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Training large language models (LLMs) is computationally expensive, partly because the loss exhibits slow power-law convergence whose origin remains debatable. Through systematic analysis of toy models and empirical evaluation of LLMs, we show that this behavior can arise intrinsically from the use of softmax and cross-entropy. When learning peaked probability distributions, e.g., next-token distributions, these components generically yield power-law vanishing losses and gradients, regardless of many microscopic details, creating a fundamental optimization bottleneck. This ultimately leads to power-law time scaling of the loss with a universal exponent of $1/3$. Our results provide a mechanistic explanation for observed neural scaling and suggest new directions for improving LLM training efficiency.

The prevailing paradigm in large language model (LLM) alignment operates via erasure, filtering unsafe data or training models to strictly refuse harmful prompts. While effective at reducing immediate toxicity, this approach fundamentally constricts the model's epistemological scope, resulting in over-cautious systems that output uninformative blanket refusals to sensitive yet benign queries. In this work, we challenge the orthodoxy that unsafe data must be discarded. We propose a dialectical approach to alignment, positing that unsafe data encodes rich, domain specific knowledge critical for nuanced, safe, and informative generation. To operationalize this, we introduce SafeMoE, a Mixture-of-Experts (MoE) framework that isolates unsafe knowledge into domain-specific Low-Rank Adapters (LoRA experts) trained exclusively on harmful corpora. To synthesize safety from these unsafe primitives, we train a lightweight gating network using a minimal, highly curated set of safe-informative responses. During inference, this router dynamically orchestrates the unsafe experts, effectively steering the generation trajectory to harness

Large text-to-image diffusion models rarely expose reliable signals of when a prompt is likely to produce a poorly aligned generation, especially when training data is undisclosed. We study whether expert disagreement inside pre-trained mixture-of-experts (MoE) diffusion models can serve as a reliable estimate for epistemic uncertainty. We introduce EMoE, a training-free method that separates expert-specific computation paths at an early MoE layer, uses the same initial noise across paths, and measures variance among their latent representations after the first denoising step. This provides an uncertainty-aware prompt signal before full image generation, without auxiliary networks or training diffusion ensembles. On COCO and CC3M, EMoE ranks prompts by text-image alignment quality metrics more consistently than diffusion-specific and router-based baselines. We further apply EMoE to multilingual prompts and find systematic language-dependent differences in disagreement and generation quality, including shared-vocabulary effects. These results position EMoE as a practical diagnostic tool for prompt risk, model

The scaling of Large Language Models (LLMs) has driven significant performance gains but created substantial challenges in inference efficiency. While Mixture of Experts (MoEs) architectures address this by decoupling model size from inference cost, training MoEs from scratch is often unstable and compute intensive. Conversion of pre-trained dense models into sparse MoEs has emerged as an alternative solution; however, existing methods typically rely on heuristic neuron clustering or random splitting to partition the Feed-Forward Network (FFN) into experts. In this work, we propose DOT-MoE, a novel framework that formulates the decomposition of dense layers as a Differentiable Optimal Transport (DOT) problem. Instead of static heuristics, we model neuron assignment as a balanced transport problem, utilizing differentiable Sinkhorn-Knopp iterations to enforce strict expert capacity constraints. Furthermore, we utilize Straight-Through Estimators (STE) to jointly learn the discrete neuron-to-expert assignment and the token-to-expert routing policy end-to-end. Extensive experiments across multiple architectures and benchmarks

Mixture of Experts (MoE) Large Language Models (LLMs) achieve strong performance at scale. However, reinforcement learning (RL) on MoE-based LLMs often suffers from training instability. A root cause is router drift, i.e., expert activations can change drastically across model updates and differ between disaggregated rollout and training phases, causing large rollout--training mismatch and unstable importance sampling weights in PPO-style RL algorithms. Routing replay mitigates this issue by freezing the replay route within each reasoning trajectory, but it ignores how the router evolves under off-policy updates and thus causes router staleness. To address this limitation, we propose Predictive Routing Replay (PR2), which augments each router with a lightweight evolution predictor that learns to anticipate short-horizon router evolution. During the rollout phase, we use the predictive routing distribution to apply top-$k$ routing, enabling gradients to reach experts that are likely to become active after updates. During the training phase, we replay the

We study LLM policy synthesis: using a language model to iteratively generate programmatic agent policies for multi-agent environments. Rather than training neural policies via reinforcement learning, our framework prompts an LLM to produce Python policy functions, evaluates them in self-play, and refines them using performance feedback across iterations. We investigate feedback engineering (the design of what evaluation information is shown to the LLM during refinement) comparing sparse feedback (scalar reward only) against dense feedback (reward plus social metrics: efficiency, equality, sustainability, peace). Across two canonical Sequential Social Dilemmas (Gathering and Cleanup) and two frontier LLMs (Claude Sonnet 4.6, Gemini 3.1 Pro), dense feedback consistently matches or exceeds sparse feedback on all metrics. We explain the asymmetry through feedback aliasing: when scalar reward alone maps distinct failure modes to the same value (e.g., under- vs. over-cleaning), social metrics break the alias and let the LLM diagnose which corrective direction to take.

Mixture-of-Experts (MoE) models have become a leading approach for decoupling parameter count from computational cost in large language models, yet effectively scaling MoE performance remains a challenge. Prior work shows that fine-grained experts enlarge the space of expert combinations and improve flexibility, but they also impose substantial routing overhead, creating a new scalability bottleneck. In this paper, we explore a complementary axis for scaling -- how expert outputs are aggregated. We theoretically show that replacing the standard weighted-summation aggregation with structural aggregation expands the expert-combination space without altering the experts or router, and enables possible multi-step reasoning within a single MoE layer. To this end, we propose DAG-MoE, a sparse MoE framework that employs a lightweight module to automatically learn the optimal aggregation structure among the selected experts. Extensive experiments under standard language modeling settings show that DAG-MoE consistently improves performance in both pretraining and fine-tuning, surpassing traditional MoE baselines.

