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Applications · Language, Speech and Dialog

Sirui Chen, Yunzhe Qi, Mengting Ai, Yifan Sun, Ruizhong Qiu, Jiaru Zou, Jingrui He

Supervised fine-tuning (SFT) relies critically on selecting training data that most benefits model's downstream performance. Gradient-based data selection methods such as TracIn and Influence Functions leverage influence to identify useful samples, but their computational cost scales poorly, making them impractical for multi-billion-parameter large language models (LLMs). A common alternative is to use off-the-shelf smaller models as proxies, but they remain suboptimal since their learning dynamics are unclear, their sizes cannot be flexibly adjusted, and they cannot be further aligned with the target model in terms of gradient-based influence estimation. To address these challenges, we introduce IProX, a two-stage framework that derives influence-preserving proxies directly from the target model. It first applies a low-rank compression stage to preserve influence information of the target model, and then an aligning stage to align both model gradients and logits, thereby constructing proxies that flexibly control computational cost while retaining the target model’s influence. Experimental results across diverse LLM families and evaluation tasks show that IProX consistently outperforms off-the-shelf proxies and baseline methods. On Qwen3-4B, a 1.5B proxy constructed with IProX achieves stronger performance than the larger 1.7B off-the-shelf proxy. Notably, on Llama3.2, IProX achieves better performance than baselines while reducing computational cost by more than half relative to the full 3B model. These results show that IProX provides effective influence-preserving proxies, making gradient-based data selection more scalable for LLMs.

Applications · Language, Speech and Dialog

Kai Li, Kejun Gao, Xiaolin Hu

Audio-visual speech separation (AVSS) methods leverage visual cues to extract target speech and have demonstrated strong separation quality in noisy acoustic environments. However, these methods usually involve a large number of parameters and require high computational cost, which is unacceptable in many applications where speech separation serves as only a preprocessing step for further speech processing. To address this issue, we propose an efficient AVSS method, named **Dolphin**. For visual feature extraction, we develop **DP‑LipCoder**, a dual‑path lightweight video encoder that transforms lip‑motion into discrete audio‑aligned semantic tokens. For audio separation, we construct a lightweight encoder–decoder separator, in which each layer incorporates a global–local attention (GLA) block to efficiently capture multi-scale dependencies. Experiments on three benchmark datasets showed that Dolphin not only surpassed the current state-of-the-art (SOTA) model in separation quality but also achieved remarkable improvements in efficiency: over 50\% fewer parameters, more than 2.4$\times$ reduction in MACs, and over 6$\times$ faster GPU inference speed. These results indicate that Dolphin offers a practical and deployable solution for high-performance AVSS in real-world scenarios. Our code and demo page are publicly available at https://cslikai.cn/Dolphin.

Deep Learning · Algorithms

Zukang Xu, Zhixiong Zhao, Xing Hu, Zhixuan Chen, Dawei Yang

Mixture of Experts (MoE) models have achieved great success by significantly improving performance while maintaining computational efficiency through sparse expert activation. However, their enormous parameter sizes and memory demands pose significant challenges for deployment in resource-constrained environments. Vector Quantization (VQ) offers a promising approach for ultra-low-bit compression in Large Language Models (LLMs) by constructing and leveraging a codebook—where weight vectors are mapped to the most similar discrete codewords within the codebook. However, its direct application to MoEs suffers from significant performance degradation caused by two critical obstacles: (1) redundant representation among experts leads to VQ repeatedly quantizing similar representations for each expert, resulting in inefficient utilization of the limited codebook capacity; and (2) cumulative outputs bias, amplified by expert aggregation, leads to distributional shifts in the quantized outputs, resulting in degraded model accuracy. To this end, we propose KBVQ-MoE, a novel VQ framework to enhance extremely low-bit quantization for MoE-based LLMs. KBVQ-MoE introduces two lightweight and offline techniques that introduce negligible runtime computational and memory overhead: (1) Input-driven redundancy elimination, where a Karhunen–Loève Transform (KLT) guided singular value decomposition (SVD) extracts and shares dominant weight components across experts. (2) Bias-corrected output stabilization, where vector quantization is applied to expert-specific (i.e., non-redundant) representations and the quantized outputs are corrected with channel-wise affine compensation. Experiments on various MoE LLMs demonstrate that KBVQ-MoE preserves accuracy substantially better than existing quantization methods. For instance, 3-bit quantization of Qwen1.5-MoE-A2.7B achieves an average accuracy of 67.99, nearly identical to the FP16 baseline of 68.07, underscoring the potential of KBVQ-MoE for efficient deployment on edge devices and other resource-constrained platforms.

