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Knowledge graph completion aims to infer unknown information in a knowledge graph that is incomplete, due to noisy or missing data.&lt;br/&gt;Geographic knowledge graphs, which are typically derived from crowd-sourced data, are often incomplete, making geographic knowledge graph completion an important problem.&lt;br/&gt;Most current methods for knowledge graph completion are generic, and do not account for the spatial nature of geographic knowledge graphs.&lt;br/&gt;The few methods that are tailored to geographic knowledge graphs are computationally expensive or are designed for a closed-world setting, which is not practical in the geography domain.&lt;br/&gt;We study this problem by evaluating existing state-of-the-art standard and geo-specific knowledge graph completion methods on a large dataset of geographic knowledge graphs.&lt;br/&gt;Our findings reveal that these methods perform poorly, leaving an open problem for the AI and graphs community.&lt;br/&gt;To aid in further research, we suggest some possible areas of work that we believe could lead to fruitful developments for this problem.

AAAI 2026

An Experimental Analysis of Geographic Knowledge Graph Completion Methods

krr: ontologies

dmkm: linked open data

knowledge graphs & kb completion

and temporal reasoning

krr: geometric

ml: graph-based machine learning

spatial

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Knowledge graph completion aims to infer unknown information in a knowledge graph that is incomplete, due to noisy or missing data. Geographic knowledge graphs, which are typically derived from crowd-sourced data, are often incomplete, making geographic knowledge graph completion an important problem. Most current methods for knowledge graph completion are generic, and do not account for the spatial nature of geographic knowledge graphs. The few methods that are tailored to geographic knowledge graphs are computationally expensive or are designed for a closed-world setting, which is not practical in the geography domain. We study this problem by evaluating existing state-of-the-art standard and geo-specific knowledge graph completion methods on a large dataset of geographic knowledge graphs. Our findings reveal that these methods perform poorly, leaving an open problem for the AI and graphs community. To aid in further research, we suggest some possible areas of work that we believe could lead to fruitful developments for this problem.

workshop paper

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We are pleased to announce the Fortieth AAAI Conference on Artificial Intelligence (AAAI-26), which will be held in Singapore EXPO from January 20 to January 27, 2026.

Chain-of-thought (CoT) prompting enables Large Language Models to solve complex problems, but deploying these models safely requires reliable confidence estimates—a capability where existing methods suffer from poor calibration and severe overconfidence on incorrect predictions. We propose Enhanced Dirichlet+Topology Risk (EDTR), a novel decoding strategy that combines topological analysis with Dirichlet-based uncertainty quantification to measure LLM confidence across multiple reasoning paths. EDTR treats each CoT as a vector in high-dimensional space and extracts eight topological risk features capturing the geometric structure of reasoning distributions: tighter, more coherent clusters indicate higher confidence while dispersed, inconsistent paths signal uncertainty. We evaluate EDTR against three state-of-the-art calibration methods across four diverse reasoning benchmarks spanning olympiad-level mathematics (AIME), grade school math (GSM8K), commonsense reasoning, and stock price prediction. EDTR achieves 41\% better calibration than competing methods with an average ECE of 0.287 and the best overall composite score of 0.672, while notably achieving perfect accuracy on AIME and exceptional calibration on GSM8K with an ECE of 0.107—domains where baselines exhibit severe overconfidence. Our work provides a geometric framework for understanding and quantifying uncertainty in multi-step LLM reasoning, enabling more reliable deployment where calibrated confidence estimates are essential.

Optimizing Chain-of-Thought Confidence via Topological and Dirichlet Risk Analysis

Explainable AI (XAI) methods aiming to probe model internals for scientific discovery ("RED XAI") must move beyond correlational saliency maps. We address this by presenting a systematic comparison of segmentation methods within a causal attribution framework. We contrast an object-aware approach using the Segment Anything Model (SAM) against a texture-aware baseline using SLIC superpixels. Both are integrated into a pipeline utilizing Grad-CAM for saliency, CLIP for concept labeling, and a causal validation step quantifying concept importance via counterfactual interventions (blur masking) measured by raw confidence drop. Evaluating on 200 ImageNet images, we uncover a critical sensitivity-reliability trade-off: SAM-based object-centric concepts show significantly higher average causal impact (81.0\% mean confidence drop vs. 37.7\% for SLIC), demonstrating greater sensitivity, but suffer from segmentation failures in 9.5\% of cases (181/200 successes). SLIC achieves perfect 100\% reliability (200/200 successes) and lower impact variance, albeit with reduced sensitivity. This trade-off provides actionable guidance for domain scientists: SLIC's robustness is preferable for high-stakes, texture-reliant tasks (e.g., medical diagnostics), while SAM's sensitivity may benefit exploratory analysis of object-centric phenomena. Our work offers quantitative evidence of this trade-off, enabling more informed XAI method selection for reliable scientific insight.