Mixture-of-Experts (MoE) large language models reduce per-token computation through sparse expert activation, but their deployment remains memory-intensive because all expert weights must be kept resident in memory. Existing MoE compression methods struggle in the ultra-low-bit regime: pruning irreversibly removes model capacity, while coarse-grained quantization fails to allocate bits according to heterogeneous expert and weight-direction importance. We propose BitsMoE, a spectral-energy-guided bit-allocation framework for MoE LLM quantization. BitsMoE decomposes each MoE layer by SVD into a shared basis and expert-specific spectral factors, retaining the shared basis without quantization to preserve common cross-expert structure and using the expert-specific factors as fine-grained quantization units. To determine the bit-width of each unit, BitsMoE formulates spectrum-wise mixed-precision quantization as an activation-aware reconstruction surrogate and solves an integer linear program that minimizes estimated reconstruction loss under a fixed bit budget. Experiments across multiple MoE LLMs show that BitsMoE substantially reduces downstream task accuracy degradation in ultra-low-bit

Mixture-of-Experts (MoE) has recently emerged as the mainstream architecture for efficiently scaling large language models while maintaining near-constant computational cost. Expert parallelism distributes parameters by partitioning experts across devices, but this introduces token-level load imbalance during inference. Expert replication is a widely adopted load-balancing technique in serving frameworks that alleviates load imbalance in large-scale deployments by replicating experts with high loads. In this work, we demonstrate that existing replication schemes often over-replicate, with many replicas providing marginal improvement. Replicas consume substantial GPU memory, which may lead to resource contention and throughput degradation. We present CRAFT, an efficient expert replication framework that maximizes load balance under a given memory budget by performing fine-grained, per-layer replication based on the estimated replication benefit. CRAFT can be seamlessly integrated into existing serving frameworks without any additional training or model changes. Our evaluation shows that CRAFT increases end-to-end serving throughput by $1.14\times$ on average (up

Mixture-of-Experts (MoE) models scale by activating only a small subset of experts per token. However, training such models remains challenging because top-$k$ routing is discrete and non-differentiable, requiring gradient estimators for expert selection whose design remains a central open problem. We introduce ProbMoE, a probabilistic routing framework that models expert selection as a distribution over cardinality-constrained expert subsets and formulates routing as probabilistic inference in this discrete subset space. We first propose ProbMoE Exact-$k$ routing, which samples $k$-expert subsets in the forward pass, and the backward pass uses gradients through each expert's exact marginal probability as a tractable surrogate for the true gradient. ProbMoE naturally generalizes to a dynamic-$k$ routing setting, where both training and inference constrain the routing cardinality to the same predefined range, allowing adaptive expert allocation per token. Across benchmarks and model backbones, ProbMoE Exact-$k$ achieves strong performance compared to competitive baselines, with improved expert utilization and

Large Language Models (LLMs) are increasingly used with formal interactive theorem provers such as Lean 4. Scaling these systems with reinforcement learning or search methods requires process reward models (PRMs) that can evaluate intermediate reasoning steps. Existing reward-model designs expose a practical trade-off. Value-head models provide continuous scores but modify the generative model interface, while generative reward models preserve textual rationales but are poorly matched to continuous floating-point regression because numeric values are split across tokens. We introduce Expected Value Alignment (EVA), a reward-modeling procedure that keeps the surface output discrete while extracting continuous scores from the model's token distribution. The model emits integer scores in a structured JSON format, and EVA computes a continuous score as the expectation over the logits of the corresponding anchor tokens. Training combines the causal language modeling objective with an auxiliary mean squared error loss on these expected values. We instantiate EVA in \textit{Leibniz},

Dynamic Sparse Training (DST) offers a promising paradigm for improving the training and inference efficiency of deep neural networks; however, we find that in large language model training, DST can suffer from optimization instability, manifested as loss spikes after topology updates. In this work, we show that the naive use of standard Adam-based optimizers leads to a cold-start issue for newly regrown parameters, resulting in excessively large updates and disrupted training dynamics. To address this issue, we propose Sparse Memory-Efficient Training (SMET), which stabilizes DST with optimizer warm-up and improves training progress through density-aware learning-rate scaling. SMET further reduces memory consumption by storing gradients and optimizer states only for active parameters. We provide a theoretical analysis of the update behaviors under SMET, showing improved optimization stability. Extensive experiments demonstrate that SMET enables stable, scalable, and memory-efficient sparse pre-training of LLMs, paving the way for sparse training as a practical alternative

Large language model agents achieve strong performance on text-based benchmarks but incur prohibitive inference costs, motivating the use of compact neural rerankers for action selection. We investigate whether a single lightweight model can perform action selection across multiple diverse environments, a capability that would eliminate per-environment model maintenance. Training DeBERTa-v3 (184M-434M parameters) jointly on ALFWorld, WebShop, and ScienceWorld with minority-class upsampling, we find that rebalanced two-environment joint training substantially improves over single-environment ALFWorld performance (net gain +0.412) while maintaining competitive WebShop performance (+0.214 vs. +0.249 single-environment). Three-environment training yields a mean combined net gain of +0.551 +/- 0.024 across 4 seeds, with per-environment results approaching specialized single-environment models while providing positive cross-domain transfer. Cross-environment adaptation is highly sample-efficient: fine-tuning on only 9.2% of target-domain data recovers 93% of full-data performance, and scaling model capacity yields limited benefits, indicating data diversity is the primary driver. Environment-aware LoRA adapter routing with PCGrad

The increasing deployment of intelligent agents in digital ecosystems, such as social media platforms, has raised significant concerns about traceability and accountability, particularly in cybersecurity and digital content protection. Traditional large language model (LLM) watermarking techniques, which rely on token-level manipulations, are ill-suited for agents due to the challenges of behavior tokenization and information loss during behavior-to-action translation. To address these issues, we propose Agent Guide, a novel behavioral watermarking framework that embeds watermarks by guiding the agent's high-level decisions (behavior) through probability biases, while preserving the naturalness of specific executions (action). Our approach decouples agent behavior into two levels, behavior (e.g., choosing to bookmark) and action (e.g., bookmarking with specific tags), and applies watermark-guided biases to the behavior probability distribution. We employ a z-statistic-based statistical analysis to detect the watermark, ensuring reliable extraction over multiple rounds. Experiments in a social media scenario with diverse agent profiles demonstrate that Agent

SwiGLU has become a standard gated activation in modern Transformer MLPs, yet its gate sharpness -- the smoothness and selectivity of the gating function -- is typically fixed throughout training. In this work, we propose Confidence-Aware SwiGLU ($\kappa$-SwiGLU), a variant of SwiGLU for Mixture-of-Experts (MoE) models that adjusts expert gate sharpness according to token-level routing confidence. Specifically, $\kappa$-SwiGLU parameterizes the SiLU gate sharpness coefficient as a learnable function of the router logit, enabling each expert gate unit to interpolate between smooth, broadly active gating and sharp, selective gating. We evaluate $\kappa$-SwiGLU on the FineWeb-Edu dataset across MoE Transformer models ranging from 8 to 28 layers. Across these settings, $\kappa$-SwiGLU improves mean CORE performance while adding negligible parameters and incurring only a small computational overhead, demonstrating that confidence-aware gate sharpness is a promising mechanism for improving MoE MLPs. The code is available at https://github.com/askerlee/kappa-swiglu.

