International Development Research Centre

While scaling laws govern aggregate large language model performance, no scaling law has linked factual recall to both model size and training-data composition. We evaluated 38 models on over 8,900 scholarly references evaluated by an automated reference verification system. Recall quality follows a sigmoid in the log-linear combination of model parameter count and topic representation in training data. These two variables alone explain 60% of the variance across 16 dense models from four families, rising to 74-94% within individual families. The form matches a superposition-inspired account in which recall is gated by a signal-to-noise ratio: signal strength scales with concept frequency and the noise floor with model capacity.

Maize breeding programmes have developed a new generation of hybrid varieties to improve smallholders’ productivity and enhance climate resilience. However, varietal turnover in Kenya remains low, suggesting that new hybrid maize varieties may not fully address smallholders’ needs or that knowledge about them remains limited. In this exploratory study, we applied a method referred to as means-end chains to understand the attributes smallholders consider when differentiating maize seed products, and the importance and value of these attributes. We interviewed 82 smallholders in two counties in Kenya and analysed the data by county and gender. Smallholders used a range of attributes to differentiate maize seed products, indicating familiarity with most maize varieties included in the study. However, the attributes that farmers used to distinguish between maize seed products were not always those of highest value when choosing seeds for planting. Preferences for attributes differed between counties and were shaped by climate and the importance of maize in livelihoods. Women and men used and preferred similar attributes, yet their choices were informed by different underlying motivations and values. Overall, participants highly valued ‘higher yield’, ‘harvest assurance’ and ‘earliness’, reflecting diverse household uses of maize to support food security, income generation and well-being. The findings suggest that farmers use a portfolio of maize varieties to meet different household needs. These results have implications for efforts to promote varietal turnover and complement previous studies by offering guidance for demand-led breeding programmes and other seed systems actors working to strengthen food security for smallholder farmers.

BACKGROUND:Patient and public involvement (PPI) is recognized as essential for scaling interventions in health and social services, but there are few guidelines to support it. We sought consensus on strategies for involving patients and the public in scaling in an equitable and meaningful way. METHODS:We conducted a participatory consensus study inspired by Delphi techniques. We used as a starting point 23 PPI strategies for scaling (on the involvement continuum, from providing information to full co-production) as identified in a 2024 scoping review. First, we established a steering committee, intended to include patient or public representatives, to validate the relevance of the 23 strategies for inclusion in an online survey consensus process to confirm their applicability to PPI. Second, researchers, health professionals, policymakers, and patient or public representatives completed the online survey to assess the validated strategies against four evaluation criteria: equity, comprehensiveness, adaptability and significance. We used the DELPHISTAR checklist to report results and the GRIPP2 framework to report PPI in the study. FINDINGS:All 23 PPI strategies were found relevant by the steering committee and proceeded to the 2-round consensus process to evaluate 92 items (23 strategies x 4 criteria). By April, 2025, 14 participants had completed the first round and nine had also completed the second. Participants included patient and public representatives (n = 5), researchers (n = 6), health professionals (n = 3) and policymakers (n = 2) mostly based in Canada (n = 10). Of 23 PPI strategies assessed, 19 achieved consensus on at least one of the four criteria. Three strategies (Service users' needs assessment, Organizational advisory groups and Co-leadership in quality and safety improvement) achieved consensus across all criteria, while four strategies did not reach consensus on any. Co-leadership in quality and safety improvement (88.3%), Co-leadership in policymaking (87.3%) and Service users' needs assessment (87.3%) achieved the highest global scores. Consensus was reached on 44/92 items, most frequently for equity. These strategies were primarily situated in the organization of health and social care and the co-production level of the involvement continuum. CONCLUSIONS:The strategies prioritized by stakeholders were not necessarily the ones most frequently discussed in the literature. We recommend systematically involving patient and public representatives throughout scaling, including when choosing PPI strategies. PATIENT OR PUBLIC CONTRIBUTION:A patient instructor was involved in the steering committee, sharing decisions on study design, data collection instruments and dissemination of findings. Patient and public representatives also took part in the consensus process, and their feedback was considered equal to that of the other experts.

Background Scaling primary care innovations to benefit broader populations is a key priority for decision-makers. While the science of effective scaling evolves, little is known about innovations that scale spontaneously , i.e., without deliberate guidance. Objectives To assess the spontaneous scaling process of STAT-C, a training workshop supporting management of sick leave related to common mental health disorders, and its perceived effects on primary care services and beneficiaries. Methods We conducted a mixed-methods descriptive single-case study using an Integrated Knowledge Translation (iKT) approach involving patient users. The case was defined as the spontaneous scaling of STAT-C, presented at the Quebec College of Family Physicians’ Innovation Symposium and assessed using a selection criteria checklist. Over one year, we observed the scaling process through monthly meetings with the innovation team and collected documents to retrace key steps. We conducted interviews with decision-makers, healthcare professionals, and end-users, along with a focus group with the innovation team. Data were analyzed thematically using documents, interviews, and meetings. The scaling process was examined using the Scaling Impact principles: justification, optimal scale, coordination, and dynamic evaluation. Results STAT-C met 71% of selection criteria. Fourteen participants were interviewed: innovation team (n = 2), healthcare professionals (n = 5), decision-makers (n = 4), and end-users (n = 3). Technical justifications included the need to standardize information across professionals (n = 10), while moral ones emphasized alignment with patient values (n = 8). Interviews revealed limited awareness of dynamic evaluation and a lack of indicators supporting further scaling. Ethical rationales reflected goal-oriented and duty-based reasoning. Preliminary data suggested improvements in healthcare professionals’ self-reported competence in managing CMHD-related sick leave, offering early indications of the innovation’s relevance. Conclusion This study highlights strategies, challenges, and outcomes of spontaneous scaling under real-world conditions, showing how pathways emerge, strategies evolve, and ethical dimensions shape decision-making.