Measuring AI Reasoning: A Guide for Researchers

In this paper, we offer a guide for researchers on evaluating reasoning in language models, building the case that reasoning should be assessed through evidence of adaptive, multi-step search rather than final-answer accuracy alone. Under an evaluation-oriented definition, reasoning requires selecting intermediate steps and halting according to input-dependent conditions, which we formalize as a search-like procedure. We show that single forward passes in scalable architectures are structurally limited in their ability to realize such variable-depth computation, motivating intermediate decoding and externalized reasoning traces as appropriate evaluation interfaces. Central to our argument is that final-answer accuracy alone is an insufficient measure of reasoning, because it provides little ability to diagnose or debug the underlying processes that produce individual solutions in frontier models. We therefore argue for a shift toward process-based evaluation, in which reasoning is assessed through the faithfulness and validity of intermediate reasoning traces as first-class evaluation targets.

Cell-Based Representation of Relational Binding in Language Models

Understanding a discourse requires tracking entities and the relations that hold between them. While Large Language Models (LLMs) perform well on relational reasoning, the mechanism by which they bind entities, relations, and attributes remains unclear. We study discourse-level relational binding and show that LLMs encode it via a Cell-based Binding Representation (CBR): a low-dimensional linear subspace in which each ``cell'' corresponds to an entity--relation index pair, and bound attributes are retrieved from the corresponding cell during inference. Using controlled multi-sentence data annotated with entity and relation indices, we identify the CBR subspace by decoding these indices from attribute-token activations with Partial Least Squares regression. Across domains and two model families, the indices are linearly decodable and form a grid-like geometry in the projected space. We further find that context-specific CBR representations are related by translation vectors in activation space, enabling cross-context transfer. Finally, activation patching shows that manipulating this subspace systematically changes relational predictions and that perturbing it disrupts performance, providing causal evidence that LLMs rely on CBR for relational binding.

Hidden Failures in Robustness: Why Supervised Uncertainty Quantification Needs Better Evaluation

Recent work has shown that the hidden states of large language models contain signals useful for uncertainty estimation and hallucination detection, motivating a growing interest in efficient probe-based approaches. Yet it remains unclear how robust existing methods are, and which probe designs provide uncertainty estimates that are reliable under distribution shift. We present a systematic study of supervised uncertainty probes across models, tasks, and OOD settings, training over 2,000 probes while varying the representation layer, feature type, and token aggregation strategy. Our evaluation highlights poor robustness in current methods, particularly in the case of long-form generations. We also find that probe robustness is driven less by architecture and more by the probe inputs. Middle-layer representations generalise more reliably than final-layer hidden states, and aggregating across response tokens is consistently more robust than relying on single-token features. These differences are often largely invisible in-distribution but become more important under distribution shift. Informed by our evaluation, we explore a simple hybrid back-off strategy for improving robustness, arguing that better evaluation is a prerequisite for building more robust probes.

Linear Representations of Hierarchical Concepts in Language Models

We investigate how and to what extent hierarchical relations (e.g., Japan $\subset$ Eastern Asia $\subset$ Asia) are encoded in the internal representations of language models. Building on Linear Relational Concepts, we train linear transformations specific to each hierarchical depth and semantic domain, and characterize representational differences associated with hierarchical relations by comparing these transformations. Going beyond prior work on the representational geometry of hierarchies in LMs, our analysis covers multi-token entities and cross-layer representations. Across multiple domains we learn such transformations and evaluate in-domain generalization to unseen data and cross-domain transfer. Experiments show that, within a domain, hierarchical relations can be linearly recovered from model representations. We then analyze how hierarchical information is encoded in representation space. We find that it is encoded in a relatively low-dimensional subspace and that this subspace tends to be domain-specific. Our main result is that hierarchy representation is highly similar across these domain-specific subspaces. Overall, we find that all models considered in our experiments encode concept hierarchies in the form of highly interpretable linear representations.

Nodes Are Early, Edges Are Late: Probing Diagram Representations in Large Vision-Language Models

Large vision-language models (LVLMs) demonstrate strong performance on diagram understanding benchmarks, yet they still struggle with understanding relationships between elements, particularly those represented by nodes and directed edges (e.g., arrows and lines). To investigate the underlying causes of this limitation, we probe the internal representation of LVLMs using a carefully constructed synthetic diagram dataset based on directed graphs. Our probing experiments reveal that edge information is not linearly separable in the vision encoder and becomes linearly encoded only in the text tokens in the language model. In contrast, node information and global structural features are already linearly encoded in individual hidden states of the vision encoder. These findings suggest that the stage at which linearly separable representations are formed varies depending on the type of visual information. In particular, the delayed emergence of edge representations may help explain why LVLMs struggle with relational understanding, such as interpreting edge directions, which require more abstract, compositionally integrated processes.

