Boredom – a pervasive mental state – promotes the pursuit of novel information by assigning negative value to monotonous conditions. Yet, how the brain extracts and represents the information content of ongoing sensory experience remains poorly understood. Here, we combine behavioral assays, neurophysiological recordings and computational modeling across humans and mice to investigate how sensory information shapes boredom-related behavior. In a cross-species choice task, both humans and mice robustly avoid monotonous sources of sensory stimulation. We formalize perceived monotony using empirical entropy as a measure of information content and show that monotony avoidance scales directly with low entropy and in humans correlates with boredom experience. Human electroencephalography and mesoscopic calcium imaging in mice reveal that the recruitment of neocortical activity tracks stimulus entropy. Two-photon calcium imaging in the auditory cortex of mice further uncovers a stimulus-invariant population code for entropy, supported by neurons tuned to information content. A recurrent network model reproduced this code through an interplay of afferent depression and recurrent facilitation. Together, we demonstrate how the information content of sensory experience is represented in cortical population activity, providing a basis for boredom-related avoidance behavior. Thus, our findings link synaptic and neuronal dynamics to boredom, acting as a safeguard mechanism to ensure high information input to the brain. ### Competing Interest Statement The authors have declared no competing interest. This work was supported by research grant Deutsche Forschungsgemeinschaft CRC1080-C05 (S.R.), Deutsche Forschungsgemeinschaft SPP 2041 Project #347573108 (S.R.), Deutsche Forschungsgemeinschaft/Agence nationale de la recherche Project #431393205 (S.R.), Deutsche Forschungsgemeinschaft DIP M-BM-^SNeurobiology of ForgettingM-BM-^T (S.R.), Rhine-Main University Alliance RMU (S.R.), JST Moonshot R & D #JPMJMS2292-A1-02 (O.T.), Deutsche Forschungsgemeinschaft #512007073 SFB/TRR379 TP B02 (O.T.), BMFTR German Center for Mental Health (DZPG, grant 01EE2505C & VISIONS TRESPE 01EE2507Q) (O.T), and a fellowship of the Focus Translational Neuroscience Mainz (J.S., L.W.). The funders had no role in study design, data collection and analysis, decision to publish or preparation of the manuscript.

Neuronal activity patterns change continuously over days and weeks, a phenomenon known as representational drift. Despite this, the geometric structure of population representations, namely the pairwise similarities between stimulus-evoked activity patterns, remains remarkably stable. How can ongoing changes in activity be consistent with stable representational similarity? We show that this is a generic consequence of random connectivity: in networks with random connectivity, output similarity is a monotonically increasing function of input similarity, independent of the specific connectivity pattern. Drift, whether driven by random synaptic turnover or Hebbian plasticity, merely transitions the network between random instantiations, leaving similarity intact. This extends to recurrent architectures and to deep neural networks, where continued training beyond performance saturation produces activity drift while preserving representational similarity. Although connectivity in the brain is not random, networks trained on high-dimensional inputs acquire connectivity that behaves statistically like a random projection, making these results broadly applicable to biological neural circuits. ### Competing Interest Statement The authors have declared no competing interest. Spanish Ministry of Science and Innovation, PCI2023-145967-2, PID2021-124702OB-I00 Spanish State Research Agency (AEI) – Severo Ochoa and María de Maeztu Program for Centers and Units of Excellence in R&D, CEX2020-001084-M German Research Foundation (DFG), FOR 5368 ARENA

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