OpenRaiser/Intern-Atlas huggingface dataset:
Which Heads Matter for Reasoning? RL-Guided KV Cache Compression
Venue: arXiv cs.CL 2026
Year: 2026

Reasoning large language models exhibit complex reasoning behaviors via extended chain-of-thought generation that are highly fragile to information loss during decoding, creating critical challenges for KV cache compression. Existing token-dropping methods directly disrupt reasoning chains by removing intermediate steps, while head-reallocation methods, designed for retrieval tasks, fail to preserve the heads essential for generative reasoning. However, no existing method can identify which attention heads genuinely maintain reasoning consistency and control generation termination. To address this, we propose RLKV, which uses reinforcement learning as a probe to discover which heads contribute to reasoning quality by directly optimizing their cache usage against actual generation outcomes. This discovery naturally leads to an efficient compression strategy: we allocate full KV cache to reasoning-critical heads while aggressively compressing others. Experiments reveal that a fraction of heads proves essential for reasoning, enabling 20--50% cache reduction with near-lossless performance and up to 1.21x speedup.
On the optimization dynamics of RLVR: Gradient gap and step size thresholds
Venue: arXiv cs.LG 2026
Year: 2026

Reinforcement Learning with Verifiable Rewards (RLVR), which uses simple binary feedback to post-train large language models, has found significant empirical success. However, a principled understanding of why it works is lacking. This paper builds a theoretical foundation for RLVR by analyzing its training process at both the full-response (trajectory) and token levels. Central to our analysis is a new quantity called the Gradient Gap, which formalizes the direction of improvement from low-reward to high-reward regions of the response space. We prove that convergence critically depends on aligning the update direction with this Gradient Gap. Moreover, we derive a sharp step-size threshold based on the magnitude of the Gradient Gap: below it, learning converges, whereas above it, performance collapses. Our theory further predicts how the critical step size must scale with response length and the success rate, thereby explaining why practical heuristics such as length normalization improve stability and showing that, with a fixed learning rate, the success rate can stagnate strictly below $100\%$. Importantly, our theory holds flexibly for any policy-gradient algorithm and so characterizes the dynamics of popular approaches such as REINFORCE and GRPO. We validate these predictions through controlled bandit simulations and language model experiments on post-training Qwen2.5-Math-7B with GRPO.
Who Said Neural Networks Aren't Linear?
Venue: arXiv cs.LG 2026
Year: 2026

Neural networks are famously nonlinear. However, linearity is defined relative to a pair of vector spaces, $f:X \to Y$. Leveraging the algebraic concept of transport of structure, we propose a method to explicitly identify non-standard vector spaces where a neural network acts as a linear operator. When sandwiching a linear operator $A$ between two invertible neural networks, $f(x)=g_y^{-1}(A g_x(x))$, the corresponding vector spaces $X$ and $Y$ are induced by newly defined addition and scaling actions derived from $g_x$ and $g_y$. We term this kind of architecture a Linearizer. This framework makes the entire arsenal of linear algebra, including SVD, pseudo-inverse, orthogonal projection and more, applicable to nonlinear mappings. Furthermore, we show that the composition of two Linearizers that share a neural network is also a Linearizer. We leverage this property and demonstrate that training diffusion models using our architecture makes the hundreds of sampling steps collapse into a single step. We further utilize our framework to enforce idempotency (i.e. $f(f(x))=f(x)$) on networks leading to a globally projective generative model and to demonstrate modular style transfer.
LadderSym: A Multimodal Interleaved Transformer for Music Practice Error Detection
Venue: arXiv cs.SD 2026
Year: 2026

