Answering the Unanswerable Is to Err Knowingly: Analyzing and Mitigating Abstention Failures in Large Reasoning Models

Large reasoning models (LRMs) have shown remarkable progress on complex reasoning tasks. However, some questions posed to LRMs are inherently unanswerable, such as math problems lacking sufficient conditions. We find that LRMs continually fail to provide appropriate abstentions when confronted with these unanswerable questions. In this paper, we systematically analyze, investigate, and resolve this issue for trustworthy AI. We first conduct a detailed analysis of the distinct response behaviors of LRMs when facing unanswerable questions. Then, we show that LRMs possess sufficient cognitive capabilities to recognize the flaws in these questions. However, they fail to exhibit appropriate abstention behavior, revealing a misalignment between their internal cognition and external response. Finally, to resolve this issue, we propose a lightweight, two-stage method that combines cognitive monitoring with inference-time intervention. Experimental results demonstrate that our method significantly improves the abstention rate while maintaining the overall reasoning performance.

Provable Low-Frequency Bias of In-Context Learning of Representations

In-context learning (ICL) enables large language models (LLMs) to acquire new behaviors from the input sequence alone without any parameter updates. Recent studies have shown that ICL can surpass the original meaning learned in pretraining stage through internalizing the structure the data-generating process (DGP) of the prompt into the hidden representations. However, the mechanisms by which LLMs achieve this ability is left open. In this paper, we present the first rigorous explanation of such phenomena by introducing a unified framework of double convergence, where hidden representations converge both over context and across layers. This double convergence process leads to an implicit bias towards smooth (low-frequency) representations, which we prove analytically and verify empirically. Our theory explains several open empirical observations, including why learned representations exhibit globally structured but locally distorted geometry, and why their total energy decays without vanishing. Moreover, our theory predicts that ICL has an intrinsic robustness towards high-frequency noise, which we empirically confirm. These results provide new insights into the underlying mechanisms of ICL, and a theoretical foundation to study it that hopefully extends to more general data distributions and settings.

Behave Your Motion: Habit-preserved Cross-category Animal Motion Transfer

Animal motion embodies species-specific behavioral habits, making the transfer of motion across categories a critical yet complex task for applications in animation and virtual reality. Existing motion transfer methods, primarily focused on human motion, emphasize skeletal alignment (motion retargeting) or stylistic consistency (motion style transfer), often neglecting the preservation of distinct habitual behaviors in animals. To bridge this gap, we propose a novel habit-preserved motion transfer framework for cross-category animal motion. Built upon a generative framework, our model introduces a habit-preservation module with category-specific habit encoder, allowing it to learn motion priors that capture distinctive habitual characteristics. Furthermore, we integrate a large language model (LLM) to facilitate the motion transfer to previously unobserved species. To evaluate the effectiveness of our approach, we introduce the DeformingThings4D-skl dataset, a quadruped dataset with skeletal bindings, and conduct extensive experiments and quantitative analyses, which validate the superiority of our proposed model.

What Happens During the Loss Plateau? Understanding Abrupt Learning in Transformers

Training Transformers on algorithmic tasks frequently demonstrates an intriguing abrupt learning phenomenon: an extended performance plateau followed by a sudden, sharp improvement. This work investigates the underlying mechanisms for such dynamics, primarily in shallow Transformers. We reveal that during the plateau, the model often develops an interpretable partial solution while simultaneously exhibiting a strong repetition bias in their outputs. This output degeneracy is accompanied by internal representation collapse, where hidden states across different tokens become nearly parallel. We further identify the slow learning of optimal attention maps as a key bottleneck. Hidden progress in attention configuration during the plateau precedes the eventual rapid convergence, and directly intervening on attention significantly alters plateau duration and the severity of repetition bias and representational collapse. We validate that these identified phenomena-repetition bias and representation collapse-are not artifacts of toy setups but also manifest in the early pre-training stage of large language models like Pythia and OLMo.

Hypercube-RAG: Hypercube-Based Retrieval-Augmented Generation for In-domain Scientific Question-Answering

Large language models (LLMs) often need to incorporate external knowledge to solve theme-specific problems. Retrieval-augmented generation (RAG), which empowers LLMs to generate more qualified responses with retrieved external data and knowledge, has shown its high promise. However, traditional semantic similarity-based RAGs struggle to return concise yet highly relevant information for domain knowledge-intensive tasks, such as scientific question-answering (QA). Built on a multi-dimensional (cube) structure called Hypercube, which can index documents in an application-driven, human-defined, multi-dimensional space, we introduce the Hypercube-RAG, a novel RAG framework for precise and efficient retrieval. Given a query, Hypercube-RAG first decomposes it based on its entities and topics and then retrieves relevant documents from cubes by aligning these decomposed components with hypercube dimensions. Experiments on three in-domain scientific QA datasets demonstrate that our method improves accuracy by 3.7% and boosts retrieval efficiency by 81.2%, measured as relative gains over the strongest RAG baseline. More importantly, our Hypercube-RAG inherently offers explainability by revealing the underlying predefined hypercube dimensions used for retrieval. The code and data sets are available at https://github.com/JimengShi/Hypercube-RAG.

