Syntactic Blind Spots: How Misalignment Leads to LLMs Mathematical Errors

Large Language Models (LLMs) demonstrate strong mathematical problem-solving abilities but frequently fail on problems that deviate syntactically from their training distribution. We identify a systematic failure mode, syntactic blind spots, in which models misapply familiar reasoning strategies to problems that are semantically straightforward but phrased in unfamiliar ways. These errors are not due to gaps in mathematical competence, but rather reflect a brittle coupling between surface form and internal representation. To test this, we rephrase incorrectly answered questions using syntactic templates drawn from correct examples. These rephrasings, which preserve semantics while reducing structural complexity, often lead to correct answers. We quantify syntactic complexity using a metric based on Dependency Locality Theory (DLT), and show that higher DLT scores are associated with increased failure rates across multiple datasets. Our findings suggest that many reasoning errors stem from structural misalignment rather than conceptual difficulty, and that syntax-aware interventions can reveal and mitigate these inductive failures.

Optimizing Latent Dimension Allocation in Hierarchical VAEs: Balancing Attenuation and Information Retention for OOD Detection

Out-of-distribution (OOD) detection is a critical task in machine learning, particularly for safety-critical applications where unexpected inputs must be reliably flagged. While hierarchical variational autoencoders (HVAEs) offer improved representational capacity over traditional VAEs, their performance is highly sensitive to how latent dimensions are distributed across layers. Existing approaches often allocate latent capacity arbitrarily, leading to ineffective representations or posterior collapse. In this work, we introduce a theoretically grounded framework for optimizing latent dimension allocation in HVAEs, drawing on principles from information theory to formalize the trade-off between information loss and representational attenuation. We prove the existence of an optimal allocation ratio $r^{\ast}$ under a fixed latent budget, and empirically show that tuning this ratio consistently improves OOD detection performance across datasets and architectures. Our approach outperforms baseline HVAE configurations and provides practical guidance for principled latent structure design, leading to more robust OOD detection with deep generative models.

"CASE: Contrastive Activation for Saliency Estimation

Saliency methods are widely used to visualize which input features are deemed relevant to a model's prediction. However, their visual plausibility can obscure critical limitations. In this work, we propose a diagnostic test for class sensitivity: a method's ability to distinguish between competing class labels on the same input. Through extensive experiments, we show that many widely used saliency methods produce nearly identical explanations regardless of the class label, calling into question their reliability. We find that class-insensitive behavior persists across architectures and datasets, suggesting the failure mode is structural rather than model-specific. Motivated by these findings, we introduce CASE, a contrastive explanation method that isolates features uniquely discriminative for the predicted class. We evaluate CASE using the proposed diagnostic and a perturbation-based fidelity test, and show that it produces faithful and more class-specific explanations than existing methods.