arXiv subjects

Menglin Yang

Publications and source records attributed to Menglin Yang.

At least 55 records · Page 3Linked to original sources

arXiv2026

Parameter-Efficient Fine-Tuning of LLMs with Mixture of Space Experts

Large Language Models (LLMs) have achieved remarkable progress, with Parameter-Efficient Fine-Tuning (PEFT) emerging as a key technique for downstream task adaptation. However, existing PEFT methods mainly operate in Euclidean space, fundamentally limiting their capacity to capture complex geometric structures inherent in language data. While alternative geometric spaces, like hyperbolic geometries for hierarchical data and spherical manifolds for circular patterns, offer theoretical advantages, forcing representations into a single manifold type ultimately limits expressiveness, even when curvature parameters are learnable. To address this, we propose Mixture of Space (MoS), a unified framework that leverages multiple geometric spaces simultaneously to learn richer, curvature-aware representations. Building on this scheme, we develop MoSLoRA, which extends Low-Rank Adaptation (LoRA) with heterogeneous geometric experts, enabling models to dynamically select or combine appropriate geometric spaces based on input context. Furthermore, to address the computational overhead of frequent manifold switching, we develop a lightweight routing mechanism. Moreover, we provide empirical insights into how curvature optimization impacts training stability and model performance. Our experiments across diverse benchmarks demonstrate that MoSLoRA consistently outperforms strong baselines, achieving up to 5.6% improvement on MATH500 and 15.9% on MAWPS.

cs.LG↗

arXiv2026

ABot-N0: Technical Report on the VLA Foundation Model for Versatile Embodied Navigation

Embodied navigation has long been fragmented by task-specific architectures. We introduce ABot-N0, a unified Vision-Language-Action (VLA) foundation model that achieves a ``Grand Unification'' across 5 core tasks: Point-Goal, Object-Goal, Instruction-Following, POI-Goal, and Person-Following. ABot-N0 utilizes a hierarchical ``Brain-Action'' architecture, pairing an LLM-based Cognitive Brain for semantic reasoning with a Flow Matching-based Action Expert for precise, continuous trajectory generation. To support large-scale learning, we developed the ABot-N0 Data Engine, curating 16.9M expert trajectories and 5.0M reasoning samples across 7,802 high-fidelity 3D scenes (10.7 $\text{km}^2$). ABot-N0 achieves new SOTA performance across 7 benchmarks, significantly outperforming specialized models. Furthermore, our Agentic Navigation System integrates a planner with hierarchical topological memory, enabling robust, long-horizon missions in dynamic real-world environments.

cs.RO↗

arXiv2026

Hyperbolic Fine-Tuning for Large Language Models

Large language models (LLMs) have demonstrated remarkable performance across various tasks. However, it remains an open question whether the default Euclidean space is the most suitable choice for LLMs. In this study, we investigate the geometric characteristics of LLMs, focusing specifically on tokens and their embeddings. Our findings reveal that token frequency follows a power-law distribution, where high-frequency tokens (e.g., the, that ) constitute the minority, while low-frequency tokens (e.g., apple, dog) constitute the majority. Furthermore, high-frequency tokens cluster near the origin, whereas low-frequency tokens are positioned farther away in the embedding space. Additionally, token embeddings exhibit hyperbolic characteristics, indicating a latent tree-like structure within the embedding space. Motivated by these observations, we propose HypLoRA, an efficient fine-tuning approach that operates in hyperbolic space to exploit these underlying hierarchical structures better. HypLoRA performs low-rank adaptation directly in hyperbolic space, thereby preserving hyperbolic modeling capabilities throughout the fine-tuning process. Extensive experiments across various base models and reasoning benchmarks, specifically arithmetic and commonsense reasoning tasks, demonstrate that HypLoRA substantially improves LLM performance.

cs.LG↗

arXiv2026

Beyond Retraining: Training-Free Unknown Class Filtering for Source-Free Open Set Domain Adaptation of Vision-Language Models

