Spectral Rank Certification for Foundation Model Adapters

Nominal LoRA rank is a design parameter; calibrated spectral evidence is a separate inferential quantity. This article develops a finite-sample framework for inferring effective rank structure in public foundation-model adapters. The theoretical core is an exact chi-square divergence for the fixed-dimensional Gaussian rank-one reference experiment, with an unknown signal direction integrated under a rotation-invariant reference prior. The resulting series yields a computable finite-sample Le Cam bound at concrete layer sizes, an explicit remainder bound for numerical truncation, and the rectangular Baik-Ben Arous-Peche (BBP) limit. A compact-manifold Laplace expansion shows that finite-sample likelihood evidence also depends on leading spectral gaps through the factor $s_1^{|m-n|}\prod_{i\ge2}(s_1^2-s_i^2)$, motivating joint calibration of clustered singular values. Building on these results, we introduce an empirical-null workflow for PEFT LoRA adapters: factor reconstruction, Monte Carlo $p$-values, stagewise and block testing, and module-wise and corpus-level BH reporting. In an audit of 26 public adapters, 684 modules, six architecture families, and 31,770 public-checkpoint spectra rows, calibrated effective rank is typically much smaller than nominal rank and differs systematically from 95\% energy retention. A measured RoBERTa-RTE slice on $n=24$ examples illustrates the measurement path from calibrated ranks to task evaluation, without treating the slice as a utility study. The main empirical finding is that calibrated effective rank is usually far below nominal rank, and that energy retention and statistical surprise answer different questions.

Large Language Models for Low-Resource Languages: A Conceptual Framework for an Electronic Explanatory Dictionary of the Tajik Language

This paper presents a conceptual framework for developing an electronic explanatory dictionary of the Tajik language using large language models (LLMs). The relevance of the work stems from the absence of a comprehensive digital lexicographic resource for Tajik that is comparable in functionality to dictionaries for high-resource languages, and from the limited adaptation of modern natural language processing technologies to low-resource language systems. Based on a systematic survey of existing linguistic, statistical, and corpus resources, we propose a dictionary architecture that integrates modules for morphological analysis, lemmatization, semantic clustering, and dictionary entry generation using LLMs. The choice of subword tokenization is justified by the agglutinative nature of Tajik morphology and its high morphological variability, along with a parameter-efficient fine-tuning (PEFT) strategy suitable for limited annotated data. The novelty of the work lies in proposing the first holistic conceptual architecture of an explanatory dictionary for Tajik that unifies classical lexicographic methods, language statistics, and generative capabilities of LLMs into a single system. The practical significance of the study is the formation of a methodological foundation for developing a full-featured electronic dictionary that can serve both as a lexicographic tool and as a core resource for machine translation, automatic summarization, sentiment analysis, and other applied NLP tasks. The paper is intended for specialists in computational linguistics, lexicography, and developers of natural language processing systems working with low-resource languages.

Point Ladder Tuning: Parameter-Efficient Hierarchical Adaptation for 3D Point Cloud Understanding

Fine-tuning pre-trained point-cloud backbones typically updates all parameters, resulting in substantial computation and memory overhead. More importantly, modern point backbones rely on aggressive tokenization and downsampling, which yields compact global tokens but irreversibly discards fine-grained local geometry, an inherent bottleneck for parameter-efficient adaptation. Consequently, existing PEFT methods that operate only on these coarsened tokens can modulate global semantics but struggle to recover the missing multi-scale locality. We present Point Ladder Tuning (PLT), a locality-aware PEFT framework that performs hierarchical, instance-conditioned adaptation while keeping the backbone frozen. PLT forms a lightweight closed loop: (i) a Hierarchical Ladder Network (HLN) constructs a multi-resolution local feature pyramid directly from raw points; (ii) a Local-Global Fusion (LGF) aligns and fuses local pyramids with intermediate backbone semantics; and (iii) a Dynamic Prompt Generator produces instance-aware multi-scale prompts to modulate the frozen backbone effectively. For dense prediction, we further introduce a lightweight segmentation head that progressively upsamples fused features and leverages backbone priors to refine fine structures. Extensive experiments on classification and dense prediction show that PLT consistently surpasses prior PEFT baselines with minimal tunable parameters. PLT achieves state-of-the-art performance using only 2.71% trainable parameters for classification and 7.69% for dense prediction, and scales favorably to larger backbones, requiring merely 0.36% parameters on PointGPT-L. The code is released at https://github.com/JunLinChang/ECCV2026-PLT.

