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Adam Wood

Publications and source records attributed to Adam Wood.

3 recordsLinked to original sources

DeepPersona: A Generative Engine for Scaling Deep Synthetic Personas

Simulating human profiles by instilling personas into large language models (LLMs) is rapidly transforming research in agentic behavioral simulation, LLM personalization, and human-AI alignment. However, most existing synthetic personas remain shallow and simplistic, capturing minimal attributes and failing to reflect the rich complexity and diversity of real human identities. We introduce DEEPPERSONA, a scalable generative engine for synthesizing narrative-complete synthetic personas through a two-stage, taxonomy-guided method. First, we algorithmically construct the largest-ever human-attribute taxonomy, comprising over hundreds of hierarchically organized attributes, by mining thousands of real user-ChatGPT conversations. Second, we progressively sample attributes from this taxonomy, conditionally generating coherent and realistic personas that average hundreds of structured attributes and roughly 1 MB of narrative text, two orders of magnitude deeper than prior works. Intrinsic evaluations confirm significant improvements in attribute diversity (32 percent higher coverage) and profile uniqueness (44 percent greater) compared to state-of-the-art baselines. Extrinsically, our personas enhance GPT-4.1-mini's personalized question answering accuracy by 11.6 percent on average across ten metrics and substantially narrow (by 31.7 percent) the gap between simulated LLM citizens and authentic human responses in social surveys. Our generated national citizens reduced the performance gap on the Big Five personality test by 17 percent relative to LLM-simulated citizens. DEEPPERSONA thus provides a rigorous, scalable, and privacy-free platform for high-fidelity human simulation and personalized AI research.

cs.AI

The Galois module structure of holomorphic poly-differentials and Riemann-Roch spaces

Suppose $X$ is a smooth projective geometrically irreducible curve over a perfect field $k$ of positive characteristic $p$. Let $G$ be a finite group acting faithfully on $X$ over $k$ such that $G$ has non-trivial, cyclic Sylow $p$-subgroups. If $E$ is a $G$-invariant Weil divisor on $X$ with $\mathrm{deg}(E)> 2g(X)-2$, we prove that the decomposition of $\mathrm{H}^0(X,\mathcal{O}_X(E))$ into a direct sum of indecomposable $kG$-modules is uniquely determined by the class of $E$ modulo $G$-invariant principal divisors, together with the ramification data of the cover $X\to X/G$. The latter is given by the lower ramification groups and the fundamental characters of the closed points of $X$ that are ramified in the cover. As a consequence, we obtain that if $m>1$ and $g(X)\ge 2$, then the $kG$-module structure of $\mathrm{H}^0(X,\Omega_X^{\otimes m})$ is uniquely determined by the class of a canonical divisor on $X/G$ modulo principal divisors, together with the ramification data of $X\to X/G$. This extends to arbitrary $m > 1$ the $m = 1$ case treated by the first author with T. Chinburg and A. Kontogeorgis. We discuss applications to the tangent space of the global deformation functor associated to $(X,G)$ and to congruences between prime level cusp forms in characteristic $0$. In particular, we complete the description of the precise $k\mathrm{PSL}(2,\mathbb{F}_\ell)$-module structure of all prime level $\ell$ cusp forms of even weight in characteristic $p=3$.

math.AG

L-space knots with tunnel number >1 by experiment

In Dunfield's catalog of the hyperbolic manifolds in the SnapPy census which are complements of L-space knots in $S^3$, we determine that $22$ have tunnel number $2$ while the remaining all have tunnel number $1$. Notably, these $22$ manifolds contain $9$ asymmetric L-space knot complements. Furthermore, using SnapPy and KLO we find presentations of these $22$ knots as closures of positive braids that realize the Morton-Franks-Williams bound on braid index. The smallest of these has genus $12$ and braid index $4$.

math.GT