Vision-language models (VLMs) have gained widespread attention for their strong zero-shot capabilities across numerous downstream tasks. However, these models assume that each test image's class label is drawn from a predefined label set and lack a reliable mechanism to reject samples from emerging unknown classes when only unlabeled data are available. To address this gap, open-set domain adaptation methods retrain models to push potential unknowns away from known clusters. Yet, some unknown samples remain stably anchored to specific known classes in the VLM feature space due to semantic relevance, which is termed as Semantic Affinity Anchoring (SAA). Forcibly repelling these samples unavoidably distorts the native geometry of VLMs and degrades performance. Meanwhile, existing score-based unknown detectors use simplistic thresholds and suffer from threshold sensitivity, resulting in sub-optimal performance. To address aforementioned issues, we propose VLM-OpenXpert, which comprises two training-free, plug-and-play inference modules. SUFF performs SVD on high-confidence unknowns to extract a low-rank "unknown subspace". Each sample's projection onto this subspace is weighted and softly removed from its feature, suppressing unknown components while preserving semantics. BGAT corrects score skewness via a Box-Cox transform, then fits a bimodal Gaussian mixture to adaptively estimate the optimal threshold balancing known-class recognition and unknown-class rejection. Experiments on 9 benchmarks and three backbones (CLIP, SigLIP, ALIGN) under source-free OSDA settings show that our training-free pipeline matches or outperforms retraining-heavy state-of-the-art methods, establishing a powerful lightweight inference calibration paradigm for open-set VLM deployment.

cs.CV↗

arXiv2025

HyperbolicRAG: Enhancing Retrieval-Augmented Generation with Hyperbolic Representations

Retrieval-augmented generation (RAG) enables large language models (LLMs) to access external knowledge, helping mitigate hallucinations and enhance domain-specific expertise. Graph-based RAG enhances structural reasoning by introducing explicit relational organization that enables information propagation across semantically connected text units. However, these methods typically rely on Euclidean embeddings that capture semantic similarity but lack a geometric notion of hierarchical depth, limiting their ability to represent abstraction relationships inherent in complex knowledge graphs. To capture both fine-grained semantics and global hierarchy, we propose HyperbolicRAG, a retrieval framework that integrates hyperbolic geometry into graph-based RAG. HyperbolicRAG introduces three key designs: (1) a depth-aware representation learner that embeds nodes within a shared Poincare manifold to align semantic similarity with hierarchical containment, (2) an unsupervised contrastive regularization that enforces geometric consistency across abstraction levels, and (3) a mutual-ranking fusion mechanism that jointly exploits retrieval signals from Euclidean and hyperbolic spaces, emphasizing cross-space agreement during inference. Extensive experiments across multiple QA benchmarks demonstrate that HyperbolicRAG outperforms competitive baselines, including both standard RAG and graph-augmented baselines.

cs.CL↗

arXiv2025

Position: Beyond Euclidean -- Foundation Models Should Embrace Non-Euclidean Geometries

In the era of foundation models and Large Language Models (LLMs), Euclidean space has been the de facto geometric setting for machine learning architectures. However, recent literature has demonstrated that this choice comes with fundamental limitations. At a large scale, real-world data often exhibits inherently non-Euclidean structures, such as multi-way relationships, hierarchies, symmetries, and non-isotropic scaling, in a variety of domains, such as languages, vision, and the natural sciences. It is challenging to effectively capture these structures within the constraints of Euclidean spaces. This position paper argues that moving beyond Euclidean geometry is not merely an optional enhancement but a necessity to maintain the scaling law for the next-generation of foundation models. By adopting these geometries, foundation models could more efficiently leverage the aforementioned structures. Task-aware adaptability that dynamically reconfigures embeddings to match the geometry of downstream applications could further enhance efficiency and expressivity. Our position is supported by a series of theoretical and empirical investigations of prevalent foundation models. Finally, we outline a roadmap for integrating non-Euclidean geometries into foundation models, including strategies for building geometric foundation models via fine-tuning, training from scratch, and hybrid approaches.

cs.LG↗

arXiv2025

HELM: Hyperbolic Large Language Models via Mixture-of-Curvature Experts

Large language models (LLMs) have shown great success in text modeling tasks across domains. However, natural language exhibits inherent semantic hierarchies and nuanced geometric structure, which current LLMs do not capture completely owing to their reliance on Euclidean operations. Recent studies have also shown that not respecting the geometry of token embeddings leads to training instabilities and degradation of generative capabilities. These findings suggest that shifting to non-Euclidean geometries can better align language models with the underlying geometry of text. We thus propose to operate fully in Hyperbolic space, known for its expansive, scale-free, and low-distortion properties. We thus introduce HELM, a family of HypErbolic Large Language Models, offering a geometric rethinking of the Transformer-based LLM that addresses the representational inflexibility, missing set of necessary operations, and poor scalability of existing hyperbolic LMs. We additionally introduce a Mixture-of-Curvature Experts model, HELM-MICE, where each expert operates in a distinct curvature space to encode more fine-grained geometric structure from text, as well as a dense model, HELM-D. For HELM-MICE, we further develop hyperbolic Multi-Head Latent Attention (HMLA) for efficient, reduced-KV-cache training and inference. For both models, we develop essential hyperbolic equivalents of rotary positional encodings and RMS normalization. We are the first to train fully hyperbolic LLMs at billion-parameter scale, and evaluate them on well-known benchmarks such as MMLU and ARC, spanning STEM problem-solving, general knowledge, and commonsense reasoning. Our results show consistent gains from our HELM architectures -- up to 4% -- over popular Euclidean architectures used in LLaMA and DeepSeek, highlighting the efficacy and enhanced reasoning afforded by hyperbolic geometry in large-scale LM pretraining.