Combining existing pre-trained LLMs is a promising approach for diverse reasoning tasks. However, task-level expert selection is often too coarse-grained, since different instances may require different expertise. To address this, we propose Skill-MoE, a symbolic, skill-based, and gradient-free Mixture-of-Experts framework for instance-level expert selection. Skill-MoE infers skills (e.g., algebra in mathematics) from each query, selects experts based on skill relevance, and lets each expert generate its own reasoning. The resulting k outputs are then synthesized by an aggregator chosen for its ability to integrate diverse responses. While instance-level selection substantially improves performance, naively implementing it incurs heavy overhead from repeated model loading and offloading. We address this with a batch inference strategy that groups instances by assigned experts, allowing each model to be loaded only once. As a result, Skill-MoE integrates 16 expert models on a single GPU with runtime comparable to prior multi-agent baselines using 4 GPUs. Across diverse

Agentic language model systems alternate between two structurally distinct step types: structured tool calls (short, deterministic, low perplexity) and open-ended planning/reasoning steps (long, complex, high perplexity). Despite this heterogeneity, current inference systems apply identical compute to every step. We introduce LayerRoute, a lightweight adapter that learns to selectively skip transformer blocks on a per-input basis. LayerRoute augments each of the 24 transformer blocks in Qwen2.5-0.5B-Instruct with: (1) a per-layer router (~897 parameters, Linear(896,1)) that outputs a hard binary gate via the straight-through estimator, and (2) LoRA adapters (rank 8, ~1.08M parameters) on the Q/K/V/O attention projections. The backbone weights remain frozen. A single end-to-end training pass on agentic data (Hermes, Glaive, GSM8K, Turing) with a gate regularisation term forces the system to discover which blocks are skippable per input type. After 3,000 steps (6.4 minutes on an A100 40GB), LayerRoute achieves a 12.91% skip differential: tool calls skip 15.25% of

Alignment has greatly improved large language models (LLMs)' output quality at the cost of diversity, yielding highly similar outputs across generations, especially in open-ended generation tasks. We propose Base-Aligned Model Collaboration (BACo), an inference-time token-level model collaboration framework that dynamically combines a base LLM with its aligned counterpart to optimize diversity and quality. Using uncertainty and content-based signals, BACo employs routing strategies to determine, at each token, which model to decode from. Prior diversity-promoting methods often improve diversity at the expense of quality or require expensive decoding or post-training. In contrast, BACo achieves both high diversity and quality post hoc within a single pass, while offering strong controllability. We introduce a family of effective routing strategies and evaluate them across three open-ended generation tasks with 13 diversity and quality metrics. BACo consistently surpasses state-of-the-art inference-time baselines. With our best router, BACo achieves a 21.3% joint improvement in diversity and quality,

Understanding the internal representations of large language models (LLMs) remains a central challenge for interpretability research. Sparse autoencoders (SAEs) offer a promising solution by decomposing activations into interpretable features, but existing approaches rely on fixed sparsity constraints that fail to account for input complexity. We propose AdaptiveK SAE (Adaptive Top K Sparse Autoencoders), a novel framework that dynamically adjusts sparsity levels based on the semantic complexity of each input. Leveraging linear probes, we demonstrate that context complexity is linearly encoded in LLM representations, and we use this signal to guide feature allocation during training. Experiments across ten language models demonstrate that this complexity-driven adaptation outperforms fixed-sparsity approaches on reconstruction fidelity, explained variance, cosine similarity and interpretability metrics while eliminating the burden of extensive hyperparameter tuning. Our code is available at: https://github.com/hiyukie/adaptiveK.

Modern large language models (LLMs) increasingly depends on efficient long-context processing and generation mechanisms, including sparse attention, retrieval-augmented generation (RAG), and compressed contextual memory, to support complex reasoning. We show that these optimizations can be unified into a four-step memory processing pipeline: Prepare Memory, Compute Relevancy, Retrieval, and Apply to Inference. Through systematic profiling, we identify a 22%-97% memory processing overhead in LLM inference and strong heterogeneity in its computational characteristics. Motivated by this insight, we argue that \textbf{heterogeneous systems} are well-suited to accelerate memory processing and thus end-to-end inference. We demonstrate this approach on a GPU-FPGA system by offloading sparse, irregular, and memory-bounded operations to FPGAs while retaining compute-intensive operations on GPUs. Evaluated on an AMD MI210 GPU and an Alveo U55C FPGA, our system is up to $2.2\times$ faster and achieves up to $4.7\times$ less energy across multiple LLM inference optimizations than the GPU baseline (similar results hold

In this paper, we study a fundamental design problem in pretraining Large Language Models (LLMs) for low-resource language regimes. Existing works adopt multi-epoch, multi-lingual, and multi-stage training to utilize the limited target-language corpus efficiently, but no prior scaling law can compare recipes spanning these approaches under the same compute budget $C$ and target-language corpus size $D_T$, leaving the optimal training setup unclear. To address this gap, we propose the $M^3$ Scaling Law, a unified predictive model parameterized by the model scale, the number of target-corpus epochs $k$, the average target-language ratio $r$, and the final-stage target-language ratio $r_f$, which places monolingual single-stage, multi-lingual single-stage, and multi-lingual multi-stage recipes on a single target-language loss surface. Across three language pairs, it extrapolates to unseen hyperparameter regions more accurately than existing scaling laws. Using $M^3$ as a surrogate objective, we derive two practical guidelines for low-resource LLM pretraining: (i) as $D_T$ decreases, the

Recent progress has expanded the use of large language models (LLMs) in drug discovery, including synthesis planning. However, objective evaluation of retrosynthesis performance remains limited. Existing benchmarks and metrics typically rely on published synthetic procedures and Top-K accuracy based on single ground-truth, which does not capture the open-ended nature of real-world synthesis planning. We propose a new benchmarking framework for single-step retrosynthesis that evaluates both general-purpose and chemistry-specialized LLMs using ChemCensor, a novel metric for chemical plausibility. By emphasizing plausibility over exact match, this approach better aligns with human synthesis planning practices. We also introduce CREED, a novel dataset comprising millions of ChemCensor-validated reaction records for LLM training, and use it to train a model that improves over the LLM baselines under this benchmark.

The rise of API-only access to state-of-the-art LLMs highlights the need for effective black-box jailbreak methods to identify model vulnerabilities in real-world settings. Without a principled objective for gradient-based optimization, most existing approaches rely on genetic algorithms, which are limited by their initialization and dependence on manually curated prompt pools. Furthermore, these methods require individual optimization for each prompt, failing to provide a comprehensive characterization of model vulnerabilities. To address this gap, we introduce VERA: Variational infErence fRamework for jAilbreaking. VERA casts black-box jailbreak prompting as a variational inference problem, training a small attacker LLM to approximate the target LLM's posterior over adversarial prompts. Once trained, the attacker can generate diverse, fluent jailbreak prompts for a target query without re-optimization. Experimental results show that VERA achieves strong performance across a range of target LLMs, highlighting the value of probabilistic inference for adversarial prompt generation.

