arXiv subjects

Patrick Cooper

Publications and source records attributed to Patrick Cooper.

17 recordsLinked to original sources

arXiv2026

Expected Free Energy as Belief-Dependent Utility for rho-POMDPs

An agent acting under partial observability must decide when to gather information and which observations are worth their cost. Standard POMDPs value information only through its eventual effect on reward. The $\rho$-POMDP framework instead rewards uncertainty reduction directly, through a belief-dependent utility $\rho$, but in practice both the choice of $\rho$ and the weight placed on it are tuned by hand for every task. We show that active inference removes this tuning entirely. Minimizing Expected Free Energy (EFE) is exactly equivalent to solving a $\rho$-POMDP whose utility is expected information gain, and the exploration weight is fixed at $w=1$ because the variational bound expresses pragmatic and epistemic value in the same units (nats). We prove this equivalence for observe-then-commit POMDPs and extend it to factored observation POMDPs, a broader class that covers interleaved observe-act problems such as non-destructive testing and mobile sensing, where gathering information leaves the hidden state unchanged. Experiments support the theory. Across environments ranging from the classic Tiger problem to RockSample and a new Structural Inspection benchmark with over 65,000 states, the untuned weight matches or outperforms reward-only planning at the same horizon, avoids the over-exploration of bonuses tuned per task, and sits near the reward-maximizing knee of the success-reward Pareto frontier. The practical payoff is an exploration objective that works out of the box. In applications such as fault detection and medical screening, where every test has a price and every missed fault has a cost, EFE supplies a belief-dependent utility that is derived rather than tuned.

cs.AI↗

arXiv2026

Narration-of-Thought: Inference-Time Scaffolding for Defeasible Ethical Reasoning in Large Language Models

Standard chain-of-thought on moral dilemmas exhibits two failure modes: stakeholder collapse (the trace names at most one party with a stake in the outcome) and uncertainty suppression (no explicit unknowns or hedges before committing to an action). We introduce narration-of-thought (NoT), a system prompt that structures chain-of-thought into five sections: protagonist, stakeholders, two-step consequences, uncertainty, then commitment. NoT adds no training, parameters, or fine-tuning. On 100 DailyDilemmas scenarios across four generators from three vendors, NoT cuts stakeholder collapse from up to 31% to under 1% and uncertainty suppression from up to 72% to 1-24% on every model. A matched-budget verbose-CoT control rules out token spend as the active ingredient; NoT retains Cliff's delta advantages of +0.79 to +0.90 on stakeholder count and +0.65 to +0.93 on uncertainty score for three of four generators, and a section ablation attributes each shift to its specific sub-instruction. Textual-gradient descent initialised at NoT improves the scaffold further; a cross-family training judge (different vendor from the generator) dominates an in-family one on every measured axis. Extended to a five-round multi-stakeholder debate protocol, the scaffold converts a 6% standoff into 95% full consensus on a calibration set and 100% combined convergence on a DailyDilemmas replication. The resulting traces externalise the stakeholders, consequences, and uncertainty grounding each commitment, providing an auditable substrate for dependable agentic deployment.

