without model inference, and next-event predictions become context-conditional, turning subtle path anomalies into clear outliers. We instantiate this idea in CHAINLSTM, a lightweight dual-task LSTM supporting per-event online detection. On the TrainTicket benchmark, CHAINLSTM achieves 94.3% F1 (+5.3 pp over DeepLog) with comparable latency recall and 99.1\% path recall. Case analysis shows that chain-aware encoding shifts median prediction probability on path anomalies from 0.91 to 0.002, suggesting a wider separation margin for threshold-based detection.

cs.SE↗

CenterMamba-SAM: Center-Prioritized Scanning and Temporal Prototypes for Brain Lesion Segmentation

Brain lesion segmentation remains challenging due to small, low-contrast lesions, anisotropic sampling, and cross-slice discontinuities. We propose CenterMamba-SAM, an end-to-end framework that freezes a pretrained backbone and trains only lightweight adapters for efficient fine-tuning. At its core is the CenterMamba encoder, which employs a novel 3x3 corner-axis-center short-sequence scanning strategy to enable center-prioritized, axis-reinforced, and diagonally compensated information aggregation. This design enhances sensitivity to weak boundaries and tiny foci while maintaining sparse yet effective feature representation. A memory-driven structural prompt generator maintains a prototype bank across neighboring slices, enabling automatic synthesis of reliable prompts without user interaction, thereby improving inter-slice coherence. The memory-augmented multi-scale decoder integrates memory attention modules at multiple levels, combining deep supervision with progressive refinement to restore fine details while preserving global consistency. Extensive experiments on public benchmarks demonstrate that CenterMamba-SAM achieves state-of-the-art performance in brain lesion segmentation.

cs.CV↗

Mean value of cubic $L$-funcitons with fixed genus

We investigate the mean value of the first moment of primitive cubic $L$-functions over $\mathbb{F}_q(T)$ in the non-Kummer setting. Specifically, we study the sum \begin{equation*} \sum_{\substack{χ primitive\ cubic\\ genus(χ)=g}}L_q(\frac{1}{2}, χ), \end{equation*} where $L_q(s,χ)$ denotes the $L$-function associated with primitive cubic character $χ$. Using double Dirichlet series, we derive an error term of size $q^{(\frac{7}{8}+\varepsilon)g}$.

math.NT↗