Chebyshev Manifold Adaptation

The paper presents a new parameter-efficient adaptation method called ChebyMA (Chebyshev Manifold Adaptation). ChebyMA adopts weight matrices through a multi-surface superposition of Chebyshev polynomial bases evaluated on learnable coordinates and combined via trainable coefficient matrices, replacing standard linear projections with highly expressive continuous function approximation. Theoretically, we establish an Approximation Expressivity Theorem, proving from the perspective of function approximation theory that single-manifold ChebyMA guarantees convergence in Frobenius norm error of reconstruction. Besides, drawing on Kolmogorov $n$-width intuition, we demonstrate the expressive advantages of multi-manifold superposition ($S > 1$) in decoupling high-dimensional complex features. Experimental results on Computer Vision CIFAR datasets(CIFAR-10, CIFAR-100)\cite{CIFAR} and Natural Language Processing (AG News, SST-2) datasets demonstrate that ChebyMA consistently achieves a superior parameter-accuracy Pareto front compared to standard full-parameter fine-tuning, LoRA\cite{LoRA}, TLoRA\cite{TLoRA}, and StelLA\cite{StelLA}. ChebyMA significantly outperforms other tested methods in tested datasets, validating its solid theoretical foundation for generality with purely vectorized computations.

ARIADNE: Agnostic Routing for Inference-time Adapter DyNamic sElection

The increasing deployment of parameter-efficient fine-tuning (PEFT) has led to model ecosystems in which a single backbone is paired with many task-specialized adapters. In this setting, inference-time queries often arrive without task labels, requiring the system to automatically select the most appropriate adapter from a growing and heterogeneous adapter pool. Existing routing methods either depend on access to adapter internals, such as weight decompositions or gradient-based statistics, or require additional router training, which limits scalability and portability as new adapters are added. We introduce ARIADNE, a training-free, adapter-agnostic routing framework for dynamic adapter selection at inference time. ARIADNE represents each adapter through a set of centroids computed from embeddings of its training set, capturing the data distribution associated with that adapter. Given an unlabeled input, it selects an adapter by measuring proximity to these centroids in latent space. Because routing is performed entirely in the input embedding space, ARIADNE is compatible with arbitrary PEFT methods and requires no modification to the adapters or training procedures. Primarily evaluated with Llama 3.2 1B Instruct on 23 diverse NLP tasks, ARIADNE recovers 97.44% of the upper bound performance. Scaling to 44 tasks, it achieves 89.7% average selection accuracy, without additional training or access to adapter internals.

The Fine-Tuning Trap: Evaluating Negative Transfer and the Role of PEFT in Sub-1B Mathematical Reasoning

Deploying Small Language Models (SLMs) on edge devices requires efficient fine-tuning strategies that adapt models to new tasks without degrading their general capabilities. In this study, we benchmark five sub-1B models (135M-1B) on mathematical reasoning tasks and uncover a critical vulnerability: Full Fine-Tuning (Full FT) actively harms performance in models under 300M parameters, often dropping accuracy below zero-shot baselines. This "negative transfer" makes Parameter-Efficient Fine-Tuning (PEFT) not just an efficiency preference, but a stability requirement. We find that while Low-Rank Adaptation (LoRA) and Weight-Decomposed LoRA (DoRA) perform comparably, their strengths vary by task; DoRA excels in complex reasoning (GSM8K), while LoRA dominates pattern matching (OrcaMath). In particular, Full FT is outperformed by LoRA on aligned models (Qwen2.5-0.5B) and even by simple 5-shot In-Context Learning on the smallest architectures (SmolLM2-135M). Based on these findings, we recommend defaulting to PEFT for all aligned sub-1B models and caution against Full FT for any architecture smaller than 500M parameters to prevent catastrophic forgetting. Reproduction of this work can be found at https://github.com/gulguluu/tiny-slm-finetune-compare.

EPM-RL: Reinforcement Learning for On-Premise Product Mapping in E-Commerce

Product mapping, the task of deciding whether two e-commerce listings refer to the same product, is a core problem for price monitoring and channel visibility. In real marketplaces, however, sellers frequently inject promotional keywords, platform-specific tags, and bundle descriptions into titles, causing the same product to appear under many different names. Recent LLM-based and multi-agent frameworks improve robustness and interpretability on such hard cases, but they often rely on expensive external APIs, repeated retrieval, and complex inference-time orchestration, making large-scale deployment costly and difficult in privacy-sensitive enterprise settings. To address these issues, we present EPM-RL, a reinforcement-learning-based framework for building an accurate and efficient on-premise e-commerce product mapping model. Our central idea is to distill high-cost agentic reasoning into a trainable in-house model. Starting from a curated set of product pairs with LLM-generated rationales and human verification, we first perform parameter-efficient fine-tuning (PEFT) on a small student model using structured reasoning outputs. We then further optimize the model with Reinforcement Learning (RL) using an agent-based reward that jointly evaluates output-format compliance, label correctness, reasoning--preference scores from specially designed judge models. Preliminary results show that EPM-RL consistently improves over PEFT-only training and offers a stronger quality--cost trade-off than commercial API-based baselines, while enabling private deployment and lower operational cost. These findings suggest that reinforcement learning can turn product mapping from a high-latency agentic pipeline into a scalable, inspectable, and production-ready in-house system.