cs.AI↗

arXiv2026

DeFAb: A Verifiable Benchmark for Defeasible Abduction in Foundation Models

A rule-based logic solver resolves every instance in our benchmark in under 50 microseconds with 100% accuracy; the best frontier language model reaches 65% at best and drops to 23.5% under rendering-robust evaluation (worst case over four surface renderings). We introduce DeFAb (Defeasible Abduction Benchmark), a dataset and generation pipeline that converts four decades of publicly funded knowledge bases into formally grounded instances for defeasible abduction: constructing hypotheses that explain anomalies by overriding defaults while preserving unrelated expectations. Because every hypothesis must pass polynomial-time checks for valid derivation, conservativity, and minimality, DeFAb makes logical rigor the instrument for measuring creativity and theoretical reasoning, scoring the disciplined construction of theory revisions rather than fluent but theory-destroying prose. The pipeline pairs taxonomic hierarchies (OpenCyc, YAGO, Wikidata) with behavioral property graphs (ConceptNet, UMLS) to produce 372,648+ instances across 33.75M materialized rules from 18 sources, in three levels with polynomial-time verifiable gold standards. Four frontier models do not reliably internalize defeasible reasoning: rendering-robust Level 2 accuracy is 7.8-23.5%; chain-of-thought variance (~36 pp) exceeds any inter-model gap; and a matched contamination control isolates a +19.4 pp Level 3 gap. We further release DeFAb-Hard (a 235-instance Level 3 difficulty variant; best model 53.3% vs 100% symbolic) and CONJURE (a kernel-verified transformative-creativity variant of 560 Lean 4/Mathlib instances whose gold answers are definitions the proof kernel did not previously contain, judge-free verifier; a pilot finds zero novel concepts). The same verifier doubles as an exact reward for preference optimization (DPO, RLVR/GRPO). Released under MIT at https://huggingface.co/datasets/PatrickAllenCooper/DeFAb.

cs.AI↗

arXiv2026

KV-Fold: One-Step KV-Cache Recurrence for Long-Context Inference

We introduce KV-Fold, a simple, training-free long-context inference protocol that treats the key-value (KV) cache as the accumulator in a left fold over sequence chunks. At each step, the model processes the next chunk conditioned on the accumulated cache, appends the newly produced keys and values, and passes the enlarged cache forward; the same one-step update is applied repeatedly, analogous to foldl in functional programming. Building on the KV cache concatenation primitive introduced for latent multi-agent communication, we repurpose it as a chunk-to-chunk recurrence for long-context inference. When processing chunk t, the model attends to the KV cache carried from earlier chunks as a prefix, reusing its internal state across segments without modifying or retraining the model. Despite its simplicity, the induced recurrence is stable: per-step drift rises briefly and then saturates into a flat plateau that persists across deep chains. This plateau is insensitive to a 10,000x change in numerical precision, robust across chunk sizes, and consistent across model families. At the task level, KV-Fold preserves exact information over long distances. On a needle-in-a-haystack benchmark, it achieves 100% exact-match retrieval across 152 trials spanning contexts from 16K to 128K tokens and chain depths up to 511 on Llama-3.1-8B, while remaining within the memory limits of a single 40GB GPU. Compared to streaming methods, which trade fidelity for bounded memory, KV-Fold maintains long-range retrieval while operating as a sequence of tractable forward passes. Overall, our results show that frozen pretrained transformers already support a stable form of KV-cache recurrence, providing a practical route to long-context inference without architectural changes or training.

cs.LG↗

arXiv2026

To Believe or Not To Believe: Comparing Supporting Information Tools to Aid Human Judgments of AI Veracity

With increasing awareness of the hallucination risks of generative artificial intelligence (AI), we see a growing shift toward providing information tooling to help users determine the veracity of AI-generated answers for themselves. User responsibility for assessing veracity is particularly critical for certain sectors that rely on on-demand, AI-generated data extraction, such as biomedical research and the legal sector. While prior work offers us a variety of ways in which systems can provide such support, there is a lack of empirical evidence on how this information is actually incorporated into the user's decision-making process. Our user study takes a step toward filling this knowledge gap. In the context of a generative AI data extraction tool, we examine the relationship between the type of supporting information (full source text, passage retrieval, and Large Language Model (LLM) explanations) and user behavior in the veracity assessment process, examined through the lens of efficiency, effectiveness, reliance and trust. We find that passage retrieval offers a reasonable compromise between accuracy and speed, with judgments of veracity comparable to using the full source text. LLM explanations, while also enabling rapid assessments, fostered inappropriate reliance and trust on the data extraction AI, such that participants were less likely to detect errors. In additiona, we analyzed the impacts of the complexity of the information need, finding preliminary evidence that inappropriate reliance is worse for complex answers. We demonstrate how, through rigorous user evaluation, we can better develop systems that allow for effective and responsible human agency in veracity assessment processes.

