Detecting Differences Is Not Understanding Structure: Large Language Models Fail at Graph Isomorphism

Large language models (LLMs) have shown impressive performance on diverse reasoning tasks, yet their capacity for structural reasoning in graphs remains unclear. We investigate whether LLMs can genuinely understand graph isomorphism -a fundamental problem in graph theory. While LLMs achieve near-perfect accuracy on isomorphism detection, we show this performance is illusory. When identical graphs are presented with permuted node labels, LLMs fail to identify their isomorphism. This finding suggests that LLMs exploit patterns rather than reasoning about abstract graph structure. Since permutation invariance is a fundamental requirement for valid structural reasoning, these results indicate that success on graph reasoning benchmarks should not be interpreted as evidence of genuine topological understanding.

Beyond Translation: Evaluating Mathematical Reasoning Capabilities of LLMs in Sinhala and Tamil

Large language models (LLMs) demonstrate strong mathematical reasoning in English, but whether these capabilities reflect genuine multilingual reasoning or reliance on translation-based processing in low-resource languages like Sinhala and Tamil remains unclear. We examine this fundamental question by evaluating whether LLMs genuinely reason mathematically in these languages or depend on implicit translation to English-like representations. Using a taxonomy of six math problem types, from basic arithmetic to complex unit conflict and optimization problems, we evaluate four prominent large language models. To avoid translation artifacts that confound language ability with translation quality, we construct a parallel dataset where each problem is natively authored by fluent speakers with mathematical training in all three languages. Our analysis demonstrates that while basic arithmetic reasoning transfers robustly across languages, complex reasoning tasks show significant degradation in Tamil and Sinhala. The pattern of failures varies by model and problem type, suggesting that apparent multilingual competence may not reflect uniform reasoning capabilities across languages. These findings challenge the common assumption that models exhibiting strong multilingual performance can reason equally effectively across languages, and highlight the need for fine-grained, type-aware evaluation in multilingual settings.

Orthogonal Activation with Implicit Group-Aware Bias Learning for Class Imbalance

Class imbalance is a common challenge in machine learning and data mining, often leading to suboptimal performance in classifiers. While deep learning excels in feature extraction, its performance still deteriorates under imbalanced data. In this work, we propose a novel activation function, named OGAB, designed to alleviate class imbalance in deep learning classifiers. OGAB incorporates orthogonality and group-aware bias learning to enhance feature distinguishability in imbalanced scenarios without explicitly requiring label information. Our key insight is that activation functions can be used to introduce strong inductive biases that can address complex data challenges beyond traditional non-linearity. Our work demonstrates that orthogonal transformations can preserve information about minority classes by maintaining feature independence, thereby preventing the dominance of majority classes in the embedding space. Further, the proposed group-aware bias mechanism automatically identifies data clusters and adjusts embeddings to enhance class separability without the need for explicit supervision. Unlike existing approaches that address class imbalance through preprocessing data modifications or post-processing corrections, our proposed approach tackles class imbalance during the training phase at the embedding learning level, enabling direct integration with the learning process. We demonstrate the effectiveness of our solution on both real-world and synthetic imbalanced datasets, showing consistent performance improvements over both traditional and learnable activation functions.

Deep Learning Meets Oversampling: A Learning Framework to Handle Imbalanced Classification

Despite extensive research spanning several decades, class imbalance is still considered a profound difficulty for both machine learning and deep learning models. While data oversampling is the foremost technique to address this issue, traditional sampling techniques are often decoupled from the training phase of the predictive model, resulting in suboptimal representations. To address this, we propose a novel learning framework that can generate synthetic data instances in a data-driven manner. The proposed framework formulates the oversampling process as a composition of discrete decision criteria, thereby enhancing the representation power of the model's learning process. Extensive experiments on the imbalanced classification task demonstrate the superiority of our framework over state-of-the-art algorithms.