Music learners can greatly benefit from tools that accurately detect errors in their practice. Existing approaches typically compare audio recordings to music scores using heuristics or learnable models. This paper introduces LadderSym, a novel Transformer-based method for music error detection. LadderSym is guided by two key observations about the state-of-the-art approaches: (1) late fusion limits inter-stream alignment and cross-modality comparison capability; and (2) reliance on score audio introduces ambiguity in the frequency spectrum, degrading performance in music with concurrent notes. To address these limitations, LadderSym introduces (1) a two-stream encoder with inter-stream alignment modules to improve audio comparison capabilities and error detection F1 scores, and (2) a multimodal strategy that leverages both audio and symbolic scores by incorporating symbolic representations as decoder prompts, reducing ambiguity and improving F1 scores. We evaluate our method on the MAESTRO-E and CocoChorales-E datasets by measuring the F1 score for each note category. Compared to the previous state of the art, LadderSym more than doubles F1 for missed notes on MAESTRO-E (26.8% -> 56.3%) and improves extra note detection by 14.4 points (72.0% -> 86.4%). Similar gains are observed on CocoChorales-E. Furthermore, we also evaluate our models on real data we curated. This work introduces insights about comparison models that could inform sequence evaluation tasks for reinforcement learning, human skill assessment, and model evaluation. Code: https://github.com/ben2002chou/LadderSYM
RAG4Tickets: AI-Powered Ticket Resolution via Retrieval-Augmented Generation on JIRA and GitHub Data
Venue: arXiv cs.SE 2026
Year: 2026

Modern software teams frequently encounter delays in resolving recurring or related issues due to fragmented knowledge scattered across JIRA tickets, developer discussions, and GitHub pull requests (PRs). To address this challenge, we propose a Retrieval-Augmented Generation (RAG) framework that integrates Sentence-Transformers for semantic embeddings with FAISS-based vector search to deliver context-aware ticket resolution recommendations. The approach embeds historical JIRA tickets, user comments, and linked PR metadata to retrieve semantically similar past cases, which are then synthesized by a Large Language Model (LLM) into grounded and explainable resolution suggestions. The framework contributes a unified pipeline linking JIRA and GitHub data, an embedding and FAISS indexing strategy for heterogeneous software artifacts, and a resolution generation module guided by retrieved evidence. Experimental evaluation using precision, recall, resolution time reduction, and developer acceptance metrics shows that the proposed system significantly improves resolution accuracy, fix quality, and knowledge reuse in modern DevOps environments.
Thinking Longer, Not Always Smarter: Evaluating LLM Capabilities in Hierarchical Legal Reasoning
Venue: arXiv cs.CL 2026
Year: 2026

Case-based reasoning is a cornerstone of U.S. legal practice, requiring professionals to argue about a current case by drawing analogies to and distinguishing from past precedents. While Large Language Models (LLMs) have shown remarkable capabilities, their proficiency in this complex, nuanced form of reasoning needs further investigation. We propose a formal framework that decomposes the process of identifying significant distinctions between cases into three-stage reasoning tasks. Our framework models cases using factual predicates called factors, organizes them into a legal knowledge hierarchy, and defines verifiable rules for identifying distinctions, analyzing their argumentative support, and evaluating their significance. Through comprehensive evaluation of modern reasoning LLMs, we reveal a paradox: while models achieve high accuracy on surface-level reasoning (Task 1), performance degrades on hierarchical reasoning (Task 2: 64.82%-92.09%) and collapses on integrated analysis (Task 3: 11.46%-33.99%). Most strikingly, we find that models consistently expend more computational resources on incorrect responses than correct ones, suggesting that "thinking longer" does not always mean "thinking smarter." Our work provides a methodology for fine-grained analysis of LLM reasoning capabilities in complex domains and reveals fundamental limitations that must be addressed for robust and trustworthy legal AI.
Coordinates from Context: Using LLMs to Ground Complex Location References
Venue: arXiv cs.CL 2026
Year: 2026

Geocoding is the task of linking a location reference to an actual geographic location and is essential for many downstream analyses of unstructured text. In this paper, we explore the challenging setting of geocoding compositional location references. Building on recent work demonstrating LLMs' abilities to reason over geospatial data, we evaluate LLMs' geospatial knowledge versus reasoning skills relevant to our task. Based on these insights, we propose an LLM-based strategy for geocoding compositional location references. We show that our approach improves performance for the task and that a relatively small fine-tuned LLM can achieve comparable performance with much larger off-the-shelf models.
Pattern Enhanced Multi-Turn Jailbreaking: Exploiting Structural Vulnerabilities in Large Language Models
Venue: arXiv cs.CL 2026
Year: 2026