cs.HC↗

arXiv2026

Active Causal Experimentalist (ACE): Learning Intervention Strategies via Direct Preference Optimization

Discovering causal relationships requires controlled experiments, but experimentalists face a sequential decision problem: each intervention reveals information that should inform what to try next. Traditional approaches such as random sampling, greedy information maximization, and round-robin coverage treat each decision in isolation, unable to learn adaptive strategies from experience. We propose Active Causal Experimentalist (ACE), which learns experimental design as a sequential policy. Our key insight is that while absolute information gains diminish as knowledge accumulates (making value-based RL unstable), relative comparisons between candidate interventions remain meaningful throughout. ACE exploits this via Direct Preference Optimization, learning from pairwise intervention comparisons rather than non-stationary reward magnitudes. Across synthetic benchmarks, physics simulations, and economic data, ACE achieves 70-71% improvement over baselines at equal intervention budgets (p < 0.001, Cohen's d ~ 2). Notably, the learned policy autonomously discovers that collider mechanisms require concentrated interventions on parent variables, a theoretically-grounded strategy that emerges purely from experience. This suggests preference-based learning can recover principled experimental strategies, complementing theory with learned domain adaptation.

cs.LG↗

arXiv2026

Monotonicity as an Architectural Bias for Robust Language Models

Large language models (LLMs) are known to exhibit brittle behavior under adversarial prompts and jailbreak attacks, even after extensive alignment and fine-tuning. This fragility reflects a broader challenge of modern neural language models: small, carefully structured perturbations in high-dimensional input spaces can induce large and unpredictable changes in internal semantic representations and output. We investigate monotonicity as an architectural inductive bias for improving the robustness of Transformer-based language models. Monotonicity constrains semantic transformations so that strengthening information, evidence, or constraints cannot lead to regressions in the corresponding internal representations. Such order-preserving behavior has long been exploited in control and safety-critical systems to simplify reasoning and improve robustness, but has traditionally been viewed as incompatible with the expressivity required by neural language models. We show that this trade-off is not inherent. By enforcing monotonicity selectively in the feed-forward sublayers of sequence-to-sequence Transformers -- while leaving attention mechanisms unconstrained -- we obtain monotone language models that preserve the performance of their pretrained counterparts. This architectural separation allows negation, contradiction, and contextual interactions to be introduced explicitly through attention, while ensuring that subsequent semantic refinement is order-preserving. Empirically, monotonicity substantially improves robustness: adversarial attack success rates drop from approximately 69% to 19%, while standard summarization performance degrades only marginally.

cs.CL↗

arXiv2024

Towards a criteria-based approach to selecting human-AI interaction mode

Artificial intelligence (AI) tools are now prevalent in many knowledge work industries. As AI becomes more capable and interactive, there is a growing need for guidance on how to employ AI most effectively. The A2C framework (Tariq, Chhetri, Nepal & Paris, 2024) distinguishes three decision-making modes for engaging AI: automation (AI completes a task, including decision/action), augmentation (AI supports human to decide) and collaboration (iterative interaction between human and AI). However, selecting the appropriate mode for a specific application is not always straightforward. The goal of the present study was to compile and trial a simple set of criteria to support recommendations about appropriate A2C mode for a given application. Drawing on human factors and computer science literature, we identified key criteria related to elements of the task, impacts on worker and support needs. From these criteria we built a scoring rubric with recommendation for A2C mode. As a preliminary test of this approach, we applied the criteria to cognitive task analysis (CTA) outputs from three tasks in the science domain - genome annotation, biological collections curation and protein crystallization - which provided insights into worker decision points, challenges and expert strategies. This paper describes the method for connecting CTA to A2C, reflecting on the challenges and future directions.