Statistical evaluation aims to estimate the generalization performance of a model using held-out i.i.d. test data sampled from the ground-truth distribution. In supervised learning settings such as classification, performance metrics such as error rate are well-defined, and test error reliably approximates population error given sufficiently large datasets. In contrast, evaluation is more challenging for generative models due to their open-ended nature: it is unclear which metrics are appropriate and whether such metrics can be reliably evaluated from finite samples. In this work, we introduce a theoretical framework for evaluating generative models and establish evaluability results for commonly used metrics. We study two categories of metrics: test-based metrics, including integral probability metrics (IPMs), and R\'enyi divergences. We show that IPMs with respect to any bounded test class can be evaluated from finite samples up to multiplicative and additive approximation errors. Moreover, when the test class has finite fat-shattering dimension, IPMs can

Small Language Models (SLMs) offer a balance between capability and computational feasibility. Neural scaling laws inform their optimal training, suggesting that they possess rich internal representations that scale with their size. However, deploying even these SLMs can be challenging under strict resource constraints. Language model probing provides methods for analyzing the linguistic knowledge encoded in a model's internals. We propose ProbScale, a framework that unifies insights from scaling laws and probing to identify parameter-efficient subnetworks within pre-trained SLMs. ProbScale utilizes the high-quality representations of well-scaled SLMs and uses task-specific probes to mathematically quantify the relevance of each layer for target downstream capabilities. This allows selecting subnetworks that optimally trade off performance against parameter size. We formulate the subnetwork selection as finding a layer subset maximizing aggregated, task-weighted probe performance under a parameter budget. Experiments on representative SLMs such as RoBERTa-Large and T5-Base demonstrate that ProbScale identifies subnetworks achieving significant parameter

Large language models (LLMs) are widely used as scalable evaluators of model responses in lieu of human annotators. However, imperfect sensitivity and specificity of the LLM judges induce bias in naive evaluation scores. We propose a simple plug-in framework that corrects this bias and enables statistically principled uncertainty quantification. Our framework constructs confidence intervals that account for uncertainty from both the test dataset and a human-labeled calibration dataset. Additionally, it uses an adaptive strategy to allocate calibration samples for tighter intervals. Importantly, we characterize parameter regimes defined by the true evaluation score and the LLM judge's sensitivity and specificity in which our LLM-based evaluation yields more reliable estimates than human-only evaluation. Moreover, we show that our framework remains unbiased under distribution shift between the test and calibration datasets, in contrast to existing approaches.

Vision-language foundation models have shown promising zero-shot generalization for Cross-Domain Few-Shot Object Detection (CD-FSOD). However, they face two critical challenges in fine-tuning: insufficient support set utilization due to sparse single-instance annotations, and severe overfitting under extremely limited target-domain samples. To address these issues, this paper proposes GiPL, an efficient two-branch training framework. In the first branch, we design an iterative pseudo-label self-training paradigm, which performs zero-shot inference on the support set to generate reliable pseudo-annotations, fuses them with ground-truth labels, and iteratively optimizes the model to fully exploit support set data. In the second branch, we introduce generative data augmentation pipeline using large vision-language models, which synthesizes domain-aligned, multi-object annotated images to enrich training samples and suppress overfitting. Extensive experiments on three challenging CD-FSOD datasets (RUOD, CARPK, CarDD) under 1/5/10-shot settings demonstrate that GiPL consistently outperforms state-of-the-art methods with significant performance gains. Code is available at \href{https://github.com/z-yaz/CDiscover}{CDiscover}.

Modern language-model fine-tuning typically pairs each prompt with a single response, even though many prompts admit multiple valid completions. This effectively reduces a multi-modal conditional distribution to a one-sample view, a phenomenon we call the "mode lottery," where training emphasizes a subset of plausible modes while leaving others underrepresented. We study multi-response training (MRT), which retains multiple responses per prompt, and develop a principled account of when and why it helps. Our key insight is that prompts and responses are distinct statistical resources: additional prompts reduce uncertainty about the input distribution, while additional responses reduce uncertainty about the conditional output distribution. This yields a variance-budget tradeoff that predicts when retaining multiple responses is worthwhile, shows diminishing returns as prompt-level uncertainty dominates, and explains why large redundant corpora can exhibit an implicit multi-response effect. We further analyze response selection, and show that Random-K-of-N is the unbiased default for distributional fine-tuning, reward-based

Recent evidence shows that people with eating disorders (EDs) are increasingly seeking guidance, advice, and emotional support from Large Language Model (LLM)-based chat systems. Although these systems are not designed to provide clinical advice, their perceived expertise, neutrality and accessibility make them a frequent, albeit risky, source of support. This paper investigates potential patterns of interaction between users with EDs and LLMs, focusing on the potential harms arising from models that uncritically adapt to, and facilitate unsafe or self-harming user requests. We find, in consultation with clinical ED experts, that specific linguistic cues in prompts increase the likelihood of unsafe responses and, through systematically varying the degree of potential risk present in the user prompt, report the extent to which LLMs uncritically adapt to problematic, and potentially dangerous user inputs.

Large neural networks achieve state-of-the-art performance on many tasks, yet their sheer size hinders deployment on resource-constrained devices. Among existing compression approaches, cross-layer parameter sharing remains relatively unexplored for transformer models. In this paper, we introduce Fine-grained Parameter Sharing (FiPS), a unified framework for compressing transformer Multi-Layer Perceptrons (MLPs) that combines cross-block parameter sharing, low-rank factorization, and sparsity in a single optimization. FiPS concatenates MLP weight matrices across a group of transformer blocks and factorizes them into a shared basis and sparse, layer-specific projection matrices. Both factors are initialized via singular value decomposition (SVD) and jointly optimized by block-wise reconstruction error minimization. FiPS compresses Vision Transformers (ViTs) by up to 33% with less than 1% top-1 accuracy loss on ImageNet-1k, and by up to 57% when combined with fine-tuning. It also compresses Large Language Models (LLMs) by up to 20% while outperforming existing SVD-based methods in perplexity and downstream benchmarks

Neural scaling laws relate loss to model size in large language models (LLMs), yet depth and width may contribute to performance differently, requiring more detailed studies. Here, we quantify how depth affects loss via analysis of LLMs and toy residual networks. We find loss scales inversely proportional to depth in LLMs, probably due to functionally similar layers reducing error through ensemble averaging rather than compositional learning or discretizing smooth dynamics. This regime is inefficient yet robust and may arise from the architectural bias of residual networks and target functions incompatible with smooth dynamics. The findings suggest that improving LLM efficiency may require architectural innovations to encourage compositional use of depth.