Large language models (LLMs) remain vulnerable to multi-turn jailbreaking attacks that exploit conversational context to bypass safety constraints gradually. These attacks target different harm categories through distinct conversational approaches. Existing multi-turn methods often rely on heuristic or ad hoc exploration strategies, providing limited insight into underlying model weaknesses. The relationship between conversation patterns and model vulnerabilities across harm categories remains poorly understood. We propose Pattern Enhanced Chain of Attack (PE-CoA), a framework of five conversation patterns to construct multi-turn jailbreaks through natural dialogue. Evaluating PE-CoA on twelve LLMs spanning ten harm categories, we achieve state-of-the-art performance, uncovering pattern-specific vulnerabilities and LLM behavioral characteristics: models exhibit distinct weakness profiles, defense to one pattern does not generalize to others, and model families share similar failure modes. These findings highlight limitations of safety training and indicate the need for pattern-aware defenses. Code available on: https://github.com/Ragib-Amin-Nihal/PE-CoA
LitE-SQL: A Lightweight and Efficient Text-to-SQL Framework with Vector-based Schema Linking and Execution-Guided Self-Correction
Venue: arXiv cs.CL 2026
Year: 2026

The Text-to-SQL task translates natural language questions into SQL queries, enabling intuitive database interaction for non-experts. While recent methods leveraging Large Language Models (LLMs) achieve strong performance, their reliance on proprietary models raise concerns about deployment feasibility and data privacy. In this work, we introduce LitE-SQL, a Lightweight and Efficient framework with two components: (i) a Schema Retriever that performs efficient schema linking using a vector database of pre-computed schema embeddings, optimized with a hard-negative supervised contrastive objective to distinguish semantically similar but functionally irrelevant columns, and (ii) a SQL Generator fine-tuned in two stages-supervised fine-tuning followed by execution-guided reinforcement-enabling execution-guided self-correction without multi-candidate sampling, which is commonly required by prior LLM-based approaches. On BIRD, LitE-SQL achieves 72.10% execution accuracy, and on Spider 1.0 it reaches 88.45%, demonstrating comparable or superior performance to LLM-based methods despite using 2x to 30x fewer parameters. Our findings demonstrate that high-quality Text-to-SQL generation is feasible with lightweight models, offering a practical solution for privacy-sensitive and resource-constrained settings.
Hierarchical Semantic RL: Tackling the Problem of Dynamic Action Space for RL-based Recommendations
Venue: arXiv cs.IR 2026
Year: 2026

Recommender Systems (RS) are fundamental to modern online services. While most existing approaches optimize for short-term engagement, recent work has begun to explore reinforcement learning (RL) to model long-term user value. However, these efforts face significant challenges due to the vast, dynamic action spaces inherent in RS, which hinder stable policy learning. To resolve this bottleneck, we introduce Hierarchical Semantic RL (HSRL), which reframes RL-based recommendation over a fixed Semantic Action Space (SAS). HSRL encodes items as Semantic IDs (SIDs) for policy learning, and maps SIDs back to their original items via a fixed lookup during execution. To align decision-making with SID generation, the Hierarchical Policy Network (HPN) operates in a coarse-to-fine manner, employing hierarchical residual state modeling to refine each level's context from the previous level's residual, thereby reducing representation-decision mismatch. In parallel, a Multi-level Critic (MLC) provides token-level value estimates, enabling fine-grained credit assignment. Across public benchmarks and a large-scale production dataset from a leading short-video advertising platform, HSRL consistently surpasses state-of-the-art baselines. In online deployment over a 7-day A/B testing, it delivers an 18.421% ADVV lift and a 1.251% increase in Revenue, supporting HSRL as a scalable paradigm for RL-based recommendation.
One Sentence, Two Embeddings: Contrastive Learning of Explicit and Implicit Semantic Representations
Venue: arXiv cs.CL 2026
Year: 2026

