Computing Actual Causes for Neural Network Predictions under Structured Causal Inputs

Using Craig Interpolation for Explanation of Neural Networks (Abstract)

Semifactual Explanations for GNN-based Classification: Formal Foundations, Complexity and Computation

GENESIS: Towards Explainable Causal Discovery

Causal Discovery (CD) from observational data faces two fundamental challenges. First, purely statistical methods often lack the power to resolve structural ambiguities in low-sample regimes. Second, although LLM-assisted hybrid approaches improve structure recovery through semantic reasoning, the influence of that reasoning on individual edge decisions remains largely opaque. Consequently, existing hybrid methods fail to satisfy a fundamental requirement: explaining why a particular edge is included or excluded in the learned directed acyclic graph (DAG). This is critical in real-world applications, where no ground-truth DAG exists and every structural decision must be independently justified. We formalize this requirement as decision traceability, requiring every inferred edge to be supported by auditable statistical evidence, Markov Blanket consistency, or explicit domain reasoning. We propose GENESIS, an explainable hybrid CD framework that decomposes graph construction into interpretable decision points. GENESIS first identifies and scores three-node structural motifs, including chains, forks, and colliders, to establish transparent structural priors, then progressively refines the graph by integrating these priors with observational evidence, invoking domain knowledge only when statistical evidence is insufficient. By design, every edge decision is resolved through an auditable source of evidence. Experiments show that GENESIS achieves 100% decision traceability across all settings, establishing explainability as a first-class objective in causal discovery. Despite this additional requirement, GENESIS consistently outperforms purely statistical CD methods on the majority of benchmark datasets across all sample regimes in terms of Structural Hamming Distance (SHD), while achieving performance comparable to state-of-the-art LLM-assisted approaches.

Mechanistic Interpretability for Neural Networks: Circuits, Sparse Features and Symbolic Reasoning

This article offers a comprehensive overview of mechanistic interpretability, an emerging field that seeks to reverse-engineer the internal algorithms of modern neural networks. While traditional explainable AI methods often stop at surface-level input-output correlations, this approach directly addresses the opaque"black box"nature of machine learning models, which is essential for ensuring safety and auditability in high-stakes deployments. The paper provides a detailed examination of Transformer circuit analysis, exploring how internal components like the residual stream, attention mechanisms, and induction heads drive complex tasks and in-context learning. It subsequently tackles the core challenge of superposition and polysemanticity, demonstrating how tools like Sparse Autoencoders (SAEs) and transcoders can decompose tangled network activations into distinct, human-interpretable features. Furthermore, the paper explores methods for actively controlling and modifying model behavior through steering vectors and causal interventions. Finally, it connects these mechanistic insights with neurosymbolic AI frameworks designed to translate neural representations into explicit, executable logical rules.

Circuit Condensation: Post-Training that Concentrates a Behavior's Causal Circuit

One approach to mechanistic interpretability explains behavior through circuits: the components and connections that carry it. Frozen discovery often returns hundreds of edges, making them hard to inspect, compare, or verify exhaustively. We introduce Circuit Condensation, which post-trains models to concentrate behaviors into smaller causal graphs. Each round prunes low-attribution edges and trains a low-rank adapter to match the original through what remains, retaining the cut only if task performance and general capability survive. Across four behaviors and eight models, condensed circuits are smaller than the strongest frozen baseline in 30 of 32 settings, by $8.1\times$ on average and up to $316\times$. Repeating the search without weight updates produces larger circuits in 29 of 32 settings, showing that weight updates, rather than search alone, drive the reduction. Testing every subset of 19 circuits finds 11 that cannot be reduced and reveals removable edges in the rest. Pair ablations expose dependencies between edges, showing that their effects cannot be understood independently. On indirect object identification, condensation isolates 24 heads, 17 of them with documented roles, against 61 heads and 36 undocumented ones for the matched frozen circuit: a sufficient sub-circuit of the published mechanism rather than a reconstruction of it. The resulting circuit tracks the original model's next-token distribution and predicts its errors.

Evaluating the Inductive Abilities of Large Language Models: Why Chain-of-Thought Reasoning Sometimes Hurts More Than Helps

This work presents a theoretical framework that reveals how reasoning steps can amplify error through three failure modes: incorrect sub-task decomposition, incorrect sub-task solving, and incorrect final answer summarization, and introduces structured interventions that adapt CoT generation according to the identified failure types.