WaveSSM: Multiscale State-Space Models for Non-stationary Signal Attention

State-space models (SSMs) have emerged as a powerful foundation for long-range sequence modeling, with the HiPPO framework showing that continuous-time projection operators can be used to derive stable, memory-efficient dynamical systems that encode the past history of the input signal. However, existing projection-based SSMs often rely on polynomial bases with global temporal support, whose inductive biases are poorly matched to signals exhibiting localized or transient structure. In this work, we introduce \emph{WaveSSM}, a collection of SSMs constructed over wavelet frames. Our key observation is that wavelet frames yield a localized support on the temporal dimension, useful for tasks requiring precise localization. Empirically, we show that on equal conditions, \textit{WaveSSM} outperforms orthogonal counterparts as S4 on real-world datasets with transient dynamics, including physiological signals on the PTB-XL dataset and raw audio on Speech Commands.

Sycophancy Hides Linearly in the Attention Heads

We find that correct-to-incorrect sycophancy signals are most linearly separable within multi-head attention activations. Motivated by the linear representation hypothesis, we train linear probes across the residual stream, multilayer perceptron (MLP), and attention layers to analyze where these signals emerge. Although separability appears in the residual stream and MLPs, steering using these probes is most effective in a sparse subset of middle-layer attention heads. Using TruthfulQA as the base dataset, we find that probes trained on it transfer effectively to other factual QA benchmarks. Furthermore, comparing our discovered direction to previously identified "truthful" directions reveals limited overlap, suggesting that factual accuracy, and deference resistance, arise from related but distinct mechanisms. Attention-pattern analysis further indicates that the influential heads attend disproportionately to expressions of user doubt, contributing to sycophantic shifts. Overall, these findings suggest that sycophancy can be mitigated through simple, targeted linear interventions that exploit the internal geometry of attention activations.

Can Language Models Handle a Non-Gregorian Calendar?

Temporal reasoning and knowledge are essential capabilities for language models (LMs). While much prior work has analyzed and improved temporal reasoning in LMs, most studies have focused solely on the Gregorian calendar. However, many non-Gregorian systems, such as the Japanese, Hijri, and Hebrew calendars, are in active use and reflect culturally grounded conceptions of time. If and how well current LMs can accurately handle such non-Gregorian calendars has not been evaluated so far. Here, we present a systematic evaluation of how well open-source LMs handle one such non-Gregorian system: the Japanese calendar. For our evaluation, we create datasets for four tasks that require both temporal knowledge and temporal reasoning. Evaluating a range of English-centric and Japanese-centric LMs, we find that some models can perform calendar conversions, but even Japanese-centric models struggle with Japanese-calendar arithmetic and with maintaining consistency across calendars. Our results highlight the importance of developing LMs that are better equipped for culture-specific calendar understanding.

Understanding and Controlling Repetition Neurons and Induction Heads in In-Context Learning

This paper investigates the relationship between large language models' (LLMs) ability to recognize repetitive input patterns and their performance on in-context learning (ICL). In contrast to prior work that has primarily focused on attention heads, we examine this relationship from the perspective of skill neurons, specifically repetition neurons. Our experiments reveal that the impact of these neurons on ICL performance varies depending on the depth of the layer in which they reside. By comparing the effects of repetition neurons and induction heads, we further identify strategies for reducing repetitive outputs while maintaining strong ICL capabilities.

TopK Language Models

Sparse autoencoders (SAEs) have become an important tool for analyzing and interpreting the activation space of transformer-based language models (LMs). However, SAEs suffer several shortcomings that diminish their utility and internal validity. Since SAEs are trained post-hoc, it is unclear if the failure to discover a particular concept is a failure on the SAE's side or due to the underlying LM not representing this concept. This problem is exacerbated by training conditions and architecture choices affecting which features an SAE learns. When tracing how LMs learn concepts during training, the lack of feature stability also makes it difficult to compare SAEs features across different checkpoints. To address these limitations, we introduce a modification to the transformer architecture that incorporates a TopK activation function at chosen layers, making the model's hidden states equivalent to the latent features of a TopK SAE. This approach eliminates the need for post-hoc training while providing interpretability comparable to SAEs. The resulting TopK LMs offer a favorable trade-off between model size, computational efficiency, and interpretability. Despite this simple architectural change, TopK LMs maintain their original capabilities while providing robust interpretability benefits. Our experiments demonstrate that the sparse representations learned by TopK LMs enable successful steering through targeted neuron interventions and facilitate detailed analysis of neuron formation processes across checkpoints and layers. These features make TopK LMs stable and reliable tools for understanding how language models learn and represent concepts, which we believe will significantly advance future research on model interpretability and controllability.