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David Jensen

Publications and source records attributed to David Jensen.

At least 19 recordsLinked to original sources
arXiv2026

Safe Bayesian Optimization with Counterfactual Policies

In many decision-making settings, new interventions are acceptable only if they do not reduce outcomes below some established threshold. For example, in clinical medicine, new treatments are often acceptable only if they do not worsen outcomes relative to an established standard of care. Safe Bayesian optimization maximizes an objective subject to safety constraints. In the setting that we consider here, safety is defined relative to a known baseline policy whose outcomes are counterfactual and therefore unobserved. Thus, the counterfactual outcomes of the baseline policy must be estimated and those (uncertain) estimates must be used to safely optimize the objective. We address this estimation problem by using conformal prediction to construct valid uncertainty intervals for counterfactual baseline outcomes, and we show how these intervals can be integrated into safe Bayesian optimization to ensure that constraint violations occur at or below a user-specified rate. We also show how to adapt these conformal estimates to different kinds of covariate shift. We provide a safety proof, experimental evidence, and a sensitivity analysis.

cs.LG↗
arXiv2026

Prym-Brill-Noether Theory for General Covers

We bound the dimension of the Prym-Brill-Noether variety for an open subset of the moduli space of \'{e}tale double covers of k-elliptic curves. We also obtain new bounds on the dimension of the Prym-Brill-Noether variety for general \'{e}tale double covers of k-gonal curves, disproving a conjecture of Creech, Len, Ritter, and Wu, and provide a new conjecture for its dimension. To do this, we completely describe the Prym-Brill-Noether variety of a double cover of a certain tropical curve known as the loop of loops. We use the combinatorics of Coxeter groups to establish several topological properties of these tropical Prym-Brill-Noether varieties, and prove a lifting result when the edge lengths are generic.

math.AG↗
arXiv2026

The Curse of Multiple Mediators: Hidden Interaction Effects in Activation Patching

Activation patching is the primary tool in mechanistic interpretability. It attributes causal responsibility for a model behavior to each of its individual components by estimating its natural indirect effect (NIE). Re-deriving the activation patching estimand from causal mediation analysis, we find that the NIE does not solely capture the causal effect through the specific component. It also contains interaction effects (INT) that measure how much the component's causal effect itself depends on the state of other components in the model. A natural response may be to try to eliminate INT by adjusting the estimator or unit of analysis, but each of these potential remedies has predictable failure modes. We demonstrate these failure modes in the GPT-2 IOI circuit; components whose causal importance is conditional on the state of other components are either invisible or artificially inflated, and INT variance explains the previously documented instability of faithfulness scores. We prove that INT scales with the distance between clean and patched component activations, is negligible when the model is locally affine, and decomposes combinatorially into pairwise and higher-order group interactions. Despite its inevitability, INT is not a nuisance to be eliminated, but rather a diagnostic for interpretability studies. Its individual and group-level magnitude and sign signal when causal conclusions are prompt-dependent, and when greedy NIE-based component ranking will miss mechanisms only discoverable through combinatorial search.

cs.LG↗
arXiv2026

Extending Causal Metamodeling to a non-Markovian Queue

Metamodels for discrete-event simulations approximate the behavior of simulation models without running expensive simulations. Prior work introduced modular dynamic Bayesian networks (MDBNs) -- a class of metamodels that can estimate a range of probabilistic and causal queries (PCQs) using a single, trained model -- but the method was limited to Markovian systems. In this paper, we initiate an extension of MDBNs to non-Markovian queues by approximating non-exponential distributions using phase-type distributions. This approach raises novel challenges, including balancing metamodeling accuracy and tractability when choosing the number of phases, efficiently learning metamodel parameters, and choosing the sampling interval that is used to approximate a continuous-time simulation by a discrete-time MDBN. We provide preliminary solutions to these challenges, yielding the first causal metamodeling technique for non-Markovian systems. Experiments on a G/M/1 queue demonstrate that the MDBN can produce accurate answers to PCQs with orders-of-magnitude speedup of inference times relative to direct simulation.

cs.LG↗
arXiv2026

The Imperative for Grand Challenges in Computing

Computing is an indispensable component of nearly all technologies and is ubiquitous for vast segments of society. It is also essential to discoveries and innovations in most disciplines. However, while past grand challenges in science have involved computing as one of the tools to address the challenge, these challenges have not been principally about computing. Why has the computing community not yet produced challenges at the scale of grandeur that we see in disciplines such as physics, astronomy, or engineering? How might we go about identifying similarly grand challenges? What are the grand challenges of computing that transcend our discipline's traditional boundaries and have the potential to dramatically improve our understanding of the world and positively shape the future of our society? There is a significant benefit in us, as a field, taking a more intentional approach to "grand challenges." We are seeking challenge problems that are sufficiently compelling as to both ignite the imagination of computer scientists and draw researchers from other disciplines to computational challenges. This paper emphasizes the importance, now more than ever, of defining and pursuing grand challenges in computing as a field, and being intentional about translation and realizing its impacts on science and society. Building on lessons from prior grand challenges, the paper explores the nature of a grand challenge today emphasizing both scale and impact, and how the community may tackle such a grand challenge, given a rapidly changing innovation ecosystem in computing. The paper concludes with a call to action for our community to come together to define grand challenges in computing for the next decade and beyond.

