Causal Manifold Fairness: Enforcing Geometric Invariance in Representation Learning

Fairness in machine learning is increasingly critical, yet standard approaches often treat data as static points in a high-dimensional space, ignoring the underlying generative structure. We posit that sensitive attributes (e.g., race, gender) do not merely shift data distributions but causally warp the geometry of the data manifold itself. To address this, we introduce Causal Manifold Fairness (CMF), a novel framework that bridges causal inference and geometric deep learning. CMF learns a latent representation where the local Riemannian geometry, defined by the metric tensor and curvature, remains invariant under counterfactual interventions on sensitive attributes. By enforcing constraints on the Jacobian and Hessian of the decoder, CMF ensures that the rules of the latent space (distances and shapes) are preserved across demographic groups. We validate CMF on synthetic Structural Causal Models (SCMs), demonstrating that it effectively disentangles sensitive geometric warping while preserving task utility, offering a rigorous quantification of the fairness-utility trade-off via geometric metrics.

Temporal Graph Network: Hallucination Detection in Multi-Turn Conversation

Hallucinations can be produced by conversational AI systems, particularly in multi-turn conversations where context changes and contradictions may eventually surface. By representing the entire conversation as a temporal graph, we present a novel graph-based method for detecting dialogue-level hallucinations. Our framework models each dialogue as a node, encoding it using a sentence transformer. We explore two different ways of connectivity: i) shared-entity edges, which connect turns that refer to the same entities; ii) temporal edges, which connect contiguous turns in the conversation. Message-passing is used to update the node embeddings, allowing flow of information between related nodes. The context-aware node embeddings are then combined using attention pooling into a single vector, which is then passed on to a classifier to determine the presence and type of hallucinations. We demonstrate that our method offers slightly improved performance over existing methods. Further, we show the attention mechanism can be used to justify the decision making process. The code and model weights are made available at: https://github.com/sambuaneesh/anlp-project.

Achieving Fair PCA Using Joint Eigenvalue Decomposition

Principal Component Analysis (PCA) is a widely used method for dimensionality reduction, but it often overlooks fairness, especially when working with data that includes demographic characteristics. This can lead to biased representations that disproportionately affect certain groups. To address this issue, our approach incorporates Joint Eigenvalue Decomposition (JEVD), a technique that enables the simultaneous diagonalization of multiple matrices, ensuring fair and efficient representations. We formally show that the optimal solution of JEVD leads to a fair PCA solution. By integrating JEVD with PCA, we strike an optimal balance between preserving data structure and promoting fairness across diverse groups. We demonstrate that our method outperforms existing baseline approaches in fairness and representational quality on various datasets. It retains the core advantages of PCA while ensuring that sensitive demographic attributes do not create disparities in the reduced representation.