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Surprisal theory links human processing effort to the predictability of an upcoming linguistic unit, but empirical work often leaves the notion of a unit underspecified. In practice, experimental stimuli are segmented into linguistically motivated units (e.g., words), while pretrained language models assign probability mass to a fixed token alphabet that typically does not align with those units. As a result, surprisal-based predictors depend implicitly on ad hoc procedures that conflate two distinct modeling choices: the definition of the unit of analysis and the choice of regions of interest over which predictions are evaluated. In this paper, we disentangle these choices and give a unified framework for reasoning about surprisal over arbitrary unit inventories. We argue that surprisal-based analyses should make these choices explicit and treat tokenization as an implementation detail rather than a scientific primitive.

Previous work examining the Uniform Information Density (UID) hypothesis has shown that while information as measured by surprisal metrics is distributed more or less evenly across documents overall, local discrepancies can arise due to functional pressures corresponding to syntactic and discourse structural constraints. However, work thus far has largely disregarded the relative salience of discourse participants. We fill this gap by studying how overall salience of entities in discourse relates to surprisal using 70K manually annotated mentions across 16 genres of English and a novel minimal-pair prompting method. Our results show that globally salient entities exhibit significantly higher surprisal than non-salient ones, even controlling for position, length, and nesting confounds. Moreover, salient entities systematically reduce surprisal for surrounding content when used as prompts, enhancing document-level predictability. This effect varies by genre, appearing strongest in topic-coherent texts and weakest in conversational contexts. Our findings refine the UID competing pressures framework by identifying global entity salience as a mechanism shaping information distribution i

Language-model (LM) surprisal is widely used as a proxy for contextual predictability and has been reported to correlate with metaphor novelty judgments. However, surprisal is tightly intertwined with lexical frequency. We explore this interaction on metaphor novelty ratings using two different word frequency measures. We analyse surprisal estimates from eight Pythia model sizes and 154 training checkpoints. Across settings, word frequency is a stronger predictor of metaphor novelty than surprisal. Across training stages, the surprisal--novelty association peaks at an early stage and then falls again, mirroring a similarly timed increase in the surprisal--frequency association. These results suggest that the often-reported optimal LM surprisal settings may incorrectly associate contextual predictability with metaphor novelty and processing difficulty, whereas lexical frequency may be the major underlying factor.

Consider the following story: A teacher announces to her students a test for the following week, such that the test will be ``surprising''. The students use this as the basis for a ``logical derivation'' and reach a contradiction, which they (falsely) interpret as saying that there cannot be a test. The teacher gives a test e.g. on Wednesday, ``surprising'' the students. Its curious turns give the story the flavor of a paradox. Alternative names are the {\it unexpected hanging paradox\/} and the {\it prediction paradox}. Discussions and analyses of the story in the philosophical and mathematical literature are abundant, spanning 80 years until today. Apparently, none of the known explanations has been generally accepted as conclusive. We offer a fresh view, in propositional logic. ``Surprise'' is captured as unprovability of a certain formula from some axiom system. ``Knowledge'' corresponds to axiom systems and can be gained by mathematical proofs. The notorious property of self-reference in the announcement is cleanly accommodated. All errors made by the students are identified. A general analysis shows that the students cannot learn anything from the announcement. This is the fi

Psycholinguistics studies show that human readers fall for coherence illusions: an incoherent discourse can seem coherent simply because a distractor matches what comes next. We investigate whether Dutch language models (6 monolingual and 4 multilingual) show the same behavior on texts that link back to earlier context with words such as 'again' and 'too'. First, we find that surprisal at the critical word tracks human acceptability judgments and eye-tracking data. Models are more surprised by incoherent continuations, but a matching distractor in the prior context reduces this surprisal. Second, attention entropy at the critical position identifies heads that behave differently under coherence vs. incoherence. We find that ablating these heads shows transfer effects across experiments, suggesting a shared mechanism. Third, we introduce energy from the associative-memory literature as a metric to quantify discourse coherence. Taken together, our results show that coherence illusions arise in Dutch LLMs, with entropy and energy exposing mechanisms that operate across settings.