Applications · Language, Speech and Dialog

jia junlong, Ziyang Chen, Xing W, Chaochen Gao, Zijia Lin, Songlin Hu, Binghui Guo

Training long-context language models to capture long-range dependencies requires specialized data construction. Current approaches, such as generic text concatenation or heuristic-based variants, frequently fail to guarantee genuine long-range dependencies. We propose \textbf{EntropyLong}, a novel data construction method that leverages predictive uncertainty to verify dependency quality. Our approach identifies high-entropy positions in documents, retrieves semantically relevant contexts from large corpora, and verifies their utility by assessing whether they reduce prediction entropy. This \textit{model-in-the-loop verification} ensures each dependency represents measurable information gain rather than spurious correlation. We construct training samples with long-range dependencies by combining original documents with these verified contextual supplements. Using FineWeb-Edu and Cosmopedia, we generate a dataset of 128K-length sequences with verified dependencies. Models trained on this data demonstrate significant improvements on RULER benchmarks, particularly in tasks requiring distant information. Following instruction fine-tuning, our models also achieve substantial gains on LongBench-v2, demonstrating enhanced long-context understanding. Extensive ablation studies further validate the necessity and effectiveness of entropy-based verification for long-context training.

Deep Learning · Attention Mechanisms

Yehjin Shin, Seojin Kim, Noseong Park

State-space models (SSMs) offer efficient alternatives to attention with linear-time recurrence. Mamba2, a recent SSM-based language model, uses selective input gating and a multi-head structure, enabling parallel computation and strong benchmark performance. However, its multi-head recurrence operates independently without structured utilization or analysis. In this work, we propose a novel method called **H**ierarchical **AD**aptive filter bank for **E**fficient **S**SMs (*HADES*), a Graph Signal Processing (GSP)-inspired framework that reinterprets Mamba2 as an adaptive filter bank on a line graph. Our hierarchical architecture introduces two filter types: shared filters for global low-pass behavior and expert filters for local high-pass behavior, achieved through structured bias on the parameter $\Delta$. *HADES* achieves comparable performance to baseline models including Mamba2 across various benchmarks in language modeling, commonsense reasoning, and long-context retrieval, while using only **58.9%** of the original parameters. In this regard, *HADES* bridges GSP and neural sequence modeling, enabling efficient, hierarchical, and interpretable filtering within state-space models.

Deep Learning · Attention Mechanisms

Pavlo Vasylenko, Hugo Pitorro, Andre Martins, Marcos V Treviso

Transformer-based architectures traditionally employ softmax to compute attention weights, which produces dense distributions over all tokens in a sequence. While effective in many settings, this density has been shown to be detrimental for tasks that demand precise focus on fixed-size patterns: as sequence length increases, non-informative tokens accumulate attention probability mass, leading to dispersion and representational collapse. We show in this paper that dynamically sparse attention mechanisms using $\alpha$-entmax can avoid these issues, due to their ability to assign exact zeros to irrelevant tokens. Furthermore, we introduce Adaptive-Scalable Entmax (ASEntmax), which endows $\alpha$-entmax with a learnable temperature parameter, allowing the attention distribution to interpolate between sparse (pattern-focused) and dense (softmax-like) regimes. Our empirical evaluation on synthetic tasks and language modeling demonstrates that ASEntmax substantially outperforms softmax, scalable softmax, and fixed-temperature $\alpha$-entmax baselines, achieving up to 1000$\times$ length extrapolation on synthetic benchmarks and superior long-context generalization on language modeling while preserving short-context performance, including better perplexity trends and higher retrieval accuracies at 8$\times$ training length.

Computer Vision · Vision Models & Multimodal

Patrik Patera, Yie-Tarng Chen, Wen-Hsien Fang

Anticipating traffic accidents in real time is critical for intelligent transportation systems, yet remains challenging under edge-device constraints. We propose a lightweight spatio-temporal framework that introduces a temporally shifted distillation strategy, enabling a student model to acquire predictive temporal dynamics from a frozen image-based teacher without requiring a video pre-trained teacher. The student combines a RepMixer spatial encoding with a RWKV-inspired recurrent module for efficient long-range temporal reasoning. To enhance robustness under partial observability, we design a masking memory strategy that leverages memory retention to reconstruct missing visual tokens, effectively simulating occlusions and future events. In addition, multi-modal vision-language supervision enriches semantic grounding. Our framework achieves state-of-the-art performance on multiple real-world dashcam benchmarks while sustaining real-time inference on resource-limited platforms such as the NVIDIA Jetson Orin Nano. Remarkably, it is 3-7$\times$ smaller than leading approaches yet delivers superior accuracy and earlier anticipation, underscoring its practicality for deployment in intelligent vehicles.