cs.CY↗
arXiv2025

The Impact of Data Characteristics on GNN Evaluation for Detecting Fake News

Graph neural networks (GNNs) are widely used for the detection of fake news by modeling the content and propagation structure of news articles on social media. We show that two of the most commonly used benchmark data sets - GossipCop and PolitiFact - are poorly suited to evaluating the utility of models that use propagation structure. Specifically, these data sets exhibit shallow, ego-like graph topologies that provide little or no ability to differentiate among modeling methods. We systematically benchmark five GNN architectures against a structure-agnostic multilayer perceptron (MLP) that uses the same node features. We show that MLPs match or closely trail the performance of GNNs, with performance gaps often within 1-2% and overlapping confidence intervals. To isolate the contribution of structure in these datasets, we conduct controlled experiments where node features are shuffled or edge structures randomized. We find that performance collapses under feature shuffling but remains stable under edge randomization. This suggests that structure plays a negligible role in these benchmarks. Structural analysis further reveals that over 75% of nodes are only one hop from the root, exhibiting minimal structural diversity. In contrast, on synthetic datasets where node features are noisy and structure is informative, GNNs significantly outperform MLPs. These findings provide strong evidence that widely used benchmarks do not meaningfully test the utility of modeling structural features, and they motivate the development of datasets with richer, more diverse graph topologies.

cs.LG↗
arXiv2025

Challenges in Understanding Modality Conflict in Vision-Language Models

This paper highlights the challenge of decomposing conflict detection from conflict resolution in Vision-Language Models (VLMs) and presents potential approaches, including using a supervised metric via linear probes and group-based attention pattern analysis. We conduct a mechanistic investigation of LLaVA-OV-7B, a state-of-the-art VLM that exhibits diverse resolution behaviors when faced with conflicting multimodal inputs. Our results show that a linearly decodable conflict signal emerges in the model's intermediate layers and that attention patterns associated with conflict detection and resolution diverge at different stages of the network. These findings support the hypothesis that detection and resolution are functionally distinct mechanisms. We discuss how such decomposition enables more actionable interpretability and targeted interventions for improving model robustness in challenging multimodal settings.

cs.LG↗
arXiv2025

Improving Generative Methods for Causal Evaluation via Simulation-Based Inference

Generating synthetic datasets that accurately reflect real-world observational data is critical for evaluating causal estimators, but it remains a challenging task. Existing generative methods offer a solution by producing synthetic datasets anchored in the observed data (source data) while allowing variation in key parameters such as the treatment effect and amount of confounding bias. However, it is often unclear which generative methods to use and which values of parameters to choose when generating synthetic datasets. Moreover, existing methods typically require users to provide fixed point estimates of such parameters. This denies users the ability to express uncertainty over both generative methods and parameter values and removes the potential for posterior inference, potentially leading to unreliable estimator comparisons. We introduce simulation-based inference for causal evaluation (SBICE), a framework that treats the generative method and its corresponding generative parameters as uncertain and infers their posterior distribution given a source dataset. Leveraging techniques in simulation-based inference, SBICE identifies suitable generative methods and infers distributions over its parameter configurations to produce synthetic datasets closely aligned with the source data distribution. Empirical results demonstrate that SBICE improves the reliability of estimator evaluations by generating realistic datasets whose causal estimates closely match the estimates of the source data, making it a robust and uncertainty-aware approach to selecting causal estimators.

cs.LG↗
arXiv2025

Tropical linear series and matroids

We study a notion of tropical linear series on metric graphs that combines two essential properties of tropicalizations of linear series on algebraic curves: the Baker-Norine rank and the independence rank. Our main results relate the local and global geometry of these tropical linear series to the combinatorial geometry of matroids and valuated matroids, respectively. As an application, we characterize exactly when the tropicalization of the canonical linear series on a single curve is equal to the locus of realizable tropical canonical divisors determined by M\"oller, Ulirsch, and Werner. We also illustrate our results with a wealth of examples; in particular, we show that the Bergman fan of every matroid appears as the local fan of a tropical linear series on a metric graph. The paper concludes with a list of ten open questions for future investigation.

math.AG↗
arXiv2025

Evaluating and Learning Robust Bandit Policies Under Uncertain Causal Mechanisms

Causal graphical models can encode large amounts structural knowledge, both from the background knowledge of domain experts and the structural knowledge discovered from randomized experiments or observational data. However, though we may know the general structure of causal relationships, we often do not know the exact causal mechanisms. In this work, we propose a causal multi-armed bandit evaluation and learning algorithm that can reason effectively despite uncertainty over conditional probability distributions. Further, we show how conditional independence testing can be used to choose variables for modeling. We find that the structural equation model (SEM) approach gives more accurate evaluations compared to traditional approaches, particularly as the range of possible causal mechanisms grows. Further, the SEM approach learns low-variance policies, and it learns an optimal policy, assuming the model is sufficiently well-specified. Traditional approaches can converge to local extrema or fail to converge at all.

