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arXiv

On the Role of Directionality in Structural Generalization

Zichao Wei

Several SLOG test categories explicitly involve directional distinctions (modifier position shifts, argument extraction positions), yet AM-Parser, the previous SOTA, uses an AM algebra whose operations do not encode direction. We redesign the symbolic backend around CCG directed types (deterministic CKY + single linear decoder, 30K learnable parameters). Under the same BERT-base encoder, the system achieves 75.9$\pm$6.4% LF exact match, surpassing AM-Parser (70.8$\pm$4.3%). Per SLOG's own category groupings, gains are highly directional: the CCG system outperforms AM-Parser on all 5 position-shift categories (+29.9pp), while AM-Parser outperforms on all 6 recursive-depth categories. Replacing the encoder with DeBERTa-v3-large yields 90.7$\pm$4.9%, with the largest encoder gains in recursive-depth categories, complementary to directionality's gains. Directional representations shift the bottleneck from the symbolic layer (AM-Parser's 0% category ceiling) to the neural layer, which improves with encoder upgrades.

arXiv

SocialCoach: Personalized Social Skill Learning with Agentic Tutoring and Practice

Tianfu Wang, Max Xiong, Jianxun Lian, Hongyuan Zhu, Zhengyu Hu, Yuxuan Lei, Linxiao Gong, Dapeng Hu, Xiaofang Li, Peiting Tsai, Nicholas Jing Yuan, Qi Zhang

Social skills such as negotiation and leadership are crucial for personal and professional success in today's interconnected world. However, scalable and effective training remains a significant challenge due to the scarcity of expert coaching. In this work, we introduce SocialCoach, an LLM-powered agentic tutoring system for personalized social skill learning. SocialCoach constructs a theory-to-practice corpus of traceable strategies, cases, and practice scenarios, and uses this corpus for both scheduling and reflective tutoring. We formulate social practice personalization as cold-start, retrieval-constrained sequential practice scheduling. Given a learner profile, simulated proficiency state, and observed practice history, a policy produces structured prescriptions that are realized through corpus retrieval. To enhance scheduling effectiveness, we optimize complete pathways with trajectory-level GRPO using rubric-judge based pairwise preferences. Additionally, we instantiate the scheduling approach in a deployed platform with goal-driven practice and knowledge-grounded reflective tutoring. Finally, in the synthetic cold-start setting, experiment results show that SocialCoach achieves higher pathway-quality ratings than baselines in scheduling and tutoring quality. We also conduct human studies to demonstrate its usefulness for real-world social skill learning.

arXiv

Language Models Compare Quantities Using Number-specific and Unit-specific Heuristics

Mutsumi Sasaki, Go Kamoda, Ryosuke Takahashi, Kosuke Sato, Kentaro Inui, Keisuke Sakaguchi, Benjamin Heinzerling

Quantities with measurement units, such as 110 cm and 1.2 m, require language models (LMs) to combine a numeral with a symbolic unit scale. Here, we study how LMs compare such quantities in controlled settings spanning several unit systems. We find that accuracy degrades near the comparison boundary, where small changes in value determine the correct answer. The resulting errors are systematic: linear surrogate models predict LM preferences from numerical-difference and unit-scale-difference cues, and causal interventions on subspaces aligned with these variables shift model's output. The results suggest that LMs compare quantities through a bag of heuristics over numerals and units, rather than first converting both expressions to an exact shared-scale representation.

arXiv

Single-Round Vector RAG vs an LLM-Compiled Wiki: A Preregistered Comparison on a Small Multi-Domain Research Corpus