Everywhere learning is a new paradigm whereby Artificial Intelligence (AI) systems are trained to satisfy loss constraints with probability one over the data distribution. This is in contrast to the standard paradigm of training AI systems to minimize average losses. We develop an approximate duality theory to substantiate a generalization analysis that establishes the proximity between solutions of empirical and statistical everywhere learning problems. Our results show that dual variables reweigh the data distribution towards points in which loss constraints are more difficult to satisfy and that generalization is controlled by the mismatch between the concentration of mass of the data distribution and the concentration of mass on points where constraints are more difficult to satisfy. We further show that we can control generalization with a sparse L1 penalty on constraint relaxations. We illustrate the merits of everywhere learning with an experiment in agentic classification for language model tasks.

Large Language Models (LLMs) are increasingly used in analytical workflows, but their suitability as exploratory data analysis (EDA) agents in business settings remains uncertain. In practice, a deployable EDA agent must provide not only useful average performance but also sufficient repeatability to support trust in its outputs. We evaluate this requirement in a controlled, business-relevant benchmark built on an agent-based supply chain simulation. The task is to identify supplier-product combinations responsible for low quality and downstream sales loss by reasoning from indirect operational traces rather than from explicit labels. Fifteen model-variant configurations from eight model families were evaluated under four experimental conditions that varied data representation, prompt clarity, and signal strength, with five trajectories per condition. Outputs were scored against deterministic ground truth using the Jaccard index and assessed through a framework that combines mean score (ms), coefficient of variation (CV), exploratory cross-condition significance tests, and Business utility, a risk-adjusted

Autoregressive (AR) large language models (LLMs) have achieved broad practical success, but sequential decoding remains a key bottleneck for low-latency deployment. Recent efficient-inference work has progressed along two axes: reducing the cost of each model invocation through efficient architectures, and reducing serial decoding steps through parallel generation. Hybrid attention backbones address the former, while diffusion language models (dLLMs) pursue the latter via iterative parallel denoising. Combining these advantages remains challenging: AR-to-dLLM conversion often fails to preserve seed-checkpoint capability, and hybrid-attention recurrent states and masking constraints make diffusion training and serving nontrivial. We present FLARE, a systematic conversion framework for hybrid-attention LLMs. Our analysis identifies transfer data quality as the primary determinant of capability preservation, outweighing loss formulation and attention-mask design. The resulting framework combines a token-equal AR-and-diffusion objective, hardware-aware kernels, and unified inference, enabling one checkpoint to support both AR-style verified decoding and diffusion-style parallel denoising. Starting from strong AR

Large Language Models (LLMs) frequently exhibit "contextual disregard" when faced with input evidence that conflicts with their internal parametric memory, leading to persistent factual hallucinations. Existing mitigation strategies primarily rely on suppressing specific neuron activations or employing computationally expensive contrastive decoding mechanisms, which often result in increased perplexity or significantly elevated inference latency. To address these limitations, we propose Resonant Context Anchoring (RCA), a lightweight inference-time intervention method grounded in the perspective of residual stream signal dynamics. RCA aims to resolve the signal attenuation of external evidence during its propagation through deep networks. The core mechanism involves the orthogonal decoupling of routing logic and information magnitude within the self-attention module. By utilizing raw pre-softmax attention scores as an instantaneous metric of semantic alignment, we construct a dynamic gain field via non-linear rectification to selectively amplify the norms of value vectors corresponding to context tokens, without altering the attention probability distribution.

On-policy reinforcement learning has become the dominant paradigm for reasoning alignment in large language models, yet its sparse, outcome-level rewards make token-level credit assignment notoriously difficult. On-Policy Distillation (OPD) alleviates this by introducing dense, token-level KL supervision from a teacher model, but typically applies this supervision uniformly across all rollouts, ignoring fundamental differences in signal quality. We propose Signal-Calibrated On-Policy Distillation Enhancement (SCOPE), a dual-path adaptive training framework that routes on-policy rollouts by correctness into two complementary supervision paths. For incorrect trajectories, SCOPE performs teacher-perplexity-weighted KL distillation to prioritize instances where the teacher demonstrates genuine corrective capability, while down-weighting unreliable guidance. For correct trajectories, it applies student-perplexity-weighted MLE to concentrate reinforcement on low-confidence samples at the capability boundary rather than over-reinforcing already mastered ones. Both paths employ a group-level normalization to adaptively calibrate weight distributions, accounting for the intrinsic difficulty variance across prompts. Extensive experiments on six reasoning benchmarks show

Large language models (LLMs) are widely recognised for their applications in natural language generation and are increasingly used for code generation tasks. However, concerns about bias in their generated outputs remain significant. This paper focuses on GPT-4o and Gemini, mainstream tools for code generation, and proposes a framework for evaluating bias in LLM-generated code, specifically examining the influence of protected attributes, prompts and web-search capability. We use two metrics: the code bias score (CBS) and the attribute change ratio (ACR), to quantify the prevalence of bias and the degree of influence of different attributes, respectively. In addition, we investigate four lightweight mitigation strategies: Few-Shot, Chain-of-Thought, Few-Shot Chain-of-Thought, and Multi-agent, aimed at mitigating bias in generated code. Our findings reveal that bias remains prevalent across different protected attributes and datasets even after applying mitigation strategies, highlighting the need for more effective approaches to reduce bias in AI-driven code generation systems.

Large Language Models (LLMs) are increasingly used for zero-shot annotation and LLM-as-a-judge tasks, yet their reliability hinges on how model-internalized priors interact with user-provided instructions. We investigate three dimensions of this interaction: (1) how an LLM's familiarity with data and task definitions affects performance, (2) the extent to which additional information in prompts can correct zero-shot errors ("decision stickiness"), and (3) model susceptibility to misaligned task definitions. Through experiments on toxicity detection across diverse datasets (spanning social media, gaming, news, and forums) using both dense and mixture-of-experts models, we find that nearly two-thirds of zero-shot errors are resistant to correction, with an overall rescue rate (fraction of initial errors corrected by prompting) of only 34.8%. High-confidence errors prove especially resistant to correction. When given misaligned definitions, LLMs follow them while maintaining confidence levels unchanged from the aligned condition. Crucially, we introduce Definition-Specific Familiarity (DSF), which measures alignment between a model's

