Machine unlearning offers a promising solution to privacy and safety concerns in large language models (LLMs) by selectively removing targeted knowledge while preserving utility. However, current methods are highly sensitive to downstream fine-tuning, which can quickly recover forgotten information-even from unrelated tasks. To address this, we introduce invariance into unlearning for the first time, inspired by invariant risk minimization (IRM). Building on this principle, we propose invariant LLM unlearning (ILU), a regularization-based framework that enhances robustness. Notably, ILU generalizes well to diverse fine-tuning tasks, even when trained using a single dataset. A task vector analysis is also provided to further elucidate the rationale behind ILU's effectiveness. Extensive experiments on the WMDP and MUSE benchmark, reveal that ILU significantly outperforms state-of-the-art unlearning methods, including negative preference optimization (NPO) and representation misdirection for unlearning (RMU). Notably, ILU achieves superior unlearning robustness across diverse downstream fine-tuning scenarios (e.g., math, paraphrase detection, and sentiment analysis) while preserving the fine-tuning performance.

Despite significant progress in transformer interpretability, an understanding of the computational mechanisms of large language models (LLMs) remains a fundamental challenge. Many approaches interpret a network's hidden representations but remain agnostic about how those representations are generated. We address this by mapping LLM inference for a given input sequence to an equivalent and interpretable linear system which reconstructs the predicted output embedding with relative error below $10^{-13}$ at double floating-point precision, requiring no additional model training. We exploit a property of transformers wherein every operation (gated activations, attention, and normalization) can be expressed as $A(x) \cdot x$, where $A(x)$ represents an input-dependent linear transform and $x$ preserves the linear pathway. To expose this linear structure, we strategically detach components of the gradient computation with respect to an input sequence, freezing the $A(x)$ terms at their values computed during inference, such that the Jacobian yields an equivalent linear mapping. This detached Jacobian of the model reconstructs the output with one linear operator per input token, which is shown for Qwen 3, Gemma 3 and Llama 3, up to Qwen 3 14B. These linear representations demonstrate that LLMs operate in extremely low-dimensional subspaces where the singular vectors can be decoded to interpretable semantic concepts. The computation for each intermediate output also has a linear equivalent, and we examine how the linear representations of individual layers and their attention and multilayer perceptron modules build predictions, and use these as steering operators to insert semantic concepts into unrelated text. Despite their global nonlinearity, LLMs can be interpreted through equivalent linear representations that reveal low-dimensional semantic structures in the next-token prediction process.

Large language models (LLMs) trained via reinforcement learning with verifiable reward (RLVR) have achieved breakthroughs on tasks with explicit, automatable verification, such as software programming and mathematical problems. Extending RLVR to electronic design automation (EDA), especially automatically generating hardware description languages (HDLs) like Verilog from natural-language (NL) specifications, however, poses three key challenges: the lack of automated and accurate verification environments, the scarcity of high-quality NL-code pairs, and the prohibitive computation cost of RLVR. To this end, we introduce CodeV-R1, an RLVR framework for training Verilog generation LLMs. First, we develop a rule-based testbench generator that performs robust equivalence checking against golden references. Second, we propose a round-trip data synthesis method that pairs open-source Verilog snippets with LLM-generated NL descriptions, verifies code-NL-code consistency via the generated testbench, and filters out inequivalent examples to yield a high-quality dataset. Third, we employ a two-stage "distill-then-RL" training pipeline: distillation for the cold start of reasoning abilities, followed by adaptive DAPO, our novel RLVR algorithm that can reduce training cost by adaptively adjusting sampling rate. The resulting model, CodeV-R1-7B, achieves 68.6% and 72.9% pass@1 on VerilogEval v2 and RTLLM v1.1, respectively, surpassing prior state-of-the-art by 12~20%, while even exceeding the performance of 671B DeepSeek-R1 on RTLLM. We have released our model, training code, and dataset to facilitate research in EDA and LLM communities.