Theodore O. Cochran

We preregistered a comparison of two ways to help an LLM answer questions over a small research corpus: a single-round Vector RAG system and an LLM-compiled markdown wiki browsed by a tool-using agent. Both systems answered the same 13 questions over 24 papers using the same answer-generating model, and their answers were scored by two blinded LLM judges. The three preregistered predictions, in registered order, came out one weakly supported, one supported, and one refuted. The wiki was predicted to synthesize better across papers; it scored much better at connecting findings, but its organization advantage fell below the registered threshold once both judges' scores were combined. RAG was predicted to hold its own on single-fact lookup, and it met the registered test, though the second judge alone would have refuted it. The wiki was predicted to be expensive to build and cheap to query; the build side held by roughly two orders of magnitude, but the query side reversed: the wiki spent about 21 times more tokens per query, so no break-even point exists. Two exploratory analyses explain the disagreement. A decomposition-retrieval variant of RAG removes almost all of the wiki's synthesis advantage at lower token cost, though not its advantage in claim-by-claim citation support. Holistic groundedness scoring disagrees with atomized citation checking by direction, and between judges: rank agreement on that criterion is near zero (rho = 0.04), against rho = 0.81 on the most concretely defined criterion. Grounded research synthesis is therefore not a single capability: systems differ in how well they organize evidence, how well their citations support each claim, and what they cost to run, and no architecture here was best on all three. Which one appears to win depends on the retrieval baseline, the scoring granularity, and the judge.

arXiv

Structural Generalization on SLOG without Hand-Written Rules

Zichao Wei

Structural generalization in semantic parsing requires systems to apply learned compositional rules to novel structural combinations. Existing approaches either rely on hand-written algebraic rules (AM-Parser) or fail to generalize structurally (Transformer-based models). We present an alternative requiring no hand-written compositional rules, based on a neural cellular automaton (NCA) with a discrete bottleneck: all compositional rules are learned from data through local iteration. On the SLOG benchmark, the system achieves an overall accuracy of $67.3 \pm 0.2\%$ across 10 seeds (AM-Parser: $70.8 \pm 4.3\%$), with 11 of 17 structural generalization categories at $100\%$ type-exact match, including three where AM-Parser scores $0$--$74\%$. Analysis reveals that all 5,539 failure instances reduce to exactly two mechanisms: novel combinations of wh-extraction context with reduced verb types, and modifiers appearing on the subject side of verbs. When we decompose results by CCG structural features, each sub-pattern either succeeds on all instances or fails on all. Intermediate scores (e.g., $41.4\%$) are mixtures of structurally distinct CCG patterns, not partial generalization. These results suggest that CCG directed types provide higher resolution than SLOG's phenomenon-level categories for characterizing structural generalization, and that the success/failure boundary is determined by the coverage of directed operations in the training data.

arXiv

Subliminal Steering: Stronger Encoding of Hidden Signals

George Morgulis, John Hewitt

Subliminal learning describes a student language model inheriting a behavioral bias by fine-tuning on seemingly innocuous data generated by a biased teacher model. Prior work has begun to characterize this phenomenon but leaves open questions about the scope of signals it can transfer, the mechanisms that explain it, and the precision with which a bias can be encoded. We tackle these problems by introducing subliminal steering, a variant of subliminal learning in which the teacher's bias is implemented not via a system prompt, as in prior work, but through a steering vector trained to maximize the likelihood of a set of target samples. First, we show that subliminal steering transfers complex multi-word biases, whereas prior work focused on single-word preferences, demonstrating a large scope of subliminally transferable signals. Moreover, the transfer is reliable enough to appear in settings previously thought not to exhibit subliminal learning, including plain SGD (not just Adam), full fine-tuning (not just LoRA), and models such as Llama and Phi. Second, we provide mechanistic evidence that subliminal learning transfers not only the target behavioral bias, but also the steering vector itself, localized to the layers at which the teacher was steered. Finally, we show that the bias is encoded with such precision that a new steering vector trained on the subliminally-laden dataset attains high cosine similarity with the original vector.

arXiv

Lost in Adaptation: Layer-Selective Recovery of Temporal Reasoning in Video-Language Models

