Vedant Jawandhia

Vedant Jawandhia, Daksh Ahuja, Ghufran Alam Siddiqui et al.

We propose PURGE, a machine unlearning algorithm built on a simple but an under-exploited observation: continual learning (CL) and machine unlearning (MU) which are fundamentally dual problems. CL tries to learn new tasks without forgetting old ones; MU tries to erase specific data without hurting retained performance representing the same underlying tension in opposite directions. PURGE leverages this duality by adapting gradient projection from A-GEM (Chaudhry et al., 2019) so that every unlearning step is constrained to not increase the retain-set loss. On top of this, it performs multi-layer representation erasure, pushing forget-set activations in intermediate layers towards the retain distribution to remove information from hidden representations rather than just suppressing it at the output. A key design choice is the retain-confusion target: rather than pushing forget outputs toward the uniform distribution, which we found to be surprisingly easy for membership inference attacks to detect, we instead target the model's natural confusion pattern on retain data. This makes the unlearned model hard to distinguish from one retrained from scratch. Two self-regulating stopping criteria (a retain-loss budget and a forget-accuracy target) let the algorithm decide on its own when to stop, removing the need for manual epoch tuning. In experiments on five datasets (CIFAR-10, MNIST, SVHN, STL10, PathMNIST) across 22 class-level forgetting tasks, PURGE consistently keeps retain accuracy above 96% while achieving MIA AUROC close to 0.5 (the ideal), outperforming gradient ascent, KL-uniform, and several published baselines on the privacy-utility frontier.

Vedant Jawandhia, Yash Sinha, Murari Mandal et al.

Large language models (LLMs) are increasingly evaluated on mathematical reasoning, yet their robustness to equivalent problem representations remains poorly understood. In geometry, identical problems can be expressed in Euclidean, coordinate, or vector forms, but existing benchmarks report accuracy on fixed formats, implicitly assuming representation invariance and masking failures caused by representational changes alone. We propose GeoRepEval, a representation-aware evaluation framework that measures correctness, invariance, and consistency at the problem level across parallel formulations, combining strict answer matching, bootstrap confidence intervals, paired McNemar tests, representation-flip analyses, and regression controls for surface complexity. We prove that our Invariance@3 metric decomposes accuracy into robust and fragile components and is bounded by the weakest representation. Evaluating eleven LLMs on 158 curated high-school geometry problems (474 instances), we find accuracy gaps of up to 14 percentage points induced solely by representation choice. Vector formulations emerge as a consistent failure point, with Invariance@3 as low as 0.044 even after controlling for length and symbolic complexity. A convert-then-solve prompting intervention improves vector accuracy by up to 52 percentage points for high-capacity models, suggesting that failures reflect representation sensitivity rather than inability; however, low-capacity models show no gains, indicating deeper limitations. These results suggest that current models rely on representation-specific heuristics rather than abstract geometric reasoning. All datasets, prompts, and scripts are released at https://github.com/vedjaw/GeoRepEval.