cs.LG↗

arXiv2025

Low-Rank Adaptation for Foundation Models: A Comprehensive Review

The rapid advancement of foundation modelslarge-scale neural networks trained on diverse, extensive datasetshas revolutionized artificial intelligence, enabling unprecedented advancements across domains such as natural language processing, computer vision, and scientific discovery. However, the substantial parameter count of these models, often reaching billions or trillions, poses significant challenges in adapting them to specific downstream tasks. Low-Rank Adaptation (LoRA) has emerged as a highly promising approach for mitigating these challenges, offering a parameter-efficient mechanism to fine-tune foundation models with minimal computational overhead. This survey provides the first comprehensive review of LoRA techniques beyond large Language Models to general foundation models, including recent techniques foundations, emerging frontiers and applications of low-rank adaptation across multiple domains. Finally, this survey discusses key challenges and future research directions in theoretical understanding, scalability, and robustness. This survey serves as a valuable resource for researchers and practitioners working with efficient foundation model adaptation.

cs.LG↗

arXiv2025

Thinking with Nothinking Calibration: A New In-Context Learning Paradigm in Reasoning Large Language Models

Reasoning large language models (RLLMs) have recently demonstrated remarkable capabilities through structured and multi-step reasoning. While prior research has primarily focused on improving their training and inference strategies, their potential for in-context learning (ICL) remains largely underexplored. To fill this gap, we propose Thinking with Nothinking Calibration (JointThinking), a new ICL paradigm that prompts the model to generate two answers in parallel: one in Thinking mode and the other in Nothinking mode. A second round of Thinking is triggered only when the two initial responses are inconsistent, using a single prompt with two different answers. Extensive experiments across multiple reasoning benchmarks demonstrate that JointThinking significantly outperforms few-shot chain-of-thought (CoT), thinking twice and majority voting. Moreover, it achieves comparable in-distribution performance to training-based SOTA reasoning method, while substantially outperforming on out-of-distribution tasks. We further conduct a systematic analysis of the calibration mechanism, showing the importance of structural thinking diversity and the benefits of consistency check. Additionally, we observe that the performance gap between actual and ideal reasoning narrows as model size increases in the second thinking, indicating the strong scalability of our approach. Finally, we discuss current limitations and outline promising directions for future ICL research in RLLMs.

cs.CL↗

arXiv2025

A Survey of Personalized Large Language Models: Progress and Future Directions

Large Language Models (LLMs) excel in handling general knowledge tasks, yet they struggle with user-specific personalization, such as understanding individual emotions, writing styles, and preferences. Personalized Large Language Models (PLLMs) tackle these challenges by leveraging individual user data, such as user profiles, historical dialogues, content, and interactions, to deliver responses that are contextually relevant and tailored to each user's specific needs. This is a highly valuable research topic, as PLLMs can significantly enhance user satisfaction and have broad applications in conversational agents, recommendation systems, emotion recognition, medical assistants, and more. This survey reviews recent advancements in PLLMs from three technical perspectives: prompting for personalized context (input level), finetuning for personalized adapters (model level), and alignment for personalized preferences (objective level). To provide deeper insights, we also discuss current limitations and outline several promising directions for future research. Updated information about this survey can be found at the https://github.com/JiahongLiu21/Awesome-Personalized-Large-Language-Models.

cs.AI↗

arXiv2025

Implicit Reasoning in Large Language Models: A Comprehensive Survey

Large Language Models (LLMs) have demonstrated strong generalization across a wide range of tasks. Reasoning with LLMs is central to solving multi-step problems and complex decision-making. To support efficient reasoning, recent studies have shifted attention from explicit chain-of-thought prompting toward implicit reasoning, where reasoning occurs silently via latent structures without emitting intermediate textual steps. Implicit reasoning brings advantages such as lower generation cost, faster inference, and better alignment with internal computation. Although prior surveys have discussed latent representations in the context of reasoning, a dedicated and mechanism-level examination of how reasoning unfolds internally within LLMs remains absent. This survey fills that gap by introducing a taxonomy centered on execution paradigms, shifting the focus from representational forms to computational strategies. We organize existing methods into three execution paradigms based on \textbf{\textit{how and where internal computation unfolds}}: latent optimization, signal-guided control, and layer-recurrent execution. We also review structural, behavioral and representation-based evidence that supports the presence of implicit reasoning in LLMs. We further provide a structured overview of the evaluation metrics and benchmarks used in existing works to assess the effectiveness and reliability of implicit reasoning. We maintain a continuously updated project at: https://github.com/digailab/awesome-llm-implicit-reasoning.

