[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-82747-en":3,"doc-seo-82747-105":29,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":13,"seo_description":14,"update_tm":27,"read_time":28},82747,549758252649,"Ivy","https://ap-avatar.wpscdn.com/avatar/8000253669c5317157?_k=1778319167496531819",8,"Research & Report","Trajectory Variance An Unsupervised Measure of Developmental Vocal Plasticity in Birdsong","Trajectory Variance quantifies how developmental age reshapes individual vocalizations in birdsong without relying on type labels. A displacement model learns age-conditioned shifts in autoencoder latent space, generates counterfactual predictions at multiple target ages for each vocalization, and uses the variance of those predictions as a per-vocalization plasticity score. On three zebra finches (183K–274K vocalizations, 40–101 days post-hatch), trajectory variance separates learned song syllables from innate calls (Cohen’s d = 0.29–0.57; AUC = 0.58–0.67) and correlates with spectral flatness (r = −0.48 to 0.75).","Trajectory Variance:  \nAn Unsupervised Measure of Developmental Vocal Plasticity in Birdsong  \nKanghwi Lee  1  \n1 Institute of Neuroinformatics, University of Zurich and ETH Zurich, Switzerland  \n[kanlee@ini.ethz.ch](kanlee@ini.ethz.ch)  \narXiv :2607 .03496v2 [ cs . SD] 13 Jul 2026  \nAbstract  \nHow much does a vocalization change over the course of development? We propose trajectory variance, a per-vocalization plasticity score that answers this question without type labels. A displacement model learns to predict age-conditioned shiftsin autoencoder latent space; the variance of its predictions across target ages quantifies how much each vocalization would change if produced at different developmental stages. Evaluated on three zebra finches (183K–274K vocalizations, 40–101 days post-hatch), trajectory variance separates learned song syllables from innate calls (Cohen’s d = 0.29–0.57, AUC = 0.58–0.67, after controlling for duration), while no nonparametric baseline achieves consistent separation. Trajectory variance also correlates with spectral flatness across all three birds (r = -0.48 to- 0.75): more plastic vocalizations tend to have more tonal, structured spectra.  \nIndex Terms: vocal development, birdsong, counterfactual generation, trajectory variance, optimal transport  \n1. Introduction  \nHow much does a vocalization change over the course of development? Static acoustic descriptors—spectral shape, duration, energy—characterize what a sound is at the moment it is produced, but not how it evolves. Analogous questions arise in single-cell genomics, where optimal-transport methods track how cell states shift along developmental trajectories [1] . We propose trajectory variance, a measure that applies counterfactual reasoning to vocal development: if this vocalization had been produced at a different age, how different would it be?  \nThe approach learns a model that predicts age-conditioned shifts in a latent representation of vocalizations. For each vocalization, counterfactual predictions are generated at several target ages, and the variance of these predictions serves as a plasticity score. Vocalizations predicted to change substantially across ages receive high trajectory variance; those predicted to remain stable receive low variance. No vocalization-type labels or manual annotation are needed.  \nWe validate this approach on zebra finch vocal development—a well-studied model system where learned song syllables coexist with innate calls [2, 3] . During a critical period from roughly 25 to 90 days post-hatch (dph), juvenile birds progress from unstructured subsong through plastic song to a crystallized adult motif [4] . Individual syllables are shaped by local exploration [5] and gradually stabilized [6], while innate calls remain comparatively unchanged. Existing computational approaches classify vocalizations by their static acoustic form [7, 8, 9, 10, 11], or characterize developmental dynamics through repertoire dating [12] and generative modeling [13] . Trajectory variance complements  \nthese: rather than classifying what a sound is or when similar sounds were produced, it measures how much a vocalization is predicted to change.  \nApplied to three birds (183K–274K vocalizations each, 40– 101 dph), trajectory variance from our displacement model reliably separates song syllables from calls with small-to-medium effect sizes (Cohen’s d = 0 .29–0.57, AUC = 0 .58–0.67 after controlling for duration), while no nonparametric baseline—Gaussian OT, per-age k-NN, or per-age optimal assignment—achieves consistent separation across all birds. Trajectory variance also correlates with spectral flatness across all three birds (r = −0 .48 to −0 .75) .  \nOur contribution is not an efficient song/call classifier—simpler methods suffice—but a per-vocalization measure of how much a vocalization is predicted to change over development.  \n2. Related Work  \nBirdsong analysis and development. Quantitative birdsong analysis has progressed","cbCaiqyWF2GJoqEy","https://ap.wps.com/l/cbCaiqyWF2GJoqEy","pdf",345573,1,5,"English","en",105,"# Introduction\n## Birdsong analysis and development\n## Related work\n# Method\n## Pipeline overview","[{\"question\":\"What is trajectory variance and what does it measure in birdsong development?\",\"answer\":\"Trajectory variance is a per-vocalization score that measures how much a vocalization is predicted to change across developmental ages. It is computed as the variance of counterfactual predictions at multiple target ages in a latent space.\"},{\"question\":\"How does the method generate counterfactual predictions without vocalization-type labels?\",\"answer\":\"The approach learns an age-conditioned displacement model that predicts latent shifts between a source age and several target ages. Counterfactual latents are generated for each target age, and their prediction variance becomes the plasticity score.\"},{\"question\":\"What results does trajectory variance achieve on zebra finches?\",\"answer\":\"Across three zebra finches, trajectory variance separates learned song syllables from innate calls with small-to-medium effect sizes (Cohen’s d = 0.29–0.57, AUC = 0.58–0.67 after controlling for duration). It also correlates with spectral flatness across birds (r = −0.48 to 0.75).\"}]",1784182662,13,{"code":4,"msg":30,"data":31},"ok",{"site_id":24,"language":23,"slug":32,"title":13,"keywords":33,"description":14,"schema_data":34,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":27},"trajectory-variance-an-unsupervised-measure-of-developmental-vocal-plasticity-in-birdsong","",{"@graph":35,"@context":85},[36,53,68],{"@type":37,"itemListElement":38},"BreadcrumbList",[39,43,47,50],{"item":40,"name":41,"@type":42,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":44,"name":45,"@type":42,"position":46},"https://docshare.wps.com/document/","Document",2,{"item":48,"name":12,"@type":42,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":42,"position":52},"https://docshare.wps.com/document/trajectory-variance-an-unsupervised-measure-of-developmental-vocal-plasticity-in-birdsong/82747/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":23,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":40,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-17","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What is trajectory variance and what does it measure in birdsong development?","Question",{"text":75,"@type":76},"Trajectory variance is a per-vocalization score that measures how much a vocalization is predicted to change across developmental ages. It is computed as the variance of counterfactual predictions at multiple target ages in a latent space.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does the method generate counterfactual predictions without vocalization-type labels?",{"text":80,"@type":76},"The approach learns an age-conditioned displacement model that predicts latent shifts between a source age and several target ages. Counterfactual latents are generated for each target age, and their prediction variance becomes the plasticity score.",{"name":82,"@type":73,"acceptedAnswer":83},"What results does trajectory variance achieve on zebra finches?",{"text":84,"@type":76},"Across three zebra finches, trajectory variance separates learned song syllables from innate calls with small-to-medium effect sizes (Cohen’s d = 0.29–0.57, AUC = 0.58–0.67 after controlling for duration). 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