SearcharxivSearch

arXiv subjects

Anna Bertiger

Publications and source records attributed to Anna Bertiger.

7 recordsLinked to original sources

Evaluating Agentic Learning Harness Capabilities Without Labels via the Scaling Hypothesis

Agentic "Continual Learning Harnesses", systems that pair an LLM with retrieval or memory to improve from feedback without retraining, have shown growing value in cybersecurity. But their value is conventionally measured by gains against labeled benchmarks, an approach that often fails in operational security settings. Benchmark labels are scarce, stale, and unrepresentative, so a practitioner often cannot tell whether a given harness helps at all or which of two is better for their task. Traditional LLM-as-a-judge offers little signal because it is no stronger than the agent it evaluates, and distillation is unreliable on scarce, sporadic, and biased labels. We propose a framework for evaluating learning harnesses end-to-end without a labeled benchmark, grounded in the scaling hypothesis. A stronger teacher model provides sparsely sampled corrections to a smaller student with a continual learning harness. We score a harness by how much its student converges toward the teacher over time. Across security tasks, model families, and harness designs, we show that improvement relative to the teacher correlates with improvement relative to a held-out gold standard, validating teacher-relative lift as a proxy for true harness uplift when labels are absent. We further show that LLM-as-a-judge between similarly powered models yields no usable signal. These results suggest that a teacher-sized model can be improved through the same harness when humans provide the same kind of sparse, high-precision corrections.

cs.AI

Evaluating LLM Generated Detection Rules in Cybersecurity

LLMs are increasingly pervasive in the security environment, with limited measures of their effectiveness, which limits trust and usefulness to security practitioners. Here, we present an open-source evaluation framework and benchmark metrics for evaluating LLM-generated cybersecurity rules. The benchmark employs a holdout set-based methodology to measure the effectiveness of LLM-generated security rules in comparison to a human-generated corpus of rules. It provides three key metrics inspired by the way experts evaluate security rules, offering a realistic, multifaceted evaluation of the effectiveness of an LLM-based security rule generator. This methodology is illustrated using rules from Sublime Security's detection team and those written by Sublime Security's Automated Detection Engineer (ADE), with a thorough analysis of ADE's skills presented in the results section.

cs.CR

An equivariant quantum Pieri rule for the Grassmannian on cylindric shapes

The quantum cohomology ring of the Grassmannian is determined by the quantum Pieri rule for multiplying by Schubert classes indexed by row or column-shaped partitions. We provide a direct equivariant generalization of Postnikov's quantum Pieri rule for the Grassmannian in terms of cylindric shapes, complementing related work of Gorbounov and Korff in quantum integrable systems. The equivariant terms in our Graham-positive rule simply encode the positions of all possible addable boxes within one cylindric skew diagram. As such, unlike the earlier equivariant quantum Pieri rule of Huang and Li and known equivariant quantum Littlewood-Richardson rules, our formula does not require any calculations in a different Grassmannian or two-step flag variety.

math.CO

Spectral embedding of weighted graphs

When analyzing weighted networks using spectral embedding, a judicious transformation of the edge weights may produce better results. To formalize this idea, we consider the asymptotic behavior of spectral embedding for different edge-weight representations, under a generic low rank model. We measure the quality of different embeddings -- which can be on entirely different scales -- by how easy it is to distinguish communities, in an information-theoretic sense. For common types of weighted graphs, such as count networks or p-value networks, we find that transformations such as tempering or thresholding can be highly beneficial, both in theory and in practice.

stat.ML

The Orbits of the Symplectic Group on the Flag Manifold

We examine the orbits of the (complex) symplectic group, $Sp_n$, on the flag manifold, $\mathscr{F}\ell(\mathbb{C}^{2n})$, in a very concrete way. We use two approaches: we Gröbner degenerate the orbits to unions of Schubert varieties (for a equations of a particular union of Schubert varieties see \cite{NWunions}) and we find a subset $\mathcal{A}$ of the orbit closures containing the basic elements of the poset of orbit closures under containment, which represent the geometric and combinatorial building blocks for the orbit closures.

math.AG

Generating the Ideals Defining Unions of Schubert Varieties

This note computes a Gröbner basis for the ideal defining a union of Schubert varieties. More precisely, it computes a Gröbner basis for unions of schemes given by northwest rank conditions on the space of all matrices of a fixed size. Schemes given by northwest rank conditions include classical determinantal varieties and matrix Schubert varieties--closures of Schubert varieties lifted from the flag manifold to the space of matrices.

math.AG

Equivariant Quantum Cohomology of the Grassmannian via the Rim Hook Rule

A driving question in (quantum) cohomology of flag varieties is to find non-recursive, positive combinatorial formulas for expressing the product of two classes in a particularly nice basis, called the Schubert basis. Bertram, Ciocan-Fontanine and Fulton provided a way to compute quantum products of Schubert classes in the Grassmannian of k-planes in complex n-space by doing classical multiplication and then applying a combinatorial rim hook rule which yields the quantum parameter. In this paper, we provide a generalization of this rim hook rule to the setting in which there is also an action of the complex torus. Combining this result with Knutson and Tao's puzzle rule then gives an effective algorithm for computing all equivariant quantum Littlewood-Richardson coefficients. Interestingly, this rule requires a specialization of torus weights modulo n, suggesting a direct connection to the Peterson isomorphism relating quantum and affine Schubert calculus.

math.AG