cs.CL↗

arXiv2025

Hypformer: Exploring Efficient Transformer Fully in Hyperbolic Space

Hyperbolic geometry have shown significant potential in modeling complex structured data, particularly those with underlying tree-like and hierarchical structures. Despite the impressive performance of various hyperbolic neural networks across numerous domains, research on adapting the Transformer to hyperbolic space remains limited. Previous attempts have mainly focused on modifying self-attention modules in the Transformer. However, these efforts have fallen short of developing a complete hyperbolic Transformer. This stems primarily from: (i) the absence of well-defined modules in hyperbolic space, including linear transformation layers, LayerNorm layers, activation functions, dropout operations, etc. (ii) the quadratic time complexity of the existing hyperbolic self-attention module w.r.t the number of input tokens, which hinders its scalability. To address these challenges, we propose, Hypformer, a novel hyperbolic Transformer based on the Lorentz model of hyperbolic geometry. In Hypformer, we introduce two foundational blocks that define the essential modules of the Transformer in hyperbolic space. Furthermore, we develop a linear self-attention mechanism in hyperbolic space, enabling hyperbolic Transformer to process billion-scale graph data and long-sequence inputs for the first time. Our experimental results confirm the effectiveness and efficiency of Hypformer across various datasets, demonstrating its potential as an effective and scalable solution for large-scale data representation and large models.

cs.LG↗

arXiv2025

Hyperbolic Graph Neural Networks: A Review of Methods and Applications

Graph representation learning in Euclidean space, despite its widespread adoption and proven utility in many domains, often struggles to effectively capture the inherent hierarchical and complex relational structures prevalent in real-world data, particularly for datasets exhibiting a highly non-Euclidean latent anatomy or power-law distributions. Hyperbolic geometry, with its constant negative curvature and exponential growth property, naturally accommodates such structures, offering a promising alternative for learning rich graph representations. This survey paper provides a comprehensive review of the rapidly evolving field of Hyperbolic Graph Learning (HGL). We systematically categorize and analyze existing methods broadly dividing them into (1) hyperbolic graph embedding-based techniques, (2) graph neural network-based hyperbolic models, and (3) emerging paradigms. Beyond methodologies, we extensively discuss diverse applications of HGL across multiple domains, including recommender systems, knowledge graphs, bioinformatics, and other relevant scenarios, demonstrating the broad applicability and effectiveness of hyperbolic geometry in real-world graph learning tasks. Most importantly, we identify several key challenges that serve as directions for advancing HGL, including handling complex data structures, developing geometry-aware learning objectives, ensuring trustworthy and scalable implementations, and integrating with foundation models, e.g., large language models. We highlight promising research opportunities in this exciting interdisciplinary area. A comprehensive repository can be found at https://github.com/digailab/awesome-hyperbolic-graph-learning.

cs.LG↗

arXiv2025

Hyperbolic Deep Learning for Foundation Models: A Survey

Foundation models pre-trained on massive datasets, including large language models (LLMs), vision-language models (VLMs), and large multimodal models, have demonstrated remarkable success in diverse downstream tasks. However, recent studies have shown fundamental limitations of these models: (1) limited representational capacity, (2) lower adaptability, and (3) diminishing scalability. These shortcomings raise a critical question: is Euclidean geometry truly the optimal inductive bias for all foundation models, or could incorporating alternative geometric spaces enable models to better align with the intrinsic structure of real-world data and improve reasoning processes? Hyperbolic spaces, a class of non-Euclidean manifolds characterized by exponential volume growth with respect to distance, offer a mathematically grounded solution. These spaces enable low-distortion embeddings of hierarchical structures (e.g., trees, taxonomies) and power-law distributions with substantially fewer dimensions compared to Euclidean counterparts. Recent advances have leveraged these properties to enhance foundation models, including improving LLMs' complex reasoning ability, VLMs' zero-shot generalization, and cross-modal semantic alignment, while maintaining parameter efficiency. This paper provides a comprehensive review of hyperbolic neural networks and their recent development for foundation models. We further outline key challenges and research directions to advance the field.

cs.LG↗

arXiv2025

Learning Along the Arrow of Time: Hyperbolic Geometry for Backward-Compatible Representation Learning