Despite Bengali being the sixth most spoken language in the world, no prior work has systematically evaluated hallucination in large language models (LLMs) for Bengali. We introduce BenHalluEval, a fine-grained hallucination evaluation framework for Bengali covering four tasks: Generative Question Answering (GQA), Bangla-English Code-Mixed QA, Summarization, and Reasoning. We construct 12,000 hallucinated candidates using GPT-5.4 across twelve task-specific hallucination types, drawn from three existing Bengali datasets, and evaluate seven LLMs spanning reasoning-oriented, multilingual, and Bengali-centric categories under a dual-track protocol that independently measures false-positive rate on ground-truth instances (Track A) and hallucination detection rate on hallucinated candidates (Track B). To jointly penalise both failure modes and prevent inflated scores from uniform response bias, we propose BenHalluScore, a dual-track calibration metric that ranges from 7.72% to 55.42% across models and tasks, revealing substantial variation in hallucination calibration. Chain-of-thought prompting, applied as a mitigation strategy, shifts response distributions without consistently improving hallucination

Hallucinations in large language models (LLMs) arise from heterogeneous failure mechanisms, making reliable detection difficult for any single global uncertainty score. In this work, we formulate hallucination detection as a mechanism-aware evidence aggregation problem, where diverse representation- and token-level signals must be interpreted under multiple latent explanations. We propose FLaG, a lightweight hallucination detection framework that models correctness through a set of latent evidence groups. Each instance is softly associated with multiple groups via an energy-based routing mechanism, and group-conditional reliability signals are combined through a principled log-marginal aggregation. This design enables FLaG to capture heterogeneous hallucination patterns while remaining invariant to decision thresholds and evaluation metrics. The framework operates as a frozen-model head, requires no modification to the underlying language model, and incurs minimal computational overhead. We further provide a theoretical perspective that connects FLaG to optimal evidence aggregation under heterogeneous error mechanisms, showing that the Bayes-optimal test statistic

Transformer-based large language models exhibit in-context learning, enabling adaptation to downstream tasks via few-shot prompting with demonstrations. In practice, such models are often fine-tuned to improve zero-shot performance on downstream tasks, allowing them to solve tasks without examples and thereby reducing inference costs. However, fine-tuning can degrade in-context learning, limiting the performance of fine-tuned models on tasks not seen during fine-tuning. Using linear attention models, we provide a theoretical analysis that characterizes how fine-tuning objectives modify attention parameters and identifies conditions under which this leads to degraded few-shot performance. We show that fine-tuning all attention parameters can harm in-context learning, whereas restricting updates to the value matrix improves zero-shot performance while preserving in-context learning. We further show that incorporating an auxiliary few-shot loss enhances in-context learning primarily on the target task, at the expense of degraded in-context learning ability on tasks not seen during fine-tuning. We provide empirical evidence from

Mixture-of-Experts (MoE) architectures scale Large Language Models (LLMs) efficiently, enabling greater capacity with reduced computational cost by dynamically routing inputs to relevant experts, yet introduce a critical vulnerability: Safety Sparsity, where safety capabilities concentrate in few experts, making them susceptible to adversarial bypassing. Meanwhile, conventional alignment methods uniformly adapt all parameters, ignoring their functional differences and inadvertently degrading performances. To address these challenges, we propose MESA (MoE Safety Alignment), a targeted alignment framework for MoE-based LLMs that strategically decentralizes safety responsibility to maximize coverage while minimizing interference with utility. Based on Optimal Transport (OT) theory, MESA operates through two mechanisms: (1) Expert Capacity Reallocation uses a transport cost matrix to distribute safety duties to the most cost-effective experts, and (2) Dynamic Routing Refinement constrains the router to precisely activate these decentralized modules. Experiments show that MESA achieves robust defensive performance against varied harmful benchmarks while preserving helpfulness. Code is available

Safe deployment of Large Language Model (LLM) agents in autonomous settings requires reliable oversight mechanisms. A central challenge is detecting scheming, where agents covertly pursue misaligned goals. One approach to mitigating such risks is LLM-based monitoring: using language models to examine agent behaviors for suspicious actions. We study constitutional black-box monitors: prompted classifiers that detect scheming using only externally observable inputs and outputs, optimized on synthetic data generated from natural-language behavior specifications. We introduce two pipelines for generating synthetic agent trajectories, STRIDE (iterative refinement) and Gloom (agent-environment simulation), from which we generate 1,000 samples each. We optimize frontier LLM monitors on these datasets via prompt sweeps, human refinement, and automated prompt optimization, and evaluate performance on 7,500 held-out trajectories from ControlArena, a suite of grounded environments where agents operate in more realistic contexts. Our results demonstrate that monitors selected purely on synthetic data can generalize to more realistic environments, capturing

The quadratic complexity of self-attention remains a bottleneck for Large Language Models (LLMs) processing ultra-long contexts. The Naive Bayes Cognitive Engine (NBCE) parallelizes long-context inference by chunking documents and routing to the lowest-entropy chunk at each decoding step. This hard-selection strategy causes semantic fragmentation during cross-chunk reasoning, as abrupt routing changes between adjacent tokens disrupt the model's contextual grounding. We present Soft-NBCE, a lightweight extension that replaces discrete chunk selection with soft entropy-weighted chunk fusion. A temperature-scaled Softmax over predictive entropies assigns continuous weights to all chunks, enabling log-space aggregation across chunk-conditioned distributions. To partially compensate for the conditional independence assumption introduced by chunking, we propose Consistency Distillation, a LoRA-based self-distillation that constrains the chunked logit distribution toward a full-context teacher via KL-divergence. On LongBench multi-hop benchmarks, Soft-NBCE with Consistency Distillation improves consistently over NBCE-style baselines (MuSiQue F1: 0.310 vs.\ 0.275 for Vanilla NBCE; HotpotQA F1: 0.479 vs.\ 0.427) while

Reward models learned from human preferences are central to aligning large language models (LLMs) via reinforcement learning from human feedback, yet they are often vulnerable to reward hacking due to noisy annotations and systematic biases such as response length or style. We propose Bayesian Non-Negative Reward Model (BNRM), a principled reward modeling framework that integrates non-negative factor analysis into Bradley-Terry (BT) preference model. BNRM represents rewards through a sparse, non-negative latent factor generative process that operates at two complementary levels: instance-specific latent variables induce disentangled reward representations, while sparsity over global latent factors acts as an implicit debiasing mechanism that suppresses spurious correlations. Together, this disentanglement-then-debiasing structure enables robust uncertainty-aware reward learning. To scale BNRM to modern LLMs, we develop an amortized variational inference network conditioned on deep model representations, allowing efficient end-to-end training. Extensive empirical results demonstrate that BNRM substantially mitigates reward over-optimization, improves robustness under distribution shifts, and