General Machine Learning · Causality

Zhichu Lu, Hongyu Zhao, Shuo Sun, Hao Peng, Rui Ding, Hongyuan Mei

Reinforcement learning with verifiable rewards (RLVR) has emerged as a promising paradigm for post-training large language models (LLMs) on complex reasoning tasks. Yet, the conditions under which RLVR yields robust generalization remain underexplored. This paper provides an empirical study of RLVR generalization in the setting of probabilistic inference over causal graphical models. This setting offers two natural axes along which to examine generalization: (i) the level of the probabilistic query---associational, interventional, or counterfactual---and (ii) the structural complexity of the query, measured by the size of its relevant subgraph. We construct a dataset of causal graphs and queries spanning these difficulty axes and fine-tune Qwen-2.5-Instruct models using RLVR or supervised fine-tuning (SFT). We vary both the model scale (3B-32B) and the query level included in training. We find that RLVR yields stronger within-level and across-level generalization than SFT, but only for specific combinations of model size and training query level. Further analysis shows that RLVR's effectiveness depends on the model's initial reasoning competence. With sufficient initial competence, RLVR improves an LLM's marginalization strategy and reduces errors in intermediate probability calculations, producing substantial accuracy gains, particularly on more complex queries. These results show that RLVR can improve specific causal reasoning subskills, with its benefits emerging only when the model has sufficient initial competence. Our code and data is available at https://github.com/zhichul/rlcausal.

Reinforcement Learning · Deep RL

Siyuan Lu, Zechuan Wang, Hongxuan Zhang, Qintong Wu, Leilei Gan, Chenyi Zhuang, Jinjie Gu, Tao Lin

Large Language Model (LLM) agents show great promise for complex multi-turn tool-use tasks, but their development is often hampered by the extreme scarcity of high-quality training data. Supervised fine-tuning (SFT) on synthetic data leads to overfitting, whereas standard reinforcement learning (RL) struggles with a critical cold-start problem and training instability. To address these challenges, we introduce $\textbf{Environment Tuning}$, a novel training paradigm that enables agents to learn complex behaviors directly from problem instances without relying on pre-collected expert trajectories. $\textbf{Environment Tuning}$ orchestrates this learning process through a structured curriculum, actionable environment augmentation that provides corrective feedback, and fine-grained progress rewards to ensure stable and efficient exploration. Using only 400 problem instances from Berkeley Function-Calling Leaderboard (BFCL) benchmark, our method not only achieves competitive in-distribution performance against strong baselines but also demonstrates superior out-of-distribution generalization, overcoming the performance collapse common to SFT-based approaches. Our work presents a paradigm shift from supervised fine-tuning on static trajectories to dynamic, environment-based exploration, paving the way for training more robust and data-efficient agents.

Applications · Language, Speech and Dialog

Chenxi Whitehouse, Sebastian Ruder, Tony Lin, Oksana Kurylo, Haruka Takagi, Janice Lam, Nicolò Busetto, Denise Diaz

Ensuring native-like quality of large language model (LLM) responses across many languages is challenging. To address this, we introduce MENLO, a framework that operationalizes the evaluation of native-like response quality based on audience design-inspired mechanisms. Using MENLO, we create a dataset of 6,423 human-annotated prompt–response preference pairs covering four quality dimensions with high inter-annotator agreement in 47 language varieties. Our evaluation reveals that zero-shot LLM judges benefit significantly from pairwise evaluation and our structured annotation rubrics, yet they still underperform human annotators on our dataset. We demonstrate substantial improvements through fine-tuning with reinforcement learning, reward shaping, and multi-task learning approaches. Additionally, we show that RL-trained judges can serve as generative reward models to enhance LLMs' multilingual proficiency, though discrepancies with human judgment remain. Our findings suggest promising directions for scalable multilingual evaluation and preference alignment. We release our dataset and evaluation framework to support further research in multilingual LLM evaluation (https://huggingface.co/datasets/facebook/menlo).

