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Memorization and Unlearning in LLMs Through the Lens of Input Loss Landscapes
Taub 601
Understanding how large language models store, retain, and remove knowledge is critical for interpretability, reliability, and compliance with privacy regulations.
My work introduces a geometric perspective on memorization and unlearning by analyzing loss behavior over semantically similar inputs through the Input Loss Landscape.
I show that retained, forgotten, and unseen examples exhibit distinct patterns that reflect active learning, suppressed knowledge, and ignored information.
Building on this observation, I propose REMIND (Residual Memorization In Neighborhood Dynamics), a black-box framework for diagnosing residual memorization. I further introduce a new semantic neighbor generation method that enables controlled exploration of local loss geometry.
These contributions provide interpretable insights into knowledge retention and forgetting, and offer practical tools for auditing, debugging, and enhancing transparency in large language models.
Incremental Dominating SetDominating Set is a fundamental problem in graph theory: given a graph, find a minimum-weight subset of vertices such that every vertex is either selected or shares an edge with a selected vertex.
In online settings where vertices arrive sequentially, comparing algorithms against an offline optimum with full knowledge of the input leads to extremely strong lower bounds, where even a simple star graph shows that any online algorithm must have competitive ratio Ω(n), with n being the number of vertices, matching the trivial strategy of selecting all vertices.
We study the incremental dominating set problem, where the optimal algorithm is constrained to the same choices available to online algorithms. This introduces a benchmark that enables a meaningful comparison between algorithms.
We present the first results for vertex-weighted graphs and randomized algorithms in this model. For incremental dominating set, we give an O(Δ)-competitive deterministic algorithm and an O(log²Δ)-competitive randomized algorithm, where Δ is the maximum degree in the graph.
We extend these results to the Connected Dominating Set problem, which requires the dominating set to be connected. When the neighborhood of each arriving vertex is known in advance, we can improve the competitive ratio of deterministic algorithms to be polylogarithmic.
Finally, we establish matching lower bounds, showing that all our results are optimal up to constant factors.