Anomaly detection methods are widely used but often rely on ad hoc rules or strong assumptions, and they often focus on tail events, missing ``inlier'' anomalies that occur in low-density gaps between modes. We propose a unified framework that defines an anomaly as an observation with unusually low probability under a (possibly misspecified) model. For each observation we compute its surprisal (the negative log generalized density) and define an anomaly score as the probability of a surprisal at least as large as that observed. This reduces anomaly detection for complex univariate or multivariate data to estimating the upper tail of a univariate surprisal distribution. We develop two model-robust estimators of these tail probabilities: an empirical estimator based on the observed surprisal distribution and an extreme-value estimator that fits a Generalized Pareto Distribution above a high threshold. For the empirical method we give conditions under which tail ordering is preserved and derive finite-sample confidence guarantees via the Dvoretzky--Kiefer--Wolfowitz inequality. For the GPD method we establish broad tail conditions ensuring classical extreme-value behavior. Simulations

A community of researchers appears to think that a machine can be surprised and have introduced various surprise measures, principally the Shannon Surprise and the Bayesian Surprise. The questions of what constitutes a surprise and how to react to one still elicit debates. In this work, we introduce Mutual Information Surprise (MIS), a new framework that redefines surprise not as anomaly measure, but as a signal of epistemic growth. Furthermore, we develop a statistical test sequence that could trigger a surprise reaction and propose a MIS-based reaction policy that dynamically governs system behavior through sampling adjustment and process forking. Empirical evaluations -- on both synthetic domains and a dynamic pollution map estimation task -- show that a system governed by the MIS-based reaction policy significantly outperforms those under classical surprise-based approaches in stability, responsiveness, and predictive accuracy. The important implication of our new proposal is that MIS quantifies the impact of new observations on mutual information, shifts surprise from reactive to reflective, enables reflection on learning progression, and thus offers a path toward self-aware a

The well-known bar instability of rotationally-supported disk galaxy models has been studied extensively since its first discovery over half a century ago. We were therefore very surprised to find cases of disks embedded in rigid halos, which on the basis of widely-cited criteria should be unstable, that appeared to be robustly stable. Here we show that the unstable bar mode in such simulations was being suppressed by changes to the disk caused by other instabilities having higher angular symmetry that were the first to saturate. Although this may seem like a promising solution to the long-standing puzzle presented by the apparent stability of real disk galaxies, we also show that instability is restored in the same models when the rigid halo is replaced by a live population of particles, where the usual stability conditions apply. Our study has been confined to a narrow range of models, and we cannot therefore exclude the possibility that mode interference may be able to prevent bar formation in other models having live halos.

In-context learning (ICL) has emerged as a powerful paradigm for task adaptation in large language models (LLMs), where models infer underlying task structures from a few demonstrations. However, ICL remains susceptible to biases that arise from prior knowledge and contextual demonstrations, which can degrade the performance of LLMs. Existing bias calibration methods typically apply fixed class priors across all inputs, limiting their efficacy in dynamic ICL settings where the context for each query differs. To address these limitations, we adopt implicit sequential Bayesian inference as a framework for interpreting ICL, identify "surprise" as an informative signal for class prior shift, and introduce a novel method--Surprise Calibration (SC). SC leverages the notion of surprise to capture the temporal dynamics of class priors, providing a more adaptive and computationally efficient solution for in-context learning. We empirically demonstrate the superiority of SC over existing bias calibration techniques across a range of benchmark natural language processing tasks.

In modeling musical surprisal expectancy with computational methods, it has been proposed to use the information content (IC) of one-step predictions from an autoregressive model as a proxy for surprisal in symbolic music. With an appropriately chosen model, the IC of musical events has been shown to correlate with human perception of surprise and complexity aspects, including tonal and rhythmic complexity. This work investigates whether an analogous methodology can be applied to music audio. We train an autoregressive Transformer model to predict compressed latent audio representations of a pretrained autoencoder network. We verify learning effects by estimating the decrease in IC with repetitions. We investigate the mean IC of musical segment types (e.g., A or B) and find that segment types appearing later in a piece have a higher IC than earlier ones on average. We investigate the IC's relation to audio and musical features and find it correlated with timbral variations and loudness and, to a lesser extent, dissonance, rhythmic complexity, and onset density related to audio and musical features. Finally, we investigate if the IC can predict EEG responses to songs and thus model

Validating the safety and performance of an autonomous vehicle (AV) requires benchmarking on real-world driving logs. However, typical driving logs contain mostly uneventful scenarios with minimal interactions between road users. Identifying interactive scenarios in real-world driving logs enables the curation of datasets that amplify critical signals and provide a more accurate assessment of an AV's performance. In this paper, we present a novel metric that identifies interactive scenarios by measuring an AV's surprise potential on others. First, we identify three dimensions of the design space to describe a family of surprise potential measures. Second, we exhaustively evaluate and compare different instantiations of the surprise potential measure within this design space on the nuScenes dataset. To determine how well a surprise potential measure correctly identifies an interactive scenario, we use a reward model learned from human preferences to assess alignment with human intuition. Our proposed surprise potential, arising from this exhaustive comparative study, achieves a correlation of more than 0.82 with the human-aligned reward function, outperforming existing approaches. L