Large language models excel at many tasks but often incur high inference costs during deployment. To mitigate hallucination, many systems use a knowledge graph to enhance retrieval-augmented generation (KG-RAG). However, the large amount of retrieved knowledge contexts increase these inference costs further. A promising solution to balance performance and cost is LLM routing, which directs simple queries to smaller LLMs and complex ones to larger LLMs. However, no dedicated routing methods currently exist for RAG, and existing training-based routers face challenges scaling to this domain due to the need for extensive training data. We observe that the score distributions produced by the retrieval scorer strongly correlate with query difficulty. Based on this, we propose an extremely simple yet effective routing framework, the first specifically designed for KG-RAG that efficiently balances performance and cost in a plug-and-play manner. It delivers over 3x higher routing effectiveness while reducing runtime to less than 0.001x compared to existing methods. Our code is available at https://github.com/hrwang00/SkewRoute.

The application of rule-based reinforcement learning (RL) to multimodal large language models (MLLMs) introduces unique challenges and potential deviations from findings in text-only domains, particularly for perception-heavy tasks. This paper provides a comprehensive study of rule-based visual RL, using jigsaw puzzles as a structured experimental framework. Jigsaw puzzles offer inherent ground truth, adjustable difficulty, and demand complex decision-making, making them ideal for this study. Our research reveals several key findings: \textit{Firstly,} we find that MLLMs, initially performing near to random guessing on the simplest jigsaw puzzles, achieve near-perfect accuracy and generalize to complex, unseen configurations through fine-tuning. \textit{Secondly,} training on jigsaw puzzles can induce generalization to other visual tasks, with effectiveness tied to specific task configurations. \textit{Thirdly,} MLLMs can learn and generalize with or without explicit reasoning, though open-source models often favor direct answering. Consequently, even when trained for step-by-step reasoning, they can ignore the thinking process in deriving the final answer. \textit{Fourthly,} we observe that complex reasoning patterns appear to be pre-existing rather than emergent, with their frequency increasing alongside training and task difficulty. \textit{Finally,} our results demonstrate that RL exhibits more effective generalization than Supervised Fine-Tuning (SFT), and an initial SFT cold start phase can hinder subsequent RL optimization. Although these observations are based on jigsaw puzzles and may vary across other visual tasks, this research contributes a valuable piece of jigsaw to the larger puzzle of collective understanding rule-based visual RL and its potential in multimodal learning. The code is available at: https://github.com/zifuwanggg/Jigsaw-R1

Autoregressive language models (LMs) generate one token at a time, yet human reasoning operates over higher-level abstractions - sentences, propositions, and concepts. This contrast raises a central question- Can LMs likewise learn to reason over structured semantic units rather than raw token sequences? In this work, we investigate whether pretrained LMs can be lifted into such abstract reasoning spaces by building on their learned representations. We present a framework that adapts a pretrained token-level LM to operate in sentence space by autoregressively predicting continuous embeddings of next sentences. We explore two embedding paradigms inspired by classical representation learning: 1) semantic embeddings, learned via autoencoding to preserve surface meaning; and 2) contextual embeddings, trained via next-sentence prediction to encode anticipatory structure. We evaluate both under two inference regimes: Discretized, which decodes each predicted embedding into text before re-encoding; and Continuous, which reasons entirely in embedding space for improved efficiency. Across four domains - mathematics, logic, commonsense, and planning - contextual embeddings under continuous inference show competitive performance with Chain-of-Thought (CoT) while reducing inference-time FLOPs on average by half. We also present early signs of scalability and modular adaptation. Finally, to visualize latent trajectories, we introduce SentenceLens, a diagnostic tool that decodes intermediate model states into interpretable sentences. Together, our results indicate that pretrained LMs can effectively transition to abstract, structured reasoning within latent embedding spaces.