When Can Large Reasoning Models Save Thinking? Mechanistic Analysis of Behavioral Divergence in Reasoning

Large reasoning models (LRMs) have significantly advanced performance on complex tasks, yet their tendency to overthink introduces inefficiencies. This study investigates the internal mechanisms of reinforcement learning (RL)-trained LRMs when prompted to save thinking, revealing three distinct thinking modes: no thinking (NT), explicit thinking (ET), and implicit thinking (IT). Through comprehensive analysis of confidence in thinking termination, attention from thinking to generation, and attentional focus on input sections, we uncover key factors influencing the reasoning behaviors. We further find that NT reduces output length at the cost of accuracy, while ET and IT maintain accuracy with reduced response length. Our findings expose fundamental inconsistencies in RL-optimized LRMs, necessitating adaptive improvements for reliable efficiency.

Let Me Grok for You: Accelerating Grokking via Embedding Transfer from a Weaker Model

''Grokking'' is a phenomenon where a neural network first memorizes training data and generalizes poorly, but then suddenly transitions to near-perfect generalization after prolonged training. While intriguing, this delayed generalization phenomenon compromises predictability and efficiency. Ideally, models should generalize directly without delay. To this end, this paper proposes GrokTransfer, a simple and principled method for accelerating grokking in training neural networks, based on the key observation that data embedding plays a crucial role in determining whether generalization is delayed. GrokTransfer first trains a smaller, weaker model to reach a nontrivial (but far from optimal) test performance. Then, the learned input embedding from this weaker model is extracted and used to initialize the embedding in the target, stronger model. We rigorously prove that, on a synthetic XOR task where delayed generalization always occurs in normal training, GrokTransfer enables the target model to generalize directly without delay. Moreover, we demonstrate that, across empirical studies of different tasks, GrokTransfer effectively reshapes the training dynamics and eliminates delayed generalization, for both fully-connected neural networks and Transformers.

Do We Truly Need So Many Samples? Multi-LLM Repeated Sampling Efficiently Scales Test-Time Compute

This paper presents a simple, effective, and cost-efficient strategy to improve LLM performance by scaling test-time compute. Our strategy builds upon the repeated-sampling-then-voting framework, with a novel twist: incorporating multiple models, even weaker ones, to leverage their complementary strengths that potentially arise from diverse training data and paradigms. By using consistency as a signal, our strategy dynamically switches between models. Theoretical analysis highlights the efficiency and performance advantages of our strategy. Extensive experiments on six datasets demonstrate that our strategy not only outperforms self-consistency and state-of-the-art multi-agent debate approaches, but also significantly reduces inference costs. Additionally, ModelSwitch requires only a few comparable LLMs to achieve optimal performance and can be extended with verification methods, demonstrating the potential of leveraging multiple LLMs in the generation-verification paradigm.

HyperGCT: A Dynamic Hyper-GNN-Learned Geometric Constraint for 3D Registration

Geometric constraints between feature matches are critical in 3D point cloud registration problems. Existing approaches typically model unordered matches as a consistency graph and sample consistent matches to generate hypotheses. However, explicit graph construction introduces noise, posing great challenges for handcrafted geometric constraints to render consistency among matches. To overcome this, we propose HyperGCT, a flexible dynamic Hyper-GNN-learned geometric constraint that leverages high-order consistency among 3D correspondences. To our knowledge, HyperGCT is the first method that mines robust geometric constraints from dynamic hypergraphs for 3D registration. By dynamically optimizing the hypergraph through vertex and edge feature aggregation, HyperGCT effectively captures the correlations among correspondences, leading to accurate hypothesis generation. Extensive experiments on 3DMatch, 3DLoMatch, KITTI-LC, and ETH show that HyperGCT achieves state-of-the-art performance. Furthermore, our method is robust to graph noise, demonstrating a significant advantage in terms of generalization. The code will be released.

Building Machine Learning Challenges for Anomaly Detection in Science

Scientific discoveries are often made by finding a pattern or object that was not predicted by the known rules of science. Oftentimes, these anomalous events or objects that do not conform to the norms are an indication that the rules of science governing the data are incomplete, and something new needs to be present to explain these unexpected outliers. The challenge of finding anomalies can be confounding since it requires codifying a complete knowledge of the known scientific behaviors and then projecting these known behaviors on the data to look for deviations. When utilizing machine learning, this presents a particular challenge since we require that the model not only understands scientific data perfectly but also recognizes when the data is inconsistent and out of the scope of its trained behavior. In this paper, we present three datasets aimed at developing machine learning-based anomaly detection for disparate scientific domains covering astrophysics, genomics, and polar science. We present the different datasets along with a scheme to make machine learning challenges around the three datasets findable, accessible, interoperable, and reusable (FAIR). Furthermore, we present an approach that generalizes to future machine learning challenges, enabling the possibility of large, more compute-intensive challenges that can ultimately lead to scientific discovery.