Zihang Fu, Haonan Wang, Jian Kang, Kenji Kawaguchi, Jiaying Wu

Multimodal adaptation can erode temporal reasoning (TR) in video-language models (VLMs), leaving models able to perceive salient events yet unable to infer their temporal and causal structure. We introduce MERIT, a gradient-free framework that repairs this capability through layer-selective model merging. MERIT assigns each self-attention layer a VLM-dominant or LLM-dominant interpolation and uses the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) to search the resulting combinatorial space under an objective that rewards TR gains while penalizing temporal perception (TP) degradation. Across three VLM families and five video benchmarks, MERIT consistently improves TR while preserving TP; recipes selected on a compact diagnostic set transfer to four unseen benchmarks, with relative gains of up to 27.8%. Interventional masking and frame-level attribution further show that the selected layers are functionally important for reasoning and that MERIT shifts decisions toward temporally distributed, causally relevant evidence. These results establish layer-selective merging as a practical post-hoc mechanism for repairing video temporal reasoning degraded during multimodal adaptation, without learning new parameters.

arXiv

MechMath: Sorrifier-Driven Formal Decomposition Workflow for Automated Theorem Proving

Ruichen Qiu, Yichuan Cao, Junqi Liu, Dakai Guo, Xiao-Shan Gao, Lihong Zhi, Ruyong Feng

Recent advances in large language models (LLMs) and LLM-based agents have substantially improved the capabilities of automated theorem proving. However, for problems that require complex mathematical reasoning, current systems seldom succeed in their initial attempt, necessitating iterative adjustments to their proof strategies. Existing approaches for handling failed attempts typically either iteratively fix errors within the proof or discard the entire proof and regenerate it from scratch. The former leads to progressively longer contexts, which degrade the model's ability to attend to the remaining unresolved subproblems, while the latter is inefficient, as it may abandon mostly correct reasoning due to localized errors. To address this dilemma, we present MechMath, an agent system centered on a Sorrifier-driven formal decomposition paradigm. By leveraging the sorry placeholder in Lean to precisely isolate unresolved subgoals while preserving the surrounding verified proof structure, MechMath extracts each failed subproblem into a clean, self-contained context and resolves it independently. This avoids both the waste of full regeneration and the excessive context length induced by repeated repairs. Experimental results on challenging mathematical competition benchmarks, including IMO 2025, Putnam 2025, miniF2F, and a subset of ProverBench, demonstrate that our agent achieves significant advantages in proving efficiency.

arXiv

AWED-PIPER: Agents, Web Applications & Expert Detectors for Personally Identifiable Information Protection & Fine-grained Named Entity Recognition across 36 languages for 6.6 Billion Speakers

Prachuryya Kaushik, Ashish Anand

Named Entity Recognition (NER) and Personally Identifiable Information (PII) anonymization are critical tasks in Natural Language Processing (NLP) for information extraction and privacy preservation. We introduce AWED-PIPER, an open-source framework comprising agentic tools, interactive web applications, and 54 state-of-the-art expert detector models that provide unified Fine-grained Named Entity Recognition (FgNER) and reversible synthetic PII pseudonymization across 36 languages spoken by over 6.6 billion people. The system couples fine-grained multilingual sequence labeling with script-aware regex detectors to identify contextual entities (Person, Location, Organization, Medical) as well as structured technical PII (Emails, native-script Phone Numbers, IP Addresses, Credit Cards). AWED-PIPER offers a dual capability: full FgNER entity extraction and privacy-preserving reversible anonymization with persistent placeholders and de-anonymization dictionary mappings. The suite spans global languages to extremely low-resource vulnerable languages like Bodo, Manipuri, Bishnupriya, and Mizo. The resources can be accessed here: PII Protector Agentic Tool: (https://github.com/PrachuryyaKaushik/AWED-PIPER), FgNER Agentic Tool: (https://github.com/PrachuryyaKaushik/AWED-FiNER), PII Web Application: (https://hf.co/spaces/prachuryyaIITG/AWED_PII_Protector), FgNER Web Application: (https://hf.co/spaces/prachuryyaIITG/AWED-FiNER), and Edge-deployable Expert Detector Models: (https://hf.co/collections/prachuryyaIITG/awed-piper).

arXiv

A Large-Scale Chinese Knowledge Graph-Text Alignment Dataset for Benchmarking Knowledge-Grounded LLMs