Computer Vision · Image and Video Generation

Aritra Bhowmik, Denis Korzhenkov, Cees G Snoek, Amirhossein Habibian, Mohsen Ghafoorian

Text-to-video diffusion models have enabled high-quality video synthesis, yet often fail to generate temporally coherent and physically plausible motion. A key reason is the models' insufficient understanding of complex motions that natural videos often entail. Recent works tackle this problem by aligning diffusion model features with those from pretrained video encoders. However, these encoders mix video appearance and dynamics into entangled features, limiting the benefit of such alignment. In this paper, we propose a motion-centric alignment framework that learns a disentangled motion subspace from a pretrained video encoder. This subspace is optimized to predict ground-truth optical flow, ensuring it captures true motion dynamics. We then align the latent features of a text-to-video diffusion model to this new subspace, enabling the generative model to internalize motion knowledge and generate more plausible videos. Our method improves the physical commonsense in a state-of-the-art video diffusion model, while preserving adherence to textual prompts, as evidenced by empirical evaluations on VideoPhy, VideoPhy2, VBench, and VBench-2.0, along with a user study.

Reinforcement Learning · Deep RL

Itamar Rocha Filho, Rosie Zhao, Sham Kakade, Eran Malach, Samy Jelassi

Reinforcement Learning with Verifiable Rewards (RLVR) is a leading approach for tuning language models on mathematical reasoning tasks. However, it remains unclear whether RLVR's gains stem from genuine reasoning improvements or simply from steering the model toward answer formats that already appear in the reference distribution. Inspired by recent evidence \citep{zhao2025echo,yue2025does}, we study this question by optimizing only the first $k$ tokens (e.g. $k=32$) of each solution, generating the remainder of the response from the reference model. We study two methods for prefix optimization, using a naive algorithm that clusters prefixes and selects the best prefix (Prefix Clustering), and a method that optimizes the prefix by finetuning a lightweight adapter model with RL (Prefix-RL). We show that tuning only the first $k$ tokens can significantly improve the accuracy on math, suggesting that at least some of the gains from RL are due to upweighting a preferable solution strategy. Our results suggest that simple prefix optimization methods can provide an efficient alternative to RL, delivering substantial improvements across different models and benchmarks for a tiny fraction of the compute required for standard RL, and that these gains are robust across prefix lengths and random seeds.

Deep Learning · Generative Models and Autoencoders

Animesh Karnewar, Denis Korzhenkov, Ioannis Lelekas, Noor Fathima, Adil Karjauv, Mohsen Ghafoorian, Amirhossein Habibian

We propose Neodragon, a video DiT (Diffusion Transformer) designed to run on a low-power NPU present in devices such as phones and laptop computers. We demonstrate that, despite video transformers' huge memory and compute cost, mobile devices can run these models when carefully optimised for efficiency. To achieve this level of efficiency, i) we replace the original large Text-Encoder with a much smaller one with minimal quality loss through our novel distillation framework which doesn’t require any image or video data. ii) We propose an Asymmetric Decoder distillation approach which allows us to replace the native codec-latent-VAE decoder with a more efficient one, without disturbing the generative latent-space of the video generation pipeline. iii) With our Block Pruning strategy, we remove entire blocks from the MMDiT denoiser based on their relative importance and recover original performance through a two-stage distillation process. iv) We reduce the diffusion sampling cost using our novel extended version of DMD (Distribution Matching Distillation) for the Pyramidal Flow-Matching objective. Neodragon generates 49 frames of [640$\times$1024] resolution within 6.7 seconds on the Qualcomm Hexagon NPU with a VBench total score of 81.61, setting a new state-of-the-art for mobile video generation.

Tyler Farghly, Patrick Rebeschini, George Deligiannidis, Arnaud Doucet

The success of denoising diffusion models raises important questions regarding their generalisation behaviour, particularly in high-dimensional settings. Notably, it has been shown that when training and sampling are performed perfectly, these models memorise training data—implying that some form of regularisation is essential for generalisation. Existing theoretical analyses primarily rely on algorithm-independent techniques such as uniform convergence, heavily utilising model structure to obtain generalisation bounds. In this work, we instead leverage the algorithmic aspects that promote generalisation in diffusion models, developing a general theory of algorithm-dependent generalisation for this setting. Borrowing from the framework of algorithmic stability, we introduce the notion of score stability, which quantifies the sensitivity of score-matching algorithms to dataset perturbations. We derive generalisation bounds in terms of score stability, and apply our framework to several fundamental learning settings, identifying sources of regularisation. In particular, we consider denoising score matching with early stopping (denoising regularisation), sampler-wide coarse discretisation (sampler regularisation), and optimising with SGD (optimisation regularisation). By grounding our analysis in algorithmic properties rather than model structure, we identify multiple sources of implicit regularisation unique to diffusion models that have so far been overlooked in the literature.