cs.HC↗

arXiv2024

CogExplore: Contextual Exploration with Language-Encoded Environment Representations

Integrating language models into robotic exploration frameworks improves performance in unmapped environments by providing the ability to reason over semantic groundings, contextual cues, and temporal states. The proposed method employs large language models (GPT-3.5 and Claude Haiku) to reason over these cues and express that reasoning in terms of natural language, which can be used to inform future states. We are motivated by the context of search-and-rescue applications where efficient exploration is critical. We find that by leveraging natural language, semantics, and tracking temporal states, the proposed method greatly reduces exploration path distance and further exposes the need for environment-dependent heuristics. Moreover, the method is highly robust to a variety of environments and noisy vision detections, as shown with a 100% success rate in a series of comprehensive experiments across three different environments conducted in a custom simulation pipeline operating in Unreal Engine.

cs.RO↗

arXiv2018

Schwinger-Dyson Equations in Coulomb Gauge Consistent with Numerical Simulation

In the present work we undertake a study of the Schwinger-Dyson equation (SDE) in the Euclidean formulation of local quantum gauge field theory, with Coulomb gauge condition $\partial_i A_i = 0$. We continue a previous study which kept only instantaneous terms in the SDE that are proportional to $\delta(t)$ in order to calculate the instantaneous part of the time component of the gluon propagator $D_{A_0 A_0}(t, R)$. We compare the results of that study with a numerical simulation of lattice gauge theory and find that the infrared critical exponents and related quantities agree to within 1\% to 3\%. This raises the question, "Why is the agreement so good, despite the systematic neglect of non-instantaneous terms?" We discovered the happy circumstance that all the non-instantaneous terms are in fact zero. They are forbidden by the symmetry of the local action in Coulomb gauge under time-dependent gauge transformations $g(t)$. This remnant gauge symmetry is not fixed by the Coulomb gauge condition. The numerical result of the present calculation is the same as in the previous study; the novelty is that we now demonstrate that all the non-instantaneous terms in the SDE vanish. We derive some elementary properties of propagators which are a consequence of the remnant gauge symmetry. In particular the time component of the gluon propagator is found to be purely instantaneous $D_{A_0 A_0}(t, R) = \delta(t) V(R)$, where $V(R)$ is the color-Coulomb potential. Our results support the simple physical scenario in which confinement is the result of a linearly rising color-Coulomb potential, $V(R) \sim \sigma R$ at large $R$.

hep-th↗

arXiv2016

Instantaneous Dynamics of QCD

We start from the observation that, in the confining phase of QCD, the instantaneous color-Coulomb potential in Coulomb gauge is confining. This suggests that, in the confining phase, the dynamics, as expressed in the set of Schwinger-Dyson equations, may be dominated by the purely instantaneous terms. We develop a calculational scheme that expresses the instantaneous dynamics in the local formulation of QCD that includes a cut-off at the Gribov horizon.

hep-th↗

arXiv2016

Some Developments in Gribov's Approach to QCD

We review several developments in the formulation of QCD provided by the GZ action. These include the GZ-action at finite temperature, the relation of the horizon condition and the Kugo-Ojima confinement criterion, the relation of the horizon condition and the dual-Meisssner effect, the alternative derivation of the GZ action provided by the Maggiore-Schaden shift, and the spontaneous breaking of BRST symmetry. We conclude with a proposal for the definition of physical states in the presence of BRST breaking.

hep-th↗

arXiv2015

Local QCD Action at Finite Temperature

In this article, we carefully derive the horizon condition at finite temperature. Only the zero Matsubara mode is affected, and this result is consistent with the suitably modified Maggiore-Schaden shift, which takes into account temporal periodicity. We thus obtain a local, BRST-invariant action for QCD at finite temperature. The large-N limit and other calculational schemes for the magnetic mass and its relation to the Gribov mass are also discussed.