Chengwei Wu, Xingrui Zhuo, Mingyang Gao, Xinghe Cheng, Zhichao Yan, Jiapu Wang

Reliable evaluation of knowledge-grounded Large Language Models (LLMs) in Chinese requires resources that explicitly align Chinese-language text with verifiable Knowledge Graph (KG) facts. Yet existing Chinese benchmarks primarily assess general language understanding and offer limited support for structured reasoning under Chinese-specific linguistic phenomena. We introduce the Chinese Data-Text Pair (CDTP), a large-scale Chinese KG-text alignment dataset comprising more than 7 million aligned instances across four broad domains. Each instance pairs a Chinese-language text with one or more textually supported KG triples, totaling 15 million triples. A multi-stage construction pipeline combining alignment filtering, manual verification, and external evidence validation improves semantic consistency and factual reliability. CDTP supports Knowledge Graph Completion (KGC), Question Answering (QA), and Triple-to-Text Generation (T2T). Across all three tasks, the benchmark design accounts for Chinese-specific phenomena, including polysemy, word-segmentation ambiguity, and context-dependent entity interpretation, enabling the evaluation of structured reasoning, ambiguity-aware factual understanding, and knowledge-grounded generation. Experiments with diverse open-source and proprietary LLMs show that model scale alone does not guarantee reliable performance on these Chinese knowledge-intensive tasks, whereas supervised fine-tuning on CDTP consistently improves in-domain performance and out-of-distribution robustness. The publicly accessible dataset, code, and evaluation protocols provide a reusable resource for developing and evaluating knowledge-grounded LLMs in Chinese.

arXiv

Vision Language Models Cannot Plan, but Can They Formalize?

Muyu He, Yuxi Zheng, Yuchen Liu, Zijian An, Bill Cai, Jiani Huang, Lifeng Zhou, Feng Liu, Ziyang Li, Li Zhang

The advancement of vision language models (VLMs) has empowered embodied agents to accomplish simple multimodal planning tasks, but not long-horizon ones requiring long sequences of actions. In text-only simulations, long-horizon planning has seen significant improvement brought by repositioning the role of LLMs. Instead of directly generating action sequences, LLMs translate the planning domain and problem into a formal planning language like the Planning Domain Definition Language (PDDL), which can call a formal solver to derive the plan in a verifiable manner. In multimodal environments, research on VLM-as-formalizer remains scarce, usually involving gross simplifications such as predefined object vocabulary or overly similar few-shot examples. In this work, we present a suite of five VLM-as-formalizer pipelines that tackle one-shot, open-vocabulary, and multimodal PDDL formalization. We evaluate those on an existing benchmark while presenting another two that for the first time account for planning with authentic, multi-view, and low-quality images. We conclude that VLM-as-formalizer greatly outperforms end-to-end plan generation. We find that visual grounding of object relations remains the primary bottleneck for weaker VLMs, while stronger models have largely overcome this limitation. While generating intermediate, textual representations such as captions or scene graphs partially compensate for the performance, their inconsistent gain leaves headroom for future research directions on multimodal planning formalization.

arXiv

Language Models that Think, Chat Better

Adithya Bhaskar, Xi Ye, Danqi Chen

Reinforcement learning with verifiable rewards (RLVR) trains language models to use long chain-of-thought reasoning (CoT) in domains like mathematics and code with rule-based verifiers. However, long CoT learned through RLVR does not generalize well to open-ended tasks -- such as writing essay outlines or making meal plans -- where humans reason routinely. This paper establishes the benefits of long CoT for general-purpose chat capabilities and introduces RL with Model-rewarded Thinking (RLMT)1, which pushes RLVR beyond verifiable domains. Using diverse real-world prompts, RLMT requires LMs to generate long CoT reasoning before responding, and optimizes them with online RL against a preference-based reward model used in RLHF. Across 40 training runs on Llama-3.1-8B and Qwen-2.5-7B (both base and instruct) and multiple optimization algorithms (DPO, PPO, and GRPO), RLMT consistently outperforms standard RLHF pipelines. This includes substantial gains of 3-7 points on three chat benchmarks (AlpacaEval2, WildBench, and ArenaHardV2), along with 1-3 point improvements on other tasks like creative writing and general knowledge. RLMT can also be applied directly to base models without an SFT stage, akin to DeepSeek-R1-Zero. Remarkably, with only 7K prompts, Llama-3.1-8B base trained with our RLMT recipe outperforms Llama-3.1-8B-Instruct post-trained with a complex multi-staged pipeline with 25M+ examples. We close with qualitative and quantitative analyses of how trained models plan their responses. Our results rethink the post-training pipeline and call upon future work to understand and employ thinking more broadly.