Causal Quantification of the Sensitivity-Reliability Trade-Off in Semantic XAI: Comparing Object-Aware (SAM) and Texture-Aware (SLIC) Segmentation

The n-body problem, fundamental to astrophysics, simulates the motion of n bodies acting under the effect of their own mutual gravitational interactions. Traditional machine learning models that are used for predicting and forecasting trajectories are often data-intensive ”black box” models, which ignore the physical laws, thereby lacking interpretability. Whereas Scientific Machine Learning ( Scientific ML ) directly embeds the known physical laws into the machine learning frame- work. Through robust modelling in the Julia programming language, our method uses the Scientific ML frameworks: Neural ordinary differential equations (NODEs) and Univer- sal differential equations (UDEs) to predict and forecast the system’s dynamics. In addition, an essential component of our analysis involves determining the ”forecasting breakdown point”, which is the smallest possible amount of training data our models need to predict future, unseen data accurately. We employ synthetically created noisy data to simulate real-world observational limitations. Our findings indicate that the UDE model is much more data efficient, needing only 20% of data for a correct forecast, whereas the Neural ODE requires 90%.

Forecasting N-Body Dynamics: A Comparative Study of Neural Ordinary Differential Equations and Universal Differential Equations

Diffusion Transformers (DiTs) have recently replaced U-Net backbones as the dominant architecture in state-of-the-art text-to-image generative models, achieving remarkable visual fidelity. However, their internal mechanisms remain largely unexplored. In this work, we investigate the emergence of high-norm activations within DiTs—tokens with unusually large magnitudes that resemble the “outlier” tokens previously identified in Vision Transformers (ViTs). Through a systematic analysis of four DiT architectures, we find that only Flux-Schnell and Pixart-sigma exhibit such activations in the image stream, primarily concentrated in the central transformer layers. Using linear probes and qualitative ablations, we show that, unlike ViT outliers, these activations do not encode global or semantic image information and their removal has negligible effect on the generation process. We refer to these as sink registers, reflecting their passive, non-semantic role. Our findings highlight an architectural divergence between ViTs and DiTs, and contribute to a deeper interpretability of diffusion-based generative models.

Diffusion Transformers use Sink Registers

Human physical reasoning relies on internal “body” representations — coarse, volumetric approximations that capture an object’s extent and support intuitive predictions about motion and physics. While psychophysical evidence suggests humans use such coarse representations, their internal structure remains largely unknown. Here we test whether vision models trained for segmentation develop comparable representations. We adapt a psychophysical experiment conducted with 50 human participants to a semantic segmentation task and test a family of seven segmentation networks, varying in size. We find that smaller models naturally form human-like coarse body representations, whereas larger models tend toward overly detailed, fine-grain encodings. Our results demonstrate that coarse representations can emerge under limited computational resources, and that machine representations can provide a scalable path toward understanding the structure of physical reasoning in the brain.

Towards Aligned Body Representations in Vision Models

Single-cell foundation models (scFMs) have demonstrated state-of-the-art performance on various tasks, such as cell-type annotation and perturbation response prediction, by learning gene regulatory networks from large-scale transcriptome data. However, a significant challenge remains: the decision-making processes of these models are less interpretable compared to traditional methods like differential gene expression analysis. Recently, transcoders have emerged as a promising approach for extracting interpretable decision circuits from large language models (LLMs). In this work, we train transcoders on all 24 layers of the cell2sentence (C2S) model, a state-of-the-art scFM, and develop systematic pipelines for biological interpretation. Our analysis reveals that over 80\% of transcoder features across most layers are biologically interpretable through Gene Set Enrichment Analysis (GSEA). Through a case study on endothelial cell classification, we demonstrate that extracted circuits correctly identify cell-type-specific genes and significantly enrich for relevant pathways (FDR = 0.0013), confirming that transcoders can uncover biologically plausible decision-making mechanisms within complex single-cell models.