Sentence embedding methods have made remarkable progress, yet they still struggle to capture the implicit semantics within sentences. This can be attributed to the inherent limitations of conventional sentence embedding methods that assign only a single vector per sentence. To overcome this limitation, we propose DualCSE, a sentence embedding method that assigns two embeddings to each sentence: one representing the explicit semantics and the other representing the implicit semantics. These embeddings coexist in the shared space, enabling the selection of the desired semantics for specific purposes such as information retrieval and text classification. Experimental results demonstrate that DualCSE can effectively encode both explicit and implicit meanings and improve the performance of the downstream task.
What Do Temporal Graph Learning Models Learn?
Venue: arXiv cs.LG 2026
Year: 2026

Learning on temporal graphs has become a central topic in graph representation learning, with numerous benchmarks indicating the strong performance of state-of-the-art models. However, recent work has raised concerns about the reliability of benchmark results, noting issues with commonly used evaluation protocols and the surprising competitiveness of simple heuristics. This contrast raises the question of which characteristics of the underlying graphs temporal graph learning models actually use to form their predictions. We address this by systematically evaluating eight models on their ability to capture eight fundamental characteristics related to the link structure of temporal graphs. These include structural characteristics such as density, temporal patterns such as recency, and edge formation mechanisms such as homophily. Using both synthetic and real-world datasets, we analyze how well models learn these characteristics. Our findings reveal a mixed picture: models capture some characteristics well but fail to reproduce others. With this, we expose important limitations. Overall, we believe that our results provide practical insights for the application of temporal graph learning models and motivate more interpretability-driven evaluations in graph learning research.
Bandits with Single-Peaked Preferences and Limited Resources
Venue: arXiv cs.LG 2026
Year: 2026

We study an online stochastic matching problem in which an algorithm sequentially matches $U$ users to $K$ arms, aiming to maximize cumulative reward over $T$ rounds under budget constraints. Without structural assumptions, computing the optimal matching is NP-hard, making online learning computationally infeasible. To overcome this barrier, we focus on single-peaked preferences -- a well-established structure in social choice theory, where users' preferences are unimodal with respect to a common order over arms. We devise an efficient algorithm for the offline budgeted matching problem, and leverage it into an efficient online algorithm with a regret of $\tilde O(UKT^{2/3})$. Our approach relies on a novel PQ tree-based order approximation method. If the single-peaked structure is known, we develop an efficient UCB-like algorithm that achieves a regret bound of $\tilde O(U\sqrt{TK})$.
WUGNECTIVES: Novel Entity Inferences of Language Models from Discourse Connectives
Venue: arXiv cs.CL 2026
Year: 2026

The role of world knowledge has been particularly crucial to predict the discourse connective that marks the discourse relation between two arguments, with language models (LMs) being generally successful at this task. We flip this premise in our work, and instead study the inverse problem of understanding whether discourse connectives can inform LMs about the world. To this end, we present WUGNECTIVES, a dataset of 8,880 stimuli that evaluates LMs' inferences about novel entities in contexts where connectives link the entities to particular attributes. On investigating 17 different LMs at various scales, and training regimens, we found that tuning an LM to show reasoning behavior yields noteworthy improvements on most connectives. At the same time, there was a large variation in LMs' overall performance across connective type, with all models systematically struggling on connectives that express a concessive meaning. Our findings pave the way for more nuanced investigations into the functional role of language cues as captured by LMs. We release WUGNECTIVES at https://github.com/kanishkamisra/wugnectives
The Geometry of Reasoning: Flowing Logics in Representation Space
Venue: arXiv cs.AI 2026
Year: 2026