arXiv

Adapting LLMs to Time Series Forecasting via Temporal Heterogeneity Modeling and Representation Alignment

Yanru Sun, Emadeldeen Eldele, Zongxia Xie, Yucheng Wang, Wenzhe Niu, Qinghua Hu, Chee Keong Kwoh, Min Wu

Recent advances have demonstrated that Large Language Models (LLMs) can be effectively adapted for time series forecasting, revealing strong potential beyond natural language tasks. However, their performance remains constrained by two fundamental challenges: the inherent heterogeneity of temporal patterns and the modality gap between continuous numerical signals and discrete language representations. In this work, we propose \textbf{TALON} (Temporal-heterogeneity And Language-Oriented Network), a unified framework that enhances LLM-based forecasting by modeling temporal heterogeneity and promoting representation alignment. Specifically, we design a Heterogeneous Temporal Encoder that partitions multivariate time series into structurally coherent segments, enabling localized expert modeling across diverse temporal patterns. To bridge the modality gap, we introduce a Representation Alignment Module that projects temporal features toward LLM-compatible representations, making time series more amenable to LLMs and thereby unlocking their modeling potential, while eliminating the need for handcrafted prompts during inference. Extensive experiments on seven real-world benchmarks demonstrate that TALON achieves superior performance across all datasets, with average MSE improvements of up to 11% over recent state-of-the-art methods, while maintaining higher efficiency. These results underscore the effectiveness of incorporating both pattern-aware modeling and representation-level alignment when adapting LLMs for time series forecasting. The code is available at: https://github.com/syrGitHub/TALON.

arXiv

Bye-bye, Bluebook? Automating Legal Drudgery With AI-Augmented Rule Following

Matthew Dahl, Eric Martínez

One of the central promises of legal AI is to automate drudgery -- the formal, repetitive tasks of lawyers' work that consume time without calling for much discretion. Yet it remains an open question how well AI models actually perform on such tasks. This article presents the first empirical examination of AI performance on perhaps the most ubiquitous and lamented form of legal drudgery: citation formatting under the Bluebook. We make four contributions. First, we develop a new benchmark of 2,058 Bluebook queries and show that, on average, frontier language models produce a fully compliant legal citation only 42.6% of the time in a zero-shot setting. Second, we conduct an experiment with five top law reviews and show that even a "reasoning" model falls far below the average score of the human candidates in these journals' annual editor-selection competitions. Third, we show that simply providing the models with the rules offers only modest improvements, calling into question the ability of retrieval-augmented generation (RAG) to ensure rule-following alone. Finally, we develop an approach that does meaningfully improve compliance: a neuro-symbolic system that first uses a model to parse natural language into structured citation elements, and then delegates the formatting to a deterministic rule-execution engine. This approach achieves an average accuracy increase of 32.4 percentage points and total accuracy of up to 85.5% on our benchmark. These results point toward a reorientation for legal AI. The original promise of automating drudgery still remains out of reach for even frontier language models on their own -- but pairing them with symbolic rule engines may offer a tractable path forward.

arXiv

DYNASHIELD: A Black-Box Moving Target Defense for LLMs via Dynamic Decoding Customization

