An Identifiability Theory of Masked Prediction: Mode Blindness and Mask Schedules
Yichao CaiJaven Qinfeng Shi
Sep 2026
Machine LearningData Science
Abstract
Masked prediction learns by inferring missing variables from visible context. This raises a fundamental question: when does near-optimal conditional prediction determine the joint data law? We study this via an $\varepsilon$-identifiability modulus measuring the largest joint-law error compatible with masked-prediction excess risk at most $\varepsilon$. For slow-mixing data laws with separated global modes, we show that a model can assign substantially incorrect probabilities to entire data regimes while incurring exponentially small excess risk. An exact information decomposition reveals why: for a fixed mask, the prediction loss detects only the portion of the mode-weight mismatch that the visible context leaves unresolved. For small mode-weight perturbations, this sensitivity is proportional to residual mode uncertainty. Once averaged over masks, this residual uncertainty governs the objective's sensitivity to global mode frequencies, with low-visibility masks restoring mode-weight sensitivity and positive full-mask mass providing universal joint-law control under the joint conditional objective. We provide computational and empirical evidence for these predictions through exact calculations, controlled optimization experiments, and measurements on natural text. More broadly, our study suggests that a predictive objective can identify global distinctions only insofar as its conditioning structure leaves them unresolved.
Agile - denoting "the quality of being agile, readiness for motion, nimbleness, activity, dexterity in motion" - software development methods are attempting to offer an answer to the eager business community asking for lighter weight along with faster and nimbler software development processes. This is especially the case with the rapidly growing and volatile Internet software industry as well as for the emerging mobile application environment. The new agile methods have evoked substantial amount of literature and debates. However, academic research on the subject is still scarce, as most of existing publications are written by practitioners or consultants. The aim of this publication is to begin filling this gap by systematically reviewing the existing literature on agile software development methodologies. This publication has three purposes. First, it proposes a definition and a classification of agile software development approaches. Second, it analyses ten software development methods that can be characterized as being "agile" against the defined criterion. Third, it compares these methods and highlights their similarities and differences. Based on this analysis, future research needs are identified and discussed.
P. Abrahamsson, O. Salo, Jussi Ronkainen et al.· arXiv.org· 728 citations· ⚡54
Context: Software startups are newly created companies with no operating history and fast in producing cutting-edge technologies. These companies develop software under highly uncertain conditions, tackling fast-growing markets under severe lack of resources. Therefore, software startups present a unique combination of characteristics which pose several challenges to software development activities. Objective: This study aims to structure and analyze the literature on software development in startup companies, determining thereby the potential for technology transfer and identifying software development work practices reported by practitioners and researchers. Method: We conducted a systematic mapping study, developing a classification schema, ranking the selected primary studies according their rigor and relevance, and analyzing reported software development work practices in startups. Results: A total of 43 primary studies were identified and mapped, synthesizing the available evidence on software development in startups. Only 16 studies are entirely dedicated to software development in startups, of which 10 result in a weak contribution (advice and implications (6); lesson learned (3); tool (1)). Nineteen studies focus on managerial and organizational factors. Moreover, only 9 studies exhibit high scientific rigor and relevance. From the reviewed primary studies, 213 software engineering work practices were extracted, categorized and analyzed. Conclusion: This mapping study provides the first systematic exploration of the state-of-art on software startup research. The existing body of knowledge is limited to a few high quality studies. Furthermore, the results indicate that software engineering work practices are chosen opportunistically, adapted and configured to provide value under the constrains imposed by the startup context.
Nicolò Paternoster, Carmine Giardino, M. Unterkalmsteiner et al.· Information and Software Tec...· 394 citations· ⚡54
A new method for surgically removing training examples from a model reveals that as datasets grow, the link between what a model learns and what it produces dissolves.
