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Cozmin Ududec

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quant-ph cond-mat.stat-mech physics.soc-ph q-fin.ST Artificial Intelligence math-ph math.MP q-fin.PM q-fin.TR

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preprint2026arXiv

Log analysis is necessary for credible evaluation of AI agents

Agent benchmarks typically report only final outcomes: pass or fail. This threatens evaluation credibility in three ways. First, scores may be inflated or deflated by shortcuts and benchmark artifacts, misrepresenting capability. Second, benchmark performance may fail to predict real-world utility due to scaffold limitations and recurring failure modes. Finally, capability scores may conceal dangerous or catastrophic actions taken by the agent. We argue that log analysis -- the systematic tracking and analysis of the inputs, execution, and outputs of an AI agent -- is necessary to overcome these validity threats and promote credible agent evaluation. In this paper, we (1) present a taxonomy of threats to credible evaluation documented through log analysis, and (2) develop a set of guiding principles for log analysis. We illustrate these principles on tau-Bench Airline, revealing that pass^5 performance was under-elicited by nearly 50% and surfacing deployment failure modes invisible to outcome metrics. We conclude with pragmatic recommendations to increase uptake of log analysis, directed at diverse stakeholders including benchmark creators, model developers, independent evaluators, and deployers.

preprint2017arXiv

Correlations and Clustering in Wholesale Electricity Markets

We study the structure of locational marginal prices in day-ahead and real-time wholesale electricity markets. In particular, we consider the case of two North American markets and show that the price correlations contain information on the locational structure of the grid. We study various clustering methods and introduce a type of correlation function based on event synchronization for spiky time series, and another based on string correlations of location names provided by the markets. This allows us to reconstruct aspects of the locational structure of the grid.

preprint2016arXiv

Optimal growth trajectories with finite carrying capacity

We consider the problem of finding optimal strategies that maximize the average growth-rate of multiplicative stochastic processes. For a geometric Brownian motion the problem is solved through the so-called Kelly criterion, according to which the optimal growth rate is achieved by investing a constant given fraction of resources at any step of the dynamics. We generalize these finding to the case of dynamical equations with finite carrying capacity, which can find applications in biology, mathematical ecology, and finance. We formulate the problem in terms of a stochastic process with multiplicative noise and a non-linear drift term that is determined by the specific functional form of carrying capacity. We solve the stochastic equation for two classes of carrying capacity functions (power laws and logarithmic), and in both cases compute optimal trajectories of the control parameter. We further test the validity of our analytical results using numerical simulations.

preprint2015arXiv

Higher-order interference and single-system postulates characterizing quantum theory

We present a new characterization of quantum theory in terms of simple physical principles that is different from previous ones in two important respects: first, it only refers to properties of single systems without any assumptions on the composition of many systems; and second, it is closer to experiment by having absence of higher-order interference as a postulate, which is currently the subject of experimental investigation. We give three postulates -- no higher-order interference, classical decomposability of states, and strong symmetry -- and prove that the only non-classical operational probabilistic theories satisfying them are real, complex, and quaternionic quantum theory, together with 3-level octonionic quantum theory and ball state spaces of arbitrary dimension. Then we show that adding observability of energy as a fourth postulate yields complex quantum theory as the unique solution, relating the emergence of the complex numbers to the possibility of Hamiltonian dynamics. We also show that there may be interesting non-quantum theories satisfying only the first two of our postulates, which would allow for higher-order interference in experiments while still respecting the contextuality analogue of the local orthogonality principle.

preprint2015arXiv

Multi-scaling of wholesale electricity prices

We empirically analyze the most volatile component of the electricity price time series from two North-American wholesale electricity markets. We show that these time series exhibit fluctuations which are not described by a Brownian Motion, as they show multi-scaling, high Hurst exponents and sharp price movements. We use the generalized Hurst exponent (GHE, $H(q)$) to show that although these time-series have strong cyclical components, the fluctuations exhibit persistent behaviour, i.e., $H(q)>0.5$. We investigate the effectiveness of the GHE as a predictive tool in a simple linear forecasting model, and study the forecast error as a function of $H(q)$, with $q=1$ and $q=2$. Our results suggest that the GHE can be used as prediction tool for these time series when the Hurst exponent is dynamically evaluated on rolling time windows of size $\approx 50 - 100$ hours. These results are also compared to the case in which the cyclical components have been subtracted from the time series, showing the importance of cyclicality in the prediction power of the Hurst exponent.

preprint2013arXiv

Information-theoretic equilibration: the appearance of irreversibility under complex quantum dynamics

The question of how irreversibility can emerge as a generic phenomena when the underlying mechanical theory is reversible has been a long-standing fundamental problem for both classical and quantum mechanics. We describe a mechanism for the appearance of irreversibility that applies to coherent, isolated systems in a pure quantum state. This equilibration mechanism requires only an assumption of sufficiently complex internal dynamics and natural information-theoretic constraints arising from the infeasibility of collecting an astronomical amount of measurement data. Remarkably, we are able to prove that irreversibility can be understood as typical without assuming decoherence or restricting to coarse-grained observables, and hence occurs under distinct conditions and time-scales than those implied by the usual decoherence point of view. We illustrate the effect numerically in several model systems and prove that the effect is typical under the standard random-matrix conjecture for complex quantum systems.

preprint2012arXiv

The structure of reversible computation determines the self-duality of quantum theory

Predictions for measurement outcomes in physical theories are usually computed by combining two distinct notions: a state, describing the physical system, and an observable, describing the measurement which is performed. In quantum theory, however, both notions are in some sense identical: outcome probabilities are given by the overlap between two state vectors - quantum theory is self-dual. In this paper, we show that this notion of self-duality can be understood from a dynamical point of view. We prove that self-duality follows from a computational primitive called bit symmetry: every logical bit can be mapped to any other logical bit by a reversible transformation. Specifically, we consider probabilistic theories more general than quantum theory, and prove that every bit-symmetric theory must necessarily be self-dual. We also show that bit symmetry yields stronger restrictions on the set of allowed bipartite states than the no-signalling principle alone, suggesting reversible time evolution as a possible reason for limitations of non-locality.

preprint2009arXiv

Three Slit Experiments and the Structure of Quantum Theory

In spite of the interference manifested in the double-slit experiment, quantum theory predicts that a measure of interference defined by Sorkin and involving various outcome probabilities from an experiment with three slits, is identically zero. We adapt Sorkin's measure into a general operational probabilistic framework for physical theories, and then study its relationship to the structure of quantum theory. In particular, we characterize the class of probabilistic theories for which the interference measure is zero as ones in which it is possible to fully determine the state of a system via specific sets of 'two-slit' experiments.