We propose utilizing match-level suspense and surprise - which capture the entertainment utility created by competitive balance and outcome uncertainty for sports spectators - as alternative policy targets for league organizers and managers. Through simulations, we derive a benchmark range for suspense and surprise based on a perfectly balanced match before analyzing over 25,000 men's matches (2010/11-2023/24) and 725 women's matches (2023/24) from Europe's top football leagues. Our findings reveal that an average match generates lower suspense compared to the benchmark range, particularly for top teams, while surprise values consistently align with the benchmark. Moreover, we observe nuanced trends over time in men's football and highlight notable differences across leagues and clubs in both men's and women's competitions. These insights enhance our understanding of how the attractiveness of matches arises from competitive balance and carry important policy implications.

Predicting corporate earnings surprises is a profitable yet challenging task, as accurate forecasts can inform significant investment decisions. However, progress in this domain has been constrained by a reliance on expensive, proprietary, and text-only data, limiting the development of advanced models. To address this gap, we introduce \textbf{FinCall-Surprise} (Financial Conference Call for Earning Surprise Prediction), the first large-scale, open-source, and multi-modal dataset for earnings surprise prediction. Comprising 2,688 unique corporate conference calls from 2019 to 2021, our dataset features word-to-word conference call textual transcripts, full audio recordings, and corresponding presentation slides. We establish a comprehensive benchmark by evaluating 26 state-of-the-art unimodal and multi-modal LLMs. Our findings reveal that (1) while many models achieve high accuracy, this performance is often an illusion caused by significant class imbalance in the real-world data. (2) Some specialized financial models demonstrate unexpected weaknesses in instruction-following and language generation. (3) Although incorporating audio and visual modalities provides some performance

Real-world videos often show routine activities punctuated by memorable, surprising events. However, most Video-LLMs process videos by sampling frames uniformly, likely missing critical moments that define a video's narrative. We introduce SPIKE, an inference-time framework that quantifies Bayesian Surprise as the belief update triggered by new visual evidence in the video stream, identifying moments where new visual evidence conflicts with prior beliefs. SPIKE effectively localizes surprise in videos, strongly correlated with humans on positive (FunQA) and negative (Oops!) surprise benchmarks. Since the beliefs of zero-shot Video-LLMs are often suboptimal, we develop SPIKE-RL, which leverages GRPO to optimize belief hypotheses based on a reward signal from the video caption. SPIKE and SPIKE-RL guide query-agnostic surprise-weighted frame sampling, which allocates more frames to interesting moments in the video. With this strategy, we achieve consistent performance gains on five downstream benchmarks over uniform sampling. By enabling Video-LLMs to track beliefs and register surprise, our work paves the way for more robust models that can revise their understanding in response to n

The effect of surprisal on processing difficulty has been a central topic of investigation in psycholinguistics. Here, we use eyetracking data to examine three language processing regimes that are common in daily life but have not been addressed with respect to this question: information seeking, repeated processing, and the combination of the two. Using standard regime-agnostic surprisal estimates we find that the prediction of surprisal theory regarding the presence of a linear effect of surprisal on processing times, extends to these regimes. However, when using surprisal estimates from regime-specific contexts that match the contexts and tasks given to humans, we find that in information seeking, such estimates do not improve the predictive power of processing times compared to standard surprisals. Further, regime-specific contexts yield near zero surprisal estimates with no predictive power for processing times in repeated reading. These findings point to misalignments of task and memory representations between humans and current language models, and question the extent to which such models can be used for estimating cognitively relevant quantities. We further discuss theoreti

Traditional finance and macroeconomic models usually assume people can form rational expectations or reach them via a learning path by minimizing prediction errors. The recent Reference Model Based Learning (RMBL) model provides a new perspective: It hypothesizes that people minimize surprises instead of errors. Following the spirit of Simon's "satisficing" criteria, RMBL predicts that they will minimize errors only when the prediction error exceeds a threshold. We conduct meta-analyses based on 18 Learning-to-Forecast Experiments (LtFEs; N=41,490). Our results from the horse race test consistently show that student participants minimize surprises instead of errors in the LtFEs. In contrast, the results based on the data from the Survey of Professional Forecasters (SPF) show no evidence that they minimize surprises. Together, our results suggest that minimizing surprises by implementing RMBL may be the simple procedure people employ when navigating complexity in forecasting.