As AI systems increasingly navigate applications in healthcare, law, and governance, understanding how they handle ethically complex scenarios becomes critical. Previous work has mainly examined the moral judgments in large language models (LLMs), rather than their underlying moral reasoning process. In contrast, we focus on a large-scale analysis of the moral reasoning traces provided by LLMs. Furthermore, unlike prior work that attempted to draw inferences from only a handful of moral dilemmas, our study leverages over 600 distinct trolley problems as probes for revealing the reasoning patterns that emerge within different LLMs. We introduce and test a taxonomy of moral rationales to systematically classify reasoning traces according to two main normative ethical theories: consequentialism and deontology. Our analysis reveals that LLM chains-of-thought tend to favor deontological principles based on moral obligations, while post-hoc explanations shift notably toward consequentialist rationales that emphasize utility. Our framework provides a foundation for understanding how LLMs process and articulate ethical considerations, an important step toward safe and interpretable deployment of LLMs in high-stakes decision-making environments. Our code is available at https://github.com/keenansamway/moral-lens .

While large reasoning models demonstrate strong performance on complex tasks, they lack the ability to adjust reasoning token usage based on task difficulty. This often leads to the "overthinking" problem -- excessive and unnecessary reasoning -- which, although potentially mitigated by human intervention to control the token budget, still fundamentally contradicts the goal of achieving fully autonomous AI. In this work, we propose Adaptive Reasoning Model (ARM), a reasoning model capable of adaptively selecting appropriate reasoning formats based on the task at hand. These formats include three efficient ones -- Direct Answer, Short CoT, and Code -- as well as a more elaborate format, Long CoT. To train ARM, we introduce Ada-GRPO, an adaptation of Group Relative Policy Optimization (GRPO), which addresses the format collapse issue in traditional GRPO. Ada-GRPO enables ARM to achieve high token efficiency, reducing tokens by an average of 30%, and up to 70%, while maintaining performance comparable to the model that relies solely on Long CoT. Furthermore, not only does it improve inference efficiency through reduced token generation, but it also brings a 2x speedup in training. In addition to the default Adaptive Mode, ARM supports two additional reasoning modes: 1) Instruction-Guided Mode, which allows users to explicitly specify the reasoning format via special tokens -- ideal when the appropriate format is known for a batch of tasks. 2) Consensus-Guided Mode, which aggregates the outputs of the three efficient formats and resorts to Long CoT in case of disagreement, prioritizing performance with higher token usage.

Temporal reasoning and planning are essential capabilities for large language models (LLMs), yet most existing benchmarks evaluate them in isolation and under limited forms of complexity. To address this gap, we introduce the Temporal Constraint-based Planning (TCP) benchmark that jointly assesses both capabilities. Each instance in TCP features a naturalistic dialogue around a collaborative project, where diverse and interdependent temporal constraints are explicitly or implicitly expressed, and models must infer an optimal schedule that satisfies all constraints. To construct TCP, we generate abstract problem prototypes that are then paired with realistic scenarios from various domains and enriched into dialogues using an LLM. A human quality check is performed on a sampled subset to confirm the reliability of our benchmark. We evaluate state-of-the-art LLMs and find that even the strongest models may struggle with TCP, highlighting its difficulty and revealing limitations in LLMs' temporal constraint-based planning abilities. We analyze underlying failure cases, open source our benchmark, and hope our findings can inspire future research.

Spatio-Temporal Graph Neural Networks (STGNNs) have emerged as a powerful tool for modeling dynamic graph-structured data across diverse domains. However, they often fail to generalize in Spatio-Temporal Out-of-Distribution (STOOD) scenarios, where both temporal dynamics and spatial structures evolve beyond the training distribution. To address this problem, we propose an innovative Spatio-Temporal Retrieval-Augmented Pattern Learning framework,STRAP, which enhances model generalization by integrating retrieval-augmented learning into the STGNN continue learning pipeline. The core of STRAP is a compact and expressive pattern library that stores representative spatio-temporal patterns enriched with historical, structural, and semantic information, which is obtained and optimized during the training phase. During inference, STRAP retrieves relevant patterns from this library based on similarity to the current input and injects them into the model via a plug-and-play prompting mechanism. This not only strengthens spatio-temporal representations but also mitigates catastrophic forgetting. Moreover, STRAP introduces a knowledge-balancing objective to harmonize new information with retrieved knowledge. Extensive experiments across multiple real-world streaming graph datasets show that STRAP consistently outperforms state-of-the-art STGNN baselines on STOOD tasks, demonstrating its robustness, adaptability, and strong generalization capability without task-specific fine-tuning.