Stimulating Collaborative Advances Leveraging Expertise in the Mathematical and Scientific Foundations of Deep Learning | 21 561

Opportunity Information: Apply for 21 561

The National Science Foundation (NSF) grant opportunity titled "Stimulating Collaborative Advances Leveraging Expertise in the Mathematical and Scientific Foundations of Deep Learning" (Funding Opportunity Number 21-561) is designed to push deep learning beyond its current, largely empirical success by investing in the kind of rigorous theory that explains why these methods work, when they fail, and how they can be made more reliable and broadly usable. The core motivation is that deep learning has delivered striking results across science and engineering, yet the field still lacks a complete theoretical foundation. That gap makes it harder for new communities to adopt the technology confidently, and it slows progress on known limitations like data hunger, instability during training, vulnerability to adversarial inputs, and challenges around interpretability, privacy, and fairness. NSF is positioning this program as a way to confront those foundational questions directly, with the expectation that better theory will translate into more trustworthy, efficient, and widely accessible deep learning approaches.

A defining feature of the solicitation is its emphasis on true cross-disciplinary collaboration. NSF intends to support research teams that combine strengths from mathematicians and statisticians, electrical engineers, and computer scientists, reflecting the reality that deep learning sits at the intersection of mathematical structure, computational algorithms, and engineered systems. While the proposals must be submitted through the Directorate for Mathematical and Physical Sciences, Division of Mathematical Sciences (MPS/DMS), the projects are explicitly planned, funded, and managed in a cross-directorate way, involving MPS, Computer and Information Science and Engineering (CISE), Engineering (ENG), and Social, Behavioral and Economic Sciences (SBE). In practice, this means proposals are expected to be written with a genuinely integrated scientific plan rather than a collection of parallel efforts, and they will be reviewed and overseen by a team of NSF program directors representing multiple fields.

The program is aimed at "research collaborations" focused on some of the hardest theoretical questions in the mathematical and scientific foundations of deep learning. The topics are intentionally broad, but they are anchored in the idea that deep learning should be studied with the same seriousness and precision applied to other mature scientific and engineering disciplines. NSF highlights many potential directions, ranging from geometric and topological perspectives on representation learning, to Bayesian and probabilistic formulations that clarify uncertainty and generalization, to game-theoretic lenses relevant to adversarial training and strategic environments. On the methods side, the solicitation encourages analytical approaches rooted in optimal transport, optimization theory, approximation theory, and information theory, as well as frameworks based on dynamical systems, partial differential equations, and mean field theory, all of which have been increasingly used to model deep networks, training dynamics, and large-scale behavior in overparameterized regimes.

In addition to purely theoretical work, the solicitation makes room for application-inspired foundational research, as long as it is aimed at generalizable understanding rather than one-off demonstrations. Examples called out include understanding how to train effectively with small datasets, improving robustness under adversarial settings, and "closing the decision-action loop," which points toward learning systems that interact with and adapt to environments rather than passively fitting static data. The opportunity also explicitly recognizes the growing importance of societal and responsible-AI concerns as foundational scientific topics. It invites deeper work on what success metrics actually mean in modern deep learning, how to build privacy safeguards into learning algorithms, how causal inference can be made compatible with deep models, and how algorithmic fairness can be defined, measured, and achieved in ways that stand on solid mathematical footing rather than informal heuristics.

Team composition requirements are unusually explicit. Principal investigator (PI) teams must collectively demonstrate expertise spanning three areas: computer science, electrical engineering, and mathematics/statistics. Beyond simply listing disciplines, proposals are expected to show substantial collaborative contributions from each community, meaning the intellectual work should be interdependent and jointly developed, not compartmentalized. NSF also signals that proposals which increase diversity and broaden participation are encouraged, aligning with broader agency priorities to expand who participates in advanced AI research and who benefits from it.

Training and workforce development are built into the program rather than treated as an optional add-on. Each funded collaboration is expected to provide training through direct research involvement of recent PhD recipients, graduate students, and/or undergraduates, and importantly, across the multidisciplinary spectrum represented by the collaboration. The intent is not only to produce new results, but also to cultivate researchers who are fluent in multiple languages of the field, for example, students who can connect rigorous mathematics to practical training algorithms, or engineers who can translate theoretical insights into system-level designs.

In terms of scale and positioning, NSF describes this program as complementing, rather than duplicating, larger initiatives like the National Artificial Intelligence Research Institutes and the Harnessing the Data Revolution program. The distinction is that this solicitation supports collaborative, cross-disciplinary foundations work through a different modality and at a different scale, focusing tightly on theory and scientific underpinnings rather than broader institute-style structures.

The opportunity is a discretionary grant program under the NSF umbrella, categorized as science and technology and other research and development, with CFDA numbers 47.041, 47.049, 47.070, and 47.075. The listed award ceiling is $1,200,000, with an expectation of about 20 awards. The original closing date for submissions was May 12, 2021, and the solicitation was created February 13, 2021. Eligibility is described as "Others (see text field entitled Additional Information on Eligibility for clarification)," which is typical NSF language indicating that eligibility details are specified in the full solicitation, often centered on U.S. institutions of higher education and certain nonprofit or research organizations, depending on the program rules.

Overall, this grant opportunity is best understood as an effort to strengthen the scientific backbone of deep learning by funding teams that can connect rigorous mathematical analysis, statistical reasoning, algorithmic innovation, and engineering perspective. NSF is essentially betting that the next wave of breakthroughs will come not just from scaling models and datasets, but from understanding the principles that govern learning, generalization, robