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Brent M. Werness

Publications and source records attributed to Brent M. Werness.

5 recordsLinked to original sources

Grad Detect: Gradient-Based Hallucination Detection in LLMs

Large Language Models (LLMs) have demonstrated remarkable capabilities across diverse tasks, yet they remain prone to generating hallucinations. Detecting these hallucinations is critical for deploying LLMs reliably in high-stakes applications. We present Grad Detect, a gradient-based approach for predicting hallucinations by analyzing layer-wise gradient patterns from a single forward-backward pass during inference. Our method shows that the internal gradient structure of a model carries rich information about the correctness of its output. This information is not accessible through output-level signals alone. We evaluate Grad Detect on several Q&A benchmarks across both hallucination detection and model abstention prediction, where it consistently outperforms confidence-based and sampling-based baselines. Through comprehensive layer ablation studies across all eleven models from four architectural families, we find that the final five layers concentrate over 97% of the discriminative gradient signal, enabling efficient deployment with minimal performance loss. Grad Detect provides a unified framework for predicting multiple dimensions of LLM reliability, offering strong predictive performance alongside interpretable insights into where and how model failures originate.

cs.LG↗

Discrete analytic functions on non-uniform lattices without global geometric control

Recent advances in the study of conformally invariant discrete random processes have lead to increasing interest in the study of discrete analogues to holomorphic functions. Of particular interest are results which provide conditions under which these discrete functions can be shown to converge to continuum versions as the lattice spacing shrinks to zero. Recent work by Skopenkov has extended these results to include a wide class of non-uniform quadrilateral lattices with a pair of regularity conditions, one local and one global. Such a result is sufficient for the study of random processes on deterministic lattices, however to establish convergence results for conformally invariant random processes on random triangulations, such a global regularity condition cannot be assumed. In this paper we provide a convergence result on quadrilateral lattices upon which we enforce only a local condition on the geometry of each face.

math.CV↗

Multi-point Green's functions for SLE and an estimate of Beffara

In this paper we define and prove of the existence of the multi-point Green's function for SLE - a normalized limit of the probability that an $SLE_κ$ curve passes near to a pair of marked points in the interior of a domain. When $κ<8$ this probability is nontrivial, and an expression can be written in terms two-sided radial SLE. One of the main components to our proof is a refinement of a bound first provided by Beffara [Ann. Probab. 36 (2008) 1421-1452]. This work contains a proof of this bound independent from the original.

math.PR↗

The parafermionic observable in SLE

The parafermionic observable has recently been used by number of authors to study discrete models, believed to be conformally invariant and to prove convergence results for these processes to SLE. We provide a definition for a one parameter family of continuum versions of the paraferminonic observable for SLE, which takes the form of a normalized limit of expressions identical to the discrete definition. We then show the limit defining the observable exists, compute the value of the observable up to a finite multiplicative constant, and prove this constant is non-zero for a wide range of kappa. Finally, we show our observable for SLE becomes a holomorphic function for a particular choice of the parameter, which helps illuminate a fundamental property of the discrete observable.

math.PR↗

Regularity of Schramm-Loewner Evolutions, annular crossings, and rough path theory

When studying stochastic processes, it is often fruitful to have an understanding of several different notions of regularity. One such notion is the optimal Hölder exponent obtainable under reparametrization. In this paper, we show that the chordal SLE_kappa path in the unit disk for kappa less than or equal to 4 can be reparametrized to be Hölder continuous of any order up to 1/(1+kappa/8). From this result, we obtain that the Young integral is well defined along such SLE paths with probability one, and hence that SLE admits a path-wise notion of integration. This allows for us to consider the expected signature of SLE, as defined in rough path theory, and to give a precise formula for its first three gradings. The main technical result required is a uniform bound on the probability that a SLE crosses an annulus k-distinct times.

math.PR↗