January 2026

arXiv:2601.03927v1 Announce Type: cross Abstract: Index tracking, also known as passive investing, has gained significant traction in financial markets due to its cost-effective and efficient approach to replicating the performance of a specific market index. This review paper provides a comprehensive overview of the various modeling approaches and strategies developed for index tracking, highlighting the strengths and limitations of each approach. We categorize the index tracking models into three broad frameworks: optimization-based models, statistical-based models and machine learning […]

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arXiv:2601.03764v1 Announce Type: cross Abstract: We analyze neural scaling laws in a solvable model of last-layer fine-tuning where targets have intrinsic, instance-heterogeneous difficulty. In our Latent Instance Difficulty (LID) model, each input’s target variance is governed by a latent “precision” drawn from a heavy-tailed distribution. While generalization loss recovers standard scaling laws, our main contribution connects this to inference. The pass@$k$ failure rate exhibits a power-law decay, $k^{-beta_text{eff}}$, but the observed exponent $beta_text{eff}$ is training-dependent. It grows with […]

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arXiv:2601.03498v1 Announce Type: cross Abstract: As intelligent systems are developed across diverse substrates – from machine learning models and neuromorphic hardware to in vitro neural cultures – understanding what gives a system agency has become increasingly important. Existing definitions, however, tend to rely on top-down descriptions that are difficult to quantify. We propose a bottom-up framework grounded in a system’s information-processing order: the extent to which its transformation of input evolves over time. We identify three orders of […]

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arXiv:2601.03368v1 Announce Type: cross Abstract: Natural languages exhibit striking regularities in their statistical structure, including notably the emergence of Zipf’s and Heaps’ laws. Despite this, it remains broadly unclear how these properties relate to the modern tokenisation schemes used in contemporary transformer models. In this note, we analyse the information content (as measured by the Shannon entropy) of various corpora under the assumption of a Zipfian frequency distribution, and derive a closed-form expression for the slot entropy expectation […]

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arXiv:2601.04149v1 Announce Type: new Abstract: Class imbalance significantly degrades classification performance, yet its effects are rarely analyzed from a unified theoretical perspective. We propose a principled framework based on three fundamental scales: the imbalance coefficient $eta$, the sample–dimension ratio $kappa$, and the intrinsic separability $Delta$. Starting from the Gaussian Bayes classifier, we derive closed-form Bayes errors and show how imbalance shifts the discriminant boundary, yielding a deterioration slope that predicts four regimes: Normal, Mild, Extreme, and Catastrophic. Using […]

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arXiv:2601.03533v1 Announce Type: new Abstract: Motivated by recent work on the experts problem in the streaming model, we consider the experts problem in the sliding window model. The sliding window model is a well-studied model that captures applications such as traffic monitoring, epidemic tracking, and automated trading, where recent information is more valuable than older data. Formally, we have $n$ experts, $T$ days, the ability to query the predictions of $q$ experts on each day, a limited amount […]

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arXiv:2601.03451v1 Announce Type: new Abstract: Modern AI systems increasingly operate inside markets and institutions where data, behavior, and incentives are endogenous. This paper develops an economic foundation for multi-agent learning by studying a principal-agent interaction in a Markov decision process with strategic externalities, where both the principal and the agent learn over time. We propose a two-phase incentive mechanism that first estimates implementable transfers and then uses them to steer long-run dynamics; under mild regret-based rationality and exploration […]

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arXiv:2601.03325v1 Announce Type: new Abstract: Identifiability is central to the interpretability of deep latent variable models, ensuring parameterisations are uniquely determined by the data-generating distribution. However, it remains underexplored for deep regime-switching time series. We develop a general theoretical framework for multi-lag Regime-Switching Models (RSMs), encompassing Markov Switching Models (MSMs) and Switching Dynamical Systems (SDSs). For MSMs, we formulate the model as a temporally structured finite mixture and prove identifiability of both the number of regimes and the […]

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arXiv:2601.03452v1 Announce Type: new Abstract: Resiliency has garnered attention in the management of critical infrastructure as a metric of system performance, but there are significant roadblocks to its implementation in a realistic decision-making framework. Contrasted to risk and reliability, which have robust quantification approaches and undergird many regulatory approaches to system safety (e.g., “risk-informed decision-making”), resiliency is a diffuse, qualitatively-understood characteristic, often treated differently or distinctly. However, in the emerging context of highly-complex, highly-interdependent critical systems, the idea […]

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arXiv:2601.03450v1 Announce Type: new Abstract: User-Defined Text Classification (UDTC) considers the challenge of classifying input text to user-specified, previously unseen classes, a setting that arises frequently in real-world applications such as enterprise analytics, content moderation, and domain-specific information retrieval. We propose a soft-contextualized encoder architecture for UDTC which contextualizes each candidate label with the label set and a static soft prompt representation of the input query. Training on diverse, multi-source datasets enables the model to generalize effectively to […]

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