Amit Sahai
Publications
SLAM: Structural Linguistic Activation Marking for Language Models
LLM watermarks must be detectable without compromising text quality, yet most existing schemes bias the next-token distribution and pay for detection with measurable quality loss. We present SLAM (Structural Linguistic Activation Marking), a novel white-box watermarking scheme that sidesteps this cost by writing the mark into structural geometry rather than token frequencies: sparse autoencoders identify residual-stream directions encoding linguistic structure (e.g., voice, tense, clause order), and we causally steer those directions at generation time, leaving lexical sampling and semantics unconstrained. On Gemma-2 2B and 9B, SLAM achieves 100% detection accuracy with a quality cost of only 1-2 reward points - compared to 7.5-11.5 for KGW, EWD, and Unigram - with naturalness and diversity preserved at near-unwatermarked levels across both models. The trade-off is a complementary robustness profile: SLAM resists word-level edits but is vulnerable to paraphrase that restructures syntax (at a quality cost), the converse of token-distribution methods.
TaoBench: Do Automated Theorem Prover LLMs Generalize Beyond MathLib?
Automated theorem proving (ATP) benchmarks largely consist of problems formalized in MathLib, so current ATP training and evaluation are heavily biased toward MathLib's definitional framework. However, frontier mathematics is often exploratory and prototype-heavy, relying on bespoke constructions that deviate from standard libraries. In this work, we evaluate the robustness of current ATP systems when applied to a novel definitional framework, specifically examining the performance gap between standard library problems and bespoke mathematical constructions. We introduce TaoBench, an undergraduate-level benchmark derived from Terence Tao's Analysis I, which formalizes analysis by constructing core mathematical concepts from scratch, without relying on standard Mathlib definitions, as well as by mixing from-scratch and MathLib constructions. For fair evaluation, we build an agentic pipeline that automatically extracts a compilable, self-contained local environment for each problem. To isolate the effect of definitional frameworks, we additionally translate every problem into a mathematically equivalent Mathlib formulation, yielding paired TaoBench-Mathlib statements for direct comparison. While state-of-the-art ATP models perform capably within the MathLib framework, performance drops by an average of roughly 26% on the definitionally equivalent Tao formulation. This indicates that the main bottleneck is limited generalization across definitional frameworks rather than task difficulty. TaoBench thus highlights a gap between benchmark performance and applicability, and provides a concrete foundation for developing and testing provers better aligned with research mathematics.