cs.LG↗
arXiv2025

Now More Than Ever, Foundational AI Research and Infrastructure Depends on the Federal Government

Leadership in the field of AI is vital for our nation's economy and security. Maintaining this leadership requires investments by the federal government. The federal investment in foundation AI research is essential for U.S. leadership in the field. Providing accessible AI infrastructure will benefit everyone. Now is the time to increase the federal support, which will be complementary to, and help drive, the nation's high-tech industry investments.

cs.CY↗
arXiv2025

Refined Brill-Noether Theory for Complete Graphs

The divisor theory of the complete graph $K_n$ is in many ways similar to that of a plane curve of degree $n$. We compute the splitting types of all divisors on the complete graph $K_n$. We see that the possible splitting types of divisors on $K_n$ exactly match the possible splitting types of line bundles on a smooth plane curve of degree $n$. This generalizes the earlier result of Cori and Le Borgne computing the ranks of all divisors on $K_n$, and the earlier work of Cools and Panizzut analyzing the possible ranks of divisors of fixed degree on $K_n$.

math.CO↗
arXiv2024

Adaptive Circuit Behavior and Generalization in Mechanistic Interpretability

Mechanistic interpretability aims to understand the inner workings of large neural networks by identifying circuits, or minimal subgraphs within the model that implement algorithms responsible for performing specific tasks. These circuits are typically discovered and analyzed using a narrowly defined prompt format. However, given the abilities of large language models (LLMs) to generalize across various prompt formats for the same task, it remains unclear how well these circuits generalize. For instance, it is unclear whether the models generalization results from reusing the same circuit components, the components behaving differently, or the use of entirely different components. In this paper, we investigate the generality of the indirect object identification (IOI) circuit in GPT-2 small, which is well-studied and believed to implement a simple, interpretable algorithm. We evaluate its performance on prompt variants that challenge the assumptions of this algorithm. Our findings reveal that the circuit generalizes surprisingly well, reusing all of its components and mechanisms while only adding additional input edges. Notably, the circuit generalizes even to prompt variants where the original algorithm should fail; we discover a mechanism that explains this which we term S2 Hacking. Our findings indicate that circuits within LLMs may be more flexible and general than previously recognized, underscoring the importance of studying circuit generalization to better understand the broader capabilities of these models.

cs.LG↗
arXiv2024

Fibonacci Sumsets and the Gonality of Strip Graphs

We provide a new perspective on the divisor theory of graphs, using additive combinatorics. As a test case for this perspective, we compute the gonality of certain families of outerplanar graphs, specifically the strip graphs. The Jacobians of such graphs are always cyclic of Fibonacci order. As a consequence, we obtain several results on the additive properties of Fibonacci numbers.

math.CO↗
arXiv2024

Compositional Models for Estimating Causal Effects

Many real-world systems can be usefully represented as sets of interacting components. Examples include computational systems, such as query processors and compilers, natural systems, such as cells and ecosystems, and social systems, such as families and organizations. However, current approaches to estimating potential outcomes and causal effects typically treat such systems as single units, represent them with a fixed set of variables, and assume a homogeneous data-generating process. In this work, we study a compositional approach for estimating individual-level potential outcomes and causal effects in structured systems, where each unit is represented by an instance-specific composition of multiple heterogeneous components. The compositional approach decomposes unit-level causal queries into more fine-grained queries, explicitly modeling how unit-level interventions affect component-level outcomes to generate a unit's outcome. We demonstrate this approach using modular neural network architectures and show that it provides benefits for causal effect estimation from observational data, such as accurate causal effect estimation for structured units, increased sample efficiency, improved overlap between treatment and control groups, and compositional generalization to units with unseen combinations of components. Remarkably, our results show that compositional modeling can improve the accuracy of causal estimation even when component-level outcomes are unobserved. We also create and use a set of real-world evaluation environments for the empirical evaluation of compositional approaches for causal effect estimation and demonstrate the role of composition structure, varying amounts of component-level data access, and component heterogeneity in the performance of compositional models as compared to the non-compositional approaches.

cs.AI↗
arXiv2024

On the Gonality of Ferrers Rook Graphs

A Ferrers rook graph is a graph whose vertices correspond to the dots in a Ferrers diagram, and where two vertices are adjacent if they are in the same row or the same column. We propose a conjectural formula for the gonality of Ferrers rook graphs, and prove this conjecture for a few infinite families of Ferrers diagrams. We also prove the conjecture for all Ferrers diagrams $F$ with $|F| \leq 8$.

math.CO↗