Backward compatible representation learning enables updated models to integrate seamlessly with existing ones, avoiding to reprocess stored data. Despite recent advances, existing compatibility approaches in Euclidean space neglect the uncertainty in the old embedding model and force the new model to reconstruct outdated representations regardless of their quality, thereby hindering the learning process of the new model. In this paper, we propose to switch perspectives to hyperbolic geometry, where we treat time as a natural axis for capturing a model's confidence and evolution. By lifting embeddings into hyperbolic space and constraining updated embeddings to lie within the entailment cone of the old ones, we maintain generational consistency across models while accounting for uncertainties in the representations. To further enhance compatibility, we introduce a robust contrastive alignment loss that dynamically adjusts alignment weights based on the uncertainty of the old embeddings. Experiments validate the superiority of the proposed method in achieving compatibility, paving the way for more resilient and adaptable machine learning systems.

cs.LG↗

arXiv2025

Towards Non-Euclidean Foundation Models: Advancing AI Beyond Euclidean Frameworks

In the era of foundation models and Large Language Models (LLMs), Euclidean space is the de facto geometric setting of our machine learning architectures. However, recent literature has demonstrated that this choice comes with fundamental limitations. To that end, non-Euclidean learning is quickly gaining traction, particularly in web-related applications where complex relationships and structures are prevalent. Non-Euclidean spaces, such as hyperbolic, spherical, and mixed-curvature spaces, have been shown to provide more efficient and effective representations for data with intrinsic geometric properties, including web-related data like social network topology, query-document relationships, and user-item interactions. Integrating foundation models with non-Euclidean geometries has great potential to enhance their ability to capture and model the underlying structures, leading to better performance in search, recommendations, and content understanding. This workshop focuses on the intersection of Non-Euclidean Foundation Models and Geometric Learning (NEGEL), exploring its potential benefits, including the potential benefits for advancing web-related technologies, challenges, and future directions. Workshop page: [https://hyperboliclearning.github.io/events/www2025workshop](https://hyperboliclearning.github.io/events/www2025workshop)

cs.CG↗

arXiv2025

HMamba: Hyperbolic Mamba for Sequential Recommendation

Sequential recommendation systems have become a cornerstone of personalized services, adept at modeling the temporal evolution of user preferences by capturing dynamic interaction sequences. Existing approaches predominantly rely on traditional models, including RNNs and Transformers. Despite their success in local pattern recognition, Transformer-based methods suffer from quadratic computational complexity and a tendency toward superficial attention patterns, limiting their ability to infer enduring preference hierarchies in sequential recommendation data. Recent advances in Mamba-based sequential models introduce linear-time efficiency but remain constrained by Euclidean geometry, failing to leverage the intrinsic hyperbolic structure of recommendation data. To bridge this gap, we propose Hyperbolic Mamba, a novel architecture that unifies the efficiency of Mamba's selective state space mechanism with hyperbolic geometry's hierarchical representational power. Our framework introduces (1) a hyperbolic selective state space that maintains curvature-aware sequence modeling and (2) stabilized Riemannian operations to enable scalable training. Experiments across four benchmarks demonstrate that Hyperbolic Mamba achieves 3-11% improvement while retaining Mamba's linear-time efficiency, enabling real-world deployment. This work establishes a new paradigm for efficient, hierarchy-aware sequential modeling.

cs.IR↗

arXiv2025

HyperCore: The Core Framework for Building Hyperbolic Foundation Models with Comprehensive Modules

Hyperbolic neural networks have emerged as a powerful tool for modeling hierarchical data across diverse modalities. Recent studies show that token distributions in foundation models exhibit scale-free properties, suggesting that hyperbolic space is a more suitable ambient space than Euclidean space for many pre-training and downstream tasks. However, existing tools lack essential components for building hyperbolic foundation models, making it difficult to leverage recent advancements. We introduce HyperCore, a comprehensive open-source framework that provides core modules for constructing hyperbolic foundation models across multiple modalities. HyperCore's modules can be effortlessly combined to develop novel hyperbolic foundation models, eliminating the need to extensively modify Euclidean modules from scratch and possible redundant research efforts. To demonstrate its versatility, we build and test the first fully hyperbolic vision transformers (LViT) with a fine-tuning pipeline, the first fully hyperbolic multimodal CLIP model (L-CLIP), and a hybrid Graph RAG with a hyperbolic graph encoder. Our experiments demonstrate that LViT outperforms its Euclidean counterpart. Additionally, we benchmark and reproduce experiments across hyperbolic GNNs, CNNs, Transformers, and vision Transformers to highlight HyperCore's advantages.

cs.LG↗