Xiaoqun Liu, Weiming Qi, Qiben Yan

Large language models (LLMs) remain vulnerable to jailbreak attacks in which adversarial prompts induce harmful outputs. Existing defenses often require access to the model internals or additional training, limiting their applicability for service providers deployed through black-box APIs. In this paper, we propose DYNASHIELD, a moving target defense framework that improves robustness by customizing decoding hyperparameters and system prompts at inference time. DYNASHIELD includes two key steps: (1) it identifies decoding configurations that reduce attack success probability, and (2) it probabilistically samples from a weighted configuration pool to introduce controlled variability in model behavior. We evaluate DYNASHIELD across 7 open-source LLMs under 4 state-of-the-art jailbreak attacks, using adversarial prompts from AdvBench. Results show substantial reductions in attack success rate compared with 7 baseline defenses, while maintaining response quality and incurring minimal inference overhead. Because DYNASHIELD operates solely through exposed runtime controls, it requires no retraining or model-internal access. These results suggest that safety-aware dynamic decoding is a promising and practically lightweight defense mechanism for black-box LLM deployments.

arXiv

Identifying parameter couplings and uncertainties of mixed-noise stochastic systems via full-covariance Gaussian mixture network

Xiaolong Wang, Xiangwen Hao, Jing Feng, Yuanyuan Liu, Yong Xu

Parameter identification of stochastic dynamical systems driven by mixed noises is challenging due to intractable likelihood functions. We propose PENN-GMD, a parameter estimation neural network that maps partially observed trajectories to a Gaussian mixture distribution (GMD) over the system parameters. Unlike conventional uncertainty estimates, the GMD employs full covariance matrices to explicitly reveal parameter couplings and multi-modal likelihood structures. The network is trained by minimizing the negative log-likelihood via a surjective parameterization that hard-encodes all GMD constraints, thereby approximating the true likelihood. We validate the method on five numerical examples with increasing complexity, including systems driven by fractional Gaussian and Lévy noises, oscillators with colored noise, coupled neurons under different observability, and an aeroelastic airfoil with unidentifiable stochastic disturbances. Results demonstrate that PENN-GMD accurately recovers likelihood distributions, captures parameter couplings, and naturally diagnoses non-identifiability through variance broadening or mode splitting. These capabilities establish PENN-GMD as a practical tool for uncertainty-aware parameter identification in complex stochastic systems where conventional likelihood-based methods are infeasible.

arXiv

MiNO: Cotangent-bundle propagator learning for PDEs

Gnankan Landry Regis N'guessan, Bum Jun Kim

Scientific machine learning for partial differential equations commonly targets solution fields, as in physics-informed neural networks, or solution maps, as in neural operators. We study a third target: the propagator itself, a phase and amplitude in phase space. The motivation is a gap in regularity. A transported discontinuity is nonsmooth in space and time, yet the rule that moves it can be a polynomial phase carrying unit amplitude, so the object that generates an evolution can be far smoother than the field it generates. The microlocal neural operator (MiNO) learns that object, using the eikonal equation for the phase and the transport equation for the amplitude, and recovers the solution by an oscillatory integral. Sharp fronts and caustics then belong to propagation geometry rather than to a field fitted pointwise. Small residuals certify more than the reconstructed field. They place the learned canonical relation, the geometry that carries singularities, close to the exact one, and they separate trainable error from the frequency-truncation tail. On a matched-budget discontinuous-advection benchmark, MiNO stops improving within 10,000 steps at the accuracy limit of its finite reconstruction window, a limit predicted in closed form, whereas a physics-informed neural network with neural-tangent-kernel loss balancing stays near its initial error. On smooth advection, the mean error is $3.84\times10^{-3}$ for MiNO and $3.12\times10^{-2}$ for a supervised Fourier neural operator. Single-branch MiNO is the smallest model compared, and one trained generator serves five unseen initial conditions without retraining.

arXiv

FinFraudBench: A Heterogeneous Graph Benchmark for Financial Fraud Detection

Yixuan Chen, Hongyu Zhan, Jie Sheng, Weiyu Han, Shuai Chen, Tianyi Zhang, Xiao Tan, Jun Xia