Social Aspects · Trustworthy Machine Learning

Sarah Ball, Greg Gluch, Shafi Goldwasser, Frauke Kreuter, Omer Reingold, Guy Rothblum

With the increased deployment of large language models (LLMs), one concern is their potential misuse for generating harmful content. Our work studies the alignment challenge, with a focus on filters to prevent the generation of unsafe information. Two natural points of intervention are the filtering of the input prompt before it reaches the model, and filtering the output after generation. Our main results demonstrate computational challenges in filtering both prompts and outputs. First, we show that there exist LLMs for which there are no efficient input-prompt filters: adversarial prompts that elicit harmful behavior can be easily constructed, which are computationally indistinguishable from benign prompts for any efficient filter. Our second main result identifies a natural setting in which output filtering is computationally intractable. All of our separation results are under cryptographic hardness assumptions. In addition to these core findings, we also formalize and study relaxed mitigation approaches, demonstrating further computational barriers. We conclude that safety cannot be achieved by designing filters external to the LLM internals (architecture and weights); in particular, black-box access to the LLM will not suffice. Based on our technical results, we argue that an aligned AI system’s intelligence cannot be separated from its judgment.

Theory · Interpretability and Visualization

Joshua Melander, Zaki Alaoui, Shenghua Liu, Surya Ganguli, Stephen Baccus

Understanding how neural networks transform inputs into outputs is crucial for interpreting and manipulating their behavior. Most existing approaches analyze internal representations by identifying hidden-layer activation patterns correlated with human-interpretable concepts. Here we take a direct approach to examine how hidden neurons act to drive network outputs. We introduce CODEC ($\textbf{Co}$ntribution $\textbf{Dec}$omposition), a method that uses sparse autoencoders to decompose network behavior into sparse motifs of hidden-neuron contributions, revealing causal processes that cannot be determined by analyzing activations alone. Applying CODEC to benchmark image-classification networks, we find that contributions grow in sparsity and dimensionality across layers and, unexpectedly, that they progressively decorrelate positive and negative effects on network outputs. We further show that decomposing contributions into sparse modes enables greater control and interpretation of intermediate layers, supporting both causal manipulations of network output and human-interpretable visualizations of distinct image components that combine to drive that output. Finally, by analyzing state-of-the-art models of neural activity in the vertebrate retina, we demonstrate that CODEC uncovers combinatorial actions of model interneurons and identifies the sources of dynamic receptive fields. Overall, CODEC provides a rich and interpretable framework for understanding how nonlinear computations evolve across hierarchical layers, establishing contribution modes as an informative unit of analysis for mechanistic insights into artificial neural networks.

Social Aspects · Fairness, Equity, Justice and Safety

Elinor Poole-Dayan, Jiayi Wu, Taylor Sorensen, Jiaxin Pei, Michiel Bakker

We introduce OVERTONBENCH, a novel framework for measuring Overton pluralism in LLMs—the extent to which diverse viewpoints are represented in model outputs. We (i) formalize Overton pluralism as a set coverage metric (OVERTONSCORE), (ii) conduct a large-scale U.S.-representative human study (N = 1208; 60 questions; 8 LLMs), and (iii) develop an automated benchmark that closely reproduces human judgments. On average, models achieve OVERTONSCOREs of 0.35–0.41, with DeepSeek V3 performing best; yet all models remain far below the theoretical maximum of 1.0, revealing substantial headroom for improvement. Because repeated large-scale human studies are costly and slow, scalable evaluation tools are essential for model development. Hence, we propose an automated benchmark that achieves high rank correlation with human judgments ($\rho = 0.88$), providing a practical proxy without replacing human assessment. By turning pluralistic alignment from a normative aim into a measurable benchmark, our work establishes a foundation for systematic progress toward more pluralistic LLMs.