We study how large language models (LLMs) ``think'' through their representation space. We propose a novel geometric framework that models an LLM's reasoning as flows -- embedding trajectories evolving where logic goes. We disentangle logical structure from semantics by employing the same natural deduction propositions with varied semantic carriers, allowing us to test whether LLMs internalize logic beyond surface form. This perspective connects reasoning with geometric quantities such as position, velocity, and curvature, enabling formal analysis in representation and concept spaces. Our theory establishes: (1) LLM reasoning corresponds to smooth flows in representation space, and (2) logical statements act as local controllers of these flows' velocities. Using learned representation proxies, we design controlled experiments to visualize and quantify reasoning flows, providing empirical validation of our theoretical framework. Our findings indicate that training solely via next-token prediction can lead LLMs to internalize logical invariants as higher-order geometry in representation space, challenging the ``stochastic parrot'' argument. Experiments across Qwen and LLaMA model families further suggest the presence of a general, possibly universal, representational law underlying machine understanding and human linguistic regularities, largely independent of specific training recipes or model architectures. Our work serves as both a conceptual foundation and practical tools for studying reasoning phenomena, offering a new lens for interpretability and formal analysis of LLMs' behavior.
Mapping Semantic & Syntactic Relationships with Geometric Rotation
Venue: arXiv cs.CL 2026
Year: 2026

Understanding how language and embedding models encode semantic relationships is fundamental to model interpretability. While early word embeddings exhibited intuitive vector arithmetic (''king'' - ''man'' + ''woman'' = ''queen''), modern high-dimensional text representations lack straightforward interpretable geometric properties. We introduce Rotor-Invariant Shift Estimation (RISE), a geometric approach that represents semantic-syntactic transformations as consistent rotational operations in embedding space, leveraging the manifold structure of modern language representations. RISE operations have the ability to operate across both languages and models without reducing performance, suggesting the existence of analogous cross-lingual geometric structure. We compare and evaluate RISE using two baseline methods, three embedding models, three datasets, and seven morphologically diverse languages in five major language groups. Our results demonstrate that RISE consistently maps discourse-level semantic-syntactic transformations with distinct grammatical features (e.g., negation and conditionality) across languages and models. This work provides the first demonstration that discourse-level semantic-syntactic transformations correspond to consistent geometric operations in multilingual embedding spaces, empirically supporting the linear representation hypothesis at the sentence level.
Probabilistic bias adjustment of seasonal predictions of Arctic Sea Ice Concentration
Venue: arXiv cs.LG 2026
Year: 2026

Seasonal forecast of Arctic sea ice concentration is key to mitigate the negative impact and assess potential opportunities posed by the rapid decline of sea ice coverage. Seasonal prediction systems based on climate models often show systematic biases and complex spatio-temporal errors that grow with the forecasts. Consequently, operational predictions are routinely bias corrected and calibrated using retrospective forecasts. For predictions of Arctic sea ice concentration, error corrections are mainly based on one-to-one post-processing methods including climatological mean or linear regression correction and, more recently, machine learning. Such deterministic adjustments are confined at best to the limited number of costly-to-run ensemble members of the raw forecast. However, decision-making requires proper quantification of uncertainty and likelihood of events, particularly of extremes. We introduce a probabilistic error correction framework based on a conditional Variational Autoencoder model to map the conditional distribution of observations given the biased model prediction. This method naturally allows for generating large ensembles of adjusted forecasts. We evaluate our model using deterministic and probabilistic metrics and show that the adjusted forecasts are better calibrated, closer to the observational distribution, and have smaller errors than climatological mean adjusted forecasts.
PairSem: LLM-Guided Pairwise Semantic Matching for Scientific Document Retrieval
Venue: arXiv cs.IR 2026
Year: 2026

Scientific document retrieval is a critical task for enabling knowledge discovery and supporting research across diverse domains. However, existing dense retrieval methods often struggle to capture fine-grained scientific concepts in texts due to their reliance on holistic embeddings and limited domain understanding. Recent approaches leverage large language models (LLMs) to extract fine-grained semantic entities and enhance semantic matching, but they typically treat entities as independent fragments, overlooking the multi-faceted nature of scientific concepts. To address this limitation, we propose Pairwise Semantic Matching (PairSem), a framework that represents relevant semantics as entity-aspect pairs, capturing complex, multi-faceted scientific concepts. PairSem is unsupervised, base retriever-agnostic, and plug-and-play, enabling precise and context-aware matching without requiring query-document labels or entity annotations. Extensive experiments on multiple datasets and retrievers demonstrate that PairSem significantly improves retrieval performance, highlighting the importance of modeling multi-aspect semantics in scientific information retrieval.