The increasing complexity of digital financial systems has reshaped financial fraud detection from isolated transaction classification into relational risk reasoning over interconnected financial entities. This shift has motivated graph-based fraud detection, where models identify fraudulent nodes by exploiting dependencies among customers, cards, merchants, categories, and locations. However, despite rapid progress in graph-based methods, existing public benchmarks remain misaligned with real-world financial systems in two important aspects. First, they often simplify financial ecosystems into homogeneous or single-node-type multi-relational graphs, failing to preserve the multi-entity and multi-relational nature of financial data. Second, they rarely provide large-scale heterogeneous financial graph datasets with realistic operating conditions such as extreme class imbalance and limited label availability, making it difficult to assess the practical effectiveness of current methods. To address these gaps, we present FinFraudBench, a heterogeneous graph benchmark for financial fraud detection. FinFraudBench contains two heterogeneous graph datasets (CreditCard-Fraud and BankTrans-Fraud) with up to 8.99M nodes and 89.23M directed typed edges. Each dataset preserves six financial entity types, fourteen directed edge types, and natural fraud rates that mirror deployment constraints. With these datasets, we establish a standardized evaluation protocol covering both ranking and imbalance-sensitive classification metrics, and evaluate representative baselines. Extensive experiments yield empirical insights into current methods' limitations and suggest promising avenues for future research. FinFraudBench is available at https://anonymous.4open.science/r/FinFraudBench-B002.

arXiv

Beyond Effective Sample Size: Effective Number of Proposals for Adaptive Importance Sampling

Ali Mousavi, Victor Elvira

Population-based adaptive importance sampling (AIS) methods use a set of proposal densities to approximate complex target distributions. Their performance is commonly assessed through effective sample size (ESS) and related weight-based diagnostics, which measure the concentration of normalized importance weights. However, a large ESS only indicates that the normalized sample weights are not strongly concentrated; it does not describe how the proposal components are arranged in the sampling space. In population-based AIS, several proposal components may generate samples in the same region of the target, so the sample weights can appear well balanced even though the effective number of distinct proposal components is small. This letter introduces the effective number of proposals (ENP), a similarity-aware proposal-level diagnostic for population-based AIS. ENP combines the total normalized weight assigned to each proposal with a redundancy measure computed from similarities among target-weighted samples, estimating the number of non-redundant empirical proposal contributions to the approximation. We establish basic effective-number properties and show that ENP detects proposal collapse and duplication missed by standard ESS. We also illustrate its use as a targeted feedback signal for proposal rejuvenation.

arXiv

An Adaptive Gradient Clipping and Noise Injection Mechanism for Differentially Private Federated Learning

Wenjing Wei, Alla Jammine, Farid Nait-Abdesselam

Differentially private federated learning must balance privacy protection against model accuracy and training efficiency. Static gradient clipping applies a fixed threshold throughout training and across model layers, which can cause excessive clipping when the threshold is too small or unnecessarily large noise when it is too large. This paper presents DDP-SA-adaptive, an adaptive gradient clipping and noise adding mechanism for differentially private federated learning with secure aggregation. At each communication round, every client determines a separate clipping threshold for each model layer from the median of its per-sample gradient norms. The resulting layer-wise thresholds adapt to the evolving gradient distributions and calibrate the Laplace noise added before the updates are encoded and secret-shared among intermediate aggregation servers. We evaluate the proposed mechanism on a federated regression task in terms of efficiency, accuracy, privacy, convergence, clipping norm, and noise magnitude. Compared with the static DDP-SA baseline, DDP-SA-adaptive reduces the number of communication rounds by 6.81%, total training time by 19.21%, and average per-round training time by 13.33%, leading to improved training efficiency. It also reduces test loss by 98.74% and increases test R2 by 3.41%, leading to improved model accuracy. To attain R2 = 0.99, the adaptive mechanism operates with a privacy budget of approximately epsilon = 0.1, compared with epsilon = 0.4 for static DDP-SA, thus providing stronger privacy protection and achieving stronger privacy guarantees. These results demonstrate that round-wise, layer-wise adaptation can improve the privacy-accuracy-efficiency trade-off of differentially private federated learning.

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