Applications · Everything Else

Zhe Wu, Donglin Mo, Hongjin Lu, Junliang Xing, Jianheng Liu, Yuheng Jing, Kai Li, Kun Shao, Jianye Hao, Yuanchun Shi

Existing mobile device control agents often perform poorly when solving complex tasks requiring long-horizon planning and precise operations, typically due to a lack of relevant task experience or unfamiliarity with skill execution. We propose $\textbf{K²-Agent}$, a hierarchical framework that models human-like cognition by separating and co-evolving declarative ("knowing what") and procedural ("knowing how") knowledge for planning and execution. K²-Agent’s high level reasoner is bootstrapped from a single demonstration per task and runs a Summarize–Reflect–Locate–Revise (SRLR) loop to distill and iteratively refine task-level declarative knowledge through self-evolution. The low-level executor is trained with our curriculum-guided Group Relative Policy Optimization (C-GRPO), which (i) constructs a balanced sample pool using decoupled reward signals and (ii) employs dynamic demonstration injection to guide the model in autonomously generating successful trajectories for training. On the challenging AndroidWorld benchmark, K$^2$-Agent achieves a new $\textbf{state of the art}$ with $\textbf{76.1\% success rate}$, ranking $\textbf{1st}$ among all methods $\textbf{using only raw screenshots and open-source backbones}$. Furthermore, K²-Agent shows powerful dual generalization: its high-level declarative knowledge transfers across diverse base models, while its low-level procedural skills achieve competitive performance on unseen tasks in ScreenSpot-v2 and Android-in-the-Wild (AitW).

Ziqing Fan, Yuqiao Xian, Yan Sun, Ke Shen, Li Shen

A fine-grained data recipe is crucial for pre-training large language models (LLMs), as it can significantly enhance training efficiency and model performance. One important ingredient in the recipe is to select samples based on scores produced by defined rules, LLM judgment, or statistical information in embeddings, which can be roughly categorized into quality and diversity metrics. Due to the high computational cost when applied to trillion-scale token pre-training datasets such as FineWeb and DCLM, these two or more types of metrics are rarely considered jointly in a single selection process. However, in our empirical study, selecting samples based on quality metrics exhibit severe diminishing returns during long-term pre-training, while selecting on diversity metrics removes too many valuable high-quality samples, both of which limit pre-trained LLMs' capabilities. Therefore, we introduce DATAMASK, a novel and efficient joint learning framework designed for large-scale pre-training data selection that can simultaneously optimize multiple types of metrics in a unified process, with this study focusing specifically on quality and diversity metrics. DATAMASK approaches the selection process as a mask learning problem, involving iterative sampling of data masks, computation of policy gradients based on predefined objectives with sampled masks, and updating of mask sampling logits. Through policy gradient-based optimization and various acceleration enhancements, it significantly reduces selection time by 98.9% compared to greedy algorithm, enabling our study to explore joint learning within trillion-scale tokens. With DATAMASK, we select a subset of about 10% from the 15 trillion-token FineWeb dataset, termed FineWeb-Mask. Evaluated across 12 diverse tasks, this high-quality and diverse subset achieves significant improvements of 3.2% on a 1.5B dense model and 1.9% on a 7B MoE model after pre-training with hundreds of billions of tokens, demonstrating its effectiveness. Source code is available at: https://github.com/ByteDance-Seed/DATAMASK.

Social Aspects · Privacy-preserving Statistics and Machine Learning

Yan Sun, Qixin ZHANG, Li Shen, Dacheng Tao

The powerful cooperation of federated learning (FL) and differential privacy (DP) provides a promising paradigm for the large-scale private clients. However, existing analyses in FL-DP mostly rely on the composition theorem and cannot tightly quantify the privacy leakage challenges, which is tight for a few communication rounds but yields an arbitrarily loose and divergent bound eventually. This also implies a counterintuitive judgment, suggesting that FL-DP may not provide adequate privacy support during long-term training under constant-level noisy perturbations, yielding discrepancy between the theoretical and experimental results. To further investigate the convergent privacy and reliability of the FL-DP framework, in this paper, we comprehensively evaluate the worst privacy of two classical methods under the non-convex and smooth objectives based on the $f$-DP analysis. With the aid of the shifted interpolation technique, we successfully prove that privacy in Noisy-FedAvg has a tight convergent bound. Moreover, with the regularization of the proxy term, privacy in Noisy-FedProx has a stable constant lower bound. Our analysis further demonstrates a solid theoretical foundation for the reliability of privacy in FL-DP. Meanwhile, our conclusions can also be losslessly converted to other classical DP analytical frameworks, e.g. $(\epsilon,\delta)$-DP and R$\'{e}$nyi-DP (RDP), to provide more fine-grained understandings for the FL-DP frameworks.