While prompt engineering is instrumental in maximizing the capabilities of Large Language Models (LLMs) during inference, the role of prompts during training remains critically underexplored. Prevailing fine-tuning paradigms typically treat training prompts as mere surface forms, assuming that semantically equivalent instructions yield identical learning outcomes. However, we reveal that this equivalence is deceptive: while paraphrased prompts often lead to comparable in-task performance, they induce drastically different cross-task impacts regarding catastrophic forgetting and generalization. Crucially, these impacts are positively correlated across tasks, indicating the existence of superior prompts that consistently yield better performance. Furthermore, we discover that these superior prompts can be robustly identified by task loss prior to learning. Leveraging these insights, we introduce State-Adaptive Prompt Optimization (SAPO), a lightweight yet effective training strategy that shifts task formulation from a static input to a dynamic, state-adaptive variable. Comprehensive experiments on diverse benchmarks confirm its effectiveness, which significantly mitigates forgetting while

Machine learning models trained on sensitive data can inadvertently leak population-level information about their training distributions -- a threat known as distribution inference attack (DIA). An adversary with black-box access can infer sensitive demographic properties, such as subgroup proportions, without observing any training data directly. While defenses such as differential privacy and property unlearning have been proposed, the link between fairness constraints and distributional leakage remains unexplored. We propose Fair Fine-tuning (FFt): a trained model is fine-tuned on samples from the complementary distribution under an Equalized Odds (EO) constraint. We provide a complete theoretical characterization, proving the tight bound $\text{Adv}(\mathcal{A},M_f) \le \Delta_{\text{EO}} \cdot W$, where $W$ quantifies how distinguishable the two training distributions are by their sensitive-attribute composition. We also establish a necessary condition for FFt to reduce adversarial advantage and prove tightness of the bound. We evaluate across six datasets spanning tabular (ACS Income, COMPAS, German Credit), image (UTKFaces),

Large language models hallucinate even when the answer lies within their parameters. While inference-time scaling can surface this latent knowledge, the most effective methods require supervision: a trained verifier or reward model. We ask what can be done with only a base language model: which intrinsic signal best identifies correct outputs, and how should it be decoded? We cast this as a score~$\times$~decoder grid pairing four scores (perplexity, contrastive, power-distribution likelihood, and self-verification) with three decoding families (optimization, sampling, consensus), and evaluate every cell on MATH500 with the base and instruction-tuned Qwen3-1.7B. While self-verification, which prompts the model to judge its own answer and is sharpened by a training-free virtual-thinking prefix, works well in most settings, no score has a fixed quality: its value depends on the decoder that consumes it and on model capability. When no supervision is available, the score and the decoding family must be chosen together.

Large language models (LLMs) are increasingly deployed as agents in dynamic real-world environments, where success depends on maintaining precise records of actions and observations. However, the resulting unbounded context growth in long-horizon agentic tasks makes two critical bottlenecks: prohibitive inference memory costs and reasoning degradation due to irrelevant information. Existing compression methods fail to fully address this, often relying on brittle heuristics or requiring parameter updates impractical for proprietary or large-scale LLMs. We introduce Agent Context Optimization (ACON), a unified framework that optimally compresses both observations and history into concise, informative representations. Distinct from prior works, ACON employs an optimization in natural language space: it iteratively refines compression guidelines based on failure analysis of the agent, ensuring critical state information is preserved without model fine-tuning. To further minimize computational overhead, we distill the optimized compressor into smaller models. Experiments on AppWorld, OfficeBench, and Multi-objective QA demonstrate that ACON reduces peak

Scaling laws for dense LLMs under infinite data are well explored, but how sparsity interacts with limited data is not. In this work, we study sparse training in data-constrained regimes where limited unique tokens require multi-epoch training. Our experiments span models up to 1.92B parameters in the fitting set, sparsity up to 93.75%, unique data budgets up to 2.6B tokens, and total training tokens up to 41.6B over 16 epochs; we further validate extrapolation on held-out dense-equivalent models up to 7.68B parameters. We find that: 1. Sparse scaling in data-limited settings: We introduce a scaling law that models loss as a function of active parameters, unique tokens, data repetition, and sparsity, accurately predicting performance across compute and data budgets. 2. Delayed data saturation: sparse training postpones diminishing returns from repeated data, making multi-epoch training more effective. 3. Resource trade-offs: With fixed data, loss-optimal sparsity is moderate ~ 50%, while compute-optimal

Safety evaluation of Large Language Models (LLMs) remains heavily English-centric, leaving Low-Resource Languages (LRLs), particularly African ones, critically underexplored. We introduce TUKABENCH, a jailbreak benchmark for seven African languages that extends JailbreakBench (JBB) beyond direct translation through four settings: human translation of JBB prompts, English adaptation to African contexts followed by human translation, human-curated prompts validated through interactions with GPT-5.2, and code-switched prompts combining English and African languages, isolating the effect of language, cultural grounding, and prompt evasiveness on model safety. Across closed and open models, prompting in African languages reduces refusal relative to English, with culturally adapted prompts leading to least refusal. The evaluation also surfaces two structural limitations: model comprehension failures and reduced LLM-as-a-judge reliability in LRLs. To capture the first, we introduce Deflection alongside Refused and Jailbroken; to assess the second, we validate outputs with human annotations, showing that judge-human agreement drops in lower-resource languages and less

Large language models (LLMs) suffer from degraded safety capabilities even when fine-tuned with benign datasets. However, existing methods for identifying safety-degrading samples in benign datasets suffer from high computational costs and significant noise issues. In this paper, we propose DataShield to efficiently and effectively identify potential safety-degrading samples. Our key intuition is based on the observation that benign fine-tuning increases the overall response compliance of LLMs. DataShield's key technical insight is to quantify each sample's contribution to the model's compliance behavior as its safety degradation score. DataShield consists of three core components: (1) Compliance Vector Extraction, which captures the LLM's compliance behavior tendency; (2) a novel Compliance-Aware Score (CAS), which automatically identifies the optimal safety-critical layer; and (3) Safety-degrading Sample Filtering, which quantifies the projection shift of training data along the compliance direction. Extensive experimental evaluation on Llama3-8B, Llama3.1-8B, and Qwen2.5-7B using the Alpaca and Dolly benign datasets validates our

Language models are increasingly used not only as standalone predictors but also as components in larger inference systems, from test-time scaling to multi-agent collaboration. We study language model networks, where pre-trained language models serve as reusable nodes and intelligence emerges from their topology, communication, and optimization. Existing systems mostly communicate through natural language: easy to deploy, but discrete, inefficient, and hard to optimize from end-task supervision. We propose LMNet, a dense and differentiable realization of this paradigm. LMNet uses stripped LLMs as vertex modules and trainable seq2seq modules as communication edges, enabling intermediate nodes to exchange dense vectors while preserving natural-language input and output at the system boundary. By bypassing intermediate embedding and de-embedding, LMNet enables efficient information transfer, end-to-end gradient optimization, and learned communication beyond hand-designed protocols. Experiments show performance with small additional training cost and effective adaptation under limited supervision.