hep-th↗

arXiv2015

Origin of Confining Force

In this article we present exact calculations that substantiate a clear picture relating the confining force of QCD to the zero-modes of the Faddeev-Popov (FP) operator $\mathcal{M}(A) = - \partial \cdot D(A)$. This is done in two steps. First we calculate the spectral decomposition of the FP operator and show that the ghost propagator $\mathcal{G}(k; A) = \langle \vec{k}| \mathcal{M}^{-1}(A) | \vec{k} \rangle$ in an external gauge potential $A$ is enhanced at low $k$ in Fourier space for configurations $A$ on the Gribov horizon. This results from the new formula in the low-$k$ regime $\mathcal{G}^{ab}(k,A) = \delta^{ab} \lambda_{|\vec{k}|}^{-1}(gA)$, where $\lambda_{|\vec{k}|}(gA)$ is the eigenvalue of the FP operator that emerges from $\lambda_{|\vec{k}|}(0) = \vec{k}^2$ at $A$ = 0. Next we derive a strict inequality signaling the divergence of the color-Coulomb potential at low momentum $k$ namely, $\widetilde{\mathcal{V}}(k) \geq k^2 G^2(k)$ for $k \to 0$, where $\widetilde{\mathcal{V}}(k)$ is the Fourier transform of the color-Coulomb potential $\mathcal{V}(r)$ and $G(k)$ is the ghost propagator in momentum space. The first result holds in the Landau and Coulomb gauges, whereas the second holds in the Coulomb gauge only. We propose a new numerical lattice gauge fixing that should be closer to the present analytic approach than other numerical gauges.

hep-th↗

arXiv2014

Looking for Integrability on the Worldsheet of Confining Strings

We study restrictions on scattering amplitudes on the worldvolume of branes and strings (such as confining flux tubes in QCD) implied by the target space Poincare symmetry. We focus on exploring the conditions for the string worldsheet theory to be integrable. We prove that for a higher dimensional membrane the scattering amplitudes for the translational Goldstone modes ("branons") are double soft. At one-loop double softness is generically violated for the string worldsheet scattering as a consequence of collinear singularities. Violation of double softness implies in turn the breakdown of integrability. We prove that if branons are the only gapless degrees of freedom then the worldsheet integrability is compatible with target space Poincare symmetry only if the number of space-time dimensions is equal to D = 26 (a critical bosonic string), and for D = 3. We extend the analysis to include massless worldsheet fermions, resulting from spontaneous breakdown of the target space supersymmetry. We check that the tree-level integrability in this case is in one-to-one correspondence with the existence of a kappa-symmetric Green-Schwarz (GS) action. As a byproduct we show that at the leading order in the derivative expansion an N = 1 superstring without kappa-symmetry in D = 3,4,6,10 dimensions exhibits an accidental enhanced supersymmetry and is equivalent to a kappa-symmetric N = 2 GS superstring.

hep-th↗

arXiv2013

Living with the Wrong Sign

We describe a UV complete asymptotically fragile Lorentz-invariant theory exhibiting superluminal signal propagation. Its low energy effective action contains "wrong" sign higher dimensional operators. Nevertheless, the theory gives rise to an S-matrix, which is defined at all energies. As expected for a non-local theory, the corresponding scattering amplitudes are not exponentially bounded on the physical sheet, but otherwise are healthy. We study some of the physical consequences of this S-matrix.

hep-th↗

arXiv2013

St\"uckelberg Fields on the Effective p-brane

We demonstrate the one-to-one correspondence between reparametrization invariant effective actions for relativistic p-branes in flat target space and effective actions for transverse brane perturbations with non-linearly realized Poincar\'e symmetry. Starting with an action with non-linearly realized symmetry we construct the corresponding reparametrization invariant action by introducing St\"uckelberg fields. They combine with the transverse modes to form a Lorentz vector. The manifest Lorentz symmetry of the reparametrization invariant action follows directly from the non-linearly realized Lorentz symmetry of the initial action in terms of the physical modes.

hep-th↗