Transcoder-based Circuit Analysis for Interpretable single-Cell Foundation Models

We introduce PerturbAgent, a large language model (LLM)-based multi-agent system for single-cell genetic perturbation studies. In biomedical research, understanding cellular responses to perturbations is essential for interpreting gene function and regulatory pathways in single-cell data. Existing methods focus only on either single-cell analysis pipelines or perturbation prediction models, and often lack this necessary biological interpretation. PerturbAgent addresses these limitations, targeting both analysis and prediction tasks while also generating comprehensive biological interpretations with results grounded in mechanisms, pathways, and existing knowledge. We further propose MAST++, a general framework that evaluates agentic performance across profile, reasoning, perception, interaction, and memory, and complement it with biological validity assessments. On public single-cell Perturb-seq and RNA-seq datasets, PerturbAgent reliably achieves high task completion and delivers citation-backed biological summaries, representing progress toward practical and interpretable agent workflows for scientific discovery.

PerturbAgent: An Agentic AI system for Analysis and Prediction of Genetic Perturbations

Transformer-based language models excel at both recall (retrieving memorized facts) and reasoning (performing multistep inference), yet it remains unclear whether these functions rely on overlapping or separable internal circuits. Understanding these mechanisms is critical for building trustworthy and scientifically interpretable AI systems.We address this question through mechanistic interpretability, using controlled linguistic puzzles to probe transformer models at the layer, head, and neuron levels. By combining layer-wise activation tracing, attention-head specialization metrics, and causal activation patching, we identify subnetworks whose perturbation selectively disrupts either factual retrieval or reasoning. Across the Qwen, LLaMA-3 and Mistral families, we find a consistent pattern: the early and middle layers primarily support recall, while the deeper layers and specific MLP pathways enable reasoning. Interventions in distinct components lead to selective impairments: Disabling identified recall circuits reduces the factual precision by up to 15 % while leaving the reasoning intact, while disabling reasoning circuits yields a comparable drop in multistep inference. These findings offer causal, interpretable evidence that recall and reasoning arise from partially distinct but complementary computational processes, advancing the mechanistic foundations of explainable AI.

Disentangling Recall and Reasoning in Transformer Models through Layer-wise Attention and Activation Analysis

There is a substantial body of literature examining the mathematical reasoning capabilities of large language models (LLMs), particularly their performance on precise arithmetic operations in autoregressive architectures. However, their ability to perform approximate reasoning in informal, fast-paced mathematical operations has received far less attention, especially among non-autoregressive decoder models. Our work addresses this gap by introducing StreetMath, a benchmark designed to evaluate models’ approximation abilities under real-world approximation scenarios. We conduct extensive evaluations across different LLM architectures: Qwen3-4B-Instruct-2507, Qwen3-4B-Thinking-2507, Dream-v0-Instruct-7B, Falcon-Mamba-7B-Instruct, and Mamba-GPT-3B. Furthermore, we apply mechanistic interpretability techniques to probe their internal computational states. Our analysis reveals that LLMs generally attempt to compute exact values or invoke external tools even in tasks that call for approximation. Moreover, while models sometimes reach the correct answer in early layers or steps, they still consume more tokens when solving approximation tasks. Additional experiments indicate that exact and approximate arithmetic operations rely on largely separate neural components. Drawing upon research on cognitive psychology, we argue that LLMs do not exhibit cognitive miserliness in the same way humans do in street math settings. We open source our work https://anonymous.4open.science/r/StreetMath-1/

StreetMath: Understanding How LLMs Approximate Mathematical Reasoning

Retrieval-Augmented Generation (RAG) systems enhance large language models (LLMs) by grounding responses in external evidence, mitigating hallucinations, and enabling access to up-to-date, domain-specific knowledge. However, existing RAG frameworks often suffer from unstable self-supervised optimization signals and inconsistent factual grounding. We introduce CREAM-RAG (Consistency-Regularized Enhanced Augmented Model for RAG), a unified framework that integrates retrieval, Direct Preference Optimization (DPO)-based self-reward reinforcement learning, and a consistency regularization objective to stabilize reward dynamics during fine-tuning. By enforcing alignment between multiple retrieved contexts and generated responses, CREAM-RAG improves factual faithfulness and semantic coherence without external supervision. Empirical evaluations on the LLaMA-2-7B model demonstrate that CREAM-RAG achieves a 35.04% average improvement over the base model across reasoning and factuality benchmarks, highlighting its effectiveness in reducing hallucinations and enhancing retrieval-grounded reasoning.

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Optimizing Chain-of-Thought Confidence via Topological and Dirichlet Risk Analysis

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