Automated Machine Learning (AutoML) has improved access to machine learning, yet existing techniques often remain limited in flexibility, transparency, and execution reliability. Code-driven AutoML offers a promising direction by synthesizing executable code for preprocessing, model training, and evaluation. However, current LLM-based approaches frequently generate code that is plausible in text yet brittle in execution, insufficiently grounded in the actual dataset, or restricted to narrow solution paths. In this paper, we introduce iML, a multi-agent code-driven AutoML framework designed around three requirements: executability, problem grounding, and broad exploration of valid solutions. iML first analyzes the task and profiles the data, then synthesizes a structured blueprint that guides modular code generation across multiple implementation tracks, including traditional ML,pretrained adaptation, and custom neural architectures. To improve reliability, iML enforces interface checking, dynamic execution, and iterative debugging during integration. We evaluate iML on MLE-BENCH and the newly introduced iML-BENCH, covering diverse Kaggle-style tasks. On

Bias in large language models (LLMs) remains a persistent challenge, often leading to stereotyping and unfair treatment across social groups. While prior work has mainly focused on individual LLMs, the emergence of multi-agent systems (MAS), where multiple LLMs collaborate and communicate, introduces new and underexplored dynamics in how bias emerges, propagates, and amplifies. To systematically investigate these dynamics, we propose a simple evaluation framework with three agent-level metrics that quantify bias emergence, propagation, and amplification throughout multi-agent interaction. We evaluate MAS across three bias benchmarks under varying LLM backbones, social-group configurations, communication behaviors, and adversarial settings. Our results show that communication can trigger up to 70\% new bias emergence, propagate bias across over 80\% of agents, and amplify stereotypes by more than 3$\times$. We further find that denser and competitive communication generally increases bias. Finally, we demonstrate that MAS are highly vulnerable to simple bias injection attacks, and existing defense

Fitting quantitative models to data is a central step in scientific workflows, yet it remains one of the least automated. Recent agent-based systems leverage language and vision-language models (VLMs) to iteratively propose and refine statistical models, but these systems struggle on more challenging modeling tasks. To address these limitations, we introduce VESTA: Visual Exploration with Statistical Tool Agents, a framework that equips VLMs with a dynamically growing exploration toolkit to guide model refinement through data transformations, hypothesis-driven visualizations, and robust statistical tests. Unlike prior systems that rely on iterative critique alone, VESTA actively explores data before and during refinement by selecting or creating diagnostic tools, which accumulate in the model's context and can be reused later. We evaluate VESTA against established baselines in three toolkit configurations: no tools, static expert-written tools, and dynamic model-written tools. To support this evaluation, we introduce DAWN (Dataset for Automated Workflows and Numerical Modeling), a

Multi-agent debate (MAD) is widely used to improve large language model (LLM) performance through test-time scaling, yet recent work shows that vanilla MAD often underperforms simple majority vote despite higher computational cost. Studies show that, under homogeneous agents and uniform belief updates, debate preserves expected correctness and therefore cannot reliably improve outcomes. Drawing on findings from human deliberation and collective decision-making, we identify two key mechanisms missing from vanilla MAD: (i) diversity of initial viewpoints and (ii) explicit, calibrated confidence communication. We propose two lightweight interventions. First, a diversity-aware initialisation that selects a more diverse pool of candidate answers, increasing the likelihood that a correct hypothesis is present at the start of debate. Second, a confidence-modulated debate protocol in which agents express calibrated confidence and condition their updates on others' confidence. We show theoretically that diversity-aware initialisation improves the prior probability of MAD success without changing the underlying update dynamics,

Linguistic cues such as "I believe" and "probably" offer an intuitive interface for communicating confidence, yet a generalisable, principled calibration framework for linguistic confidence expressions remains underexplored. In particular, co-occurring linguistic cues, contextual variation, and subjective audience interpretation pose unique challenges. We therefore model linguistic confidence as a distribution over plausible perceived probability values that a statement is correct, capturing interpretation variability that scalar representations discard. Within this distributional framework, we introduce faithfulness as a complementary evaluation dimension and present Faithfulness Divergence (FD), an information-theoretic metric quantifying the surprise induced in audience beliefs upon truth revelation. Building on these foundations, we present Retrieval-Augmented Linguistic Calibration (RALC), a lightweight post-hoc pipeline that propagates calibrated confidence signals back into natural language via retrieval-augmented rewriting. Across three QA benchmarks and five LLM families, RALC improves in-domain faithfulness and calibration up to 66% and 58%, respectively, outperforming black-box and grey-box calibration baselines.

Large Language Model (LLM) based Chinese Grammatical Error Correction (CGEC) systems face two critical challenges: general-purpose models lack specialized linguistic priors for subtle grammatical distinctions, and Supervised Fine-Tuning (SFT) with Maximum Likelihood Estimation fails to optimize for precision-focused metrics, leading to systematic over-correction. We propose CSRP, a three-stage framework that progressively builds correction capability through Continual Pre-training (CPT) on 5.9M balanced samples to internalize domain knowledge, Chain-of-Thought SFT with explicit error reasoning for diagnostic transparency, and Group Relative Policy Optimization with a novel Efficiency-Aware Reward that explicitly penalizes unnecessary edits. On the NACGEC benchmark, CSRP achieves state-of-the-art performance with 50.99 $F_{0.5}$ and 57.17 precision, substantially outperforming previous best results while effectively mitigating the over-correction bias inherent in MLE-trained models. Our method also advances CSCD spelling correction to 59.61 F1, surpassing GPT-4 by 5.20 points. Comprehensive ablation studies demonstrate that the RL alignment stage contributes a 8\% relative gain over the

Network faults propagate layer by layer along topology and protocol dependencies, yet operations systems typically observe only symptomatic alerts at the tail end of propagation chains, where distinct root-cause faults may produce highly similar end-point symptoms. Existing approaches, whether rule-based, machine learning (ML)-based, or large language model (LLM)-based, fundamentally map the alert set to a diagnosis in a single pass and are structurally incapable of resolving this end-point ambiguity. This paper proposes PropLLM, which is the first to integrate the hop-by-hop scene reconstruction paradigm with the generative reasoning capabilities of LLMs. Starting from end-point alerts, PropLLM traces back hop-by-hop along the propagation path, retrieving verifiable factual evidence from a dual-layer knowledge graph (KG) at each hop, while the proposed Temporal Causal Propagation Attention (TCPA) mechanism encodes known topological causal priors directly into the attention computation to guide the model along the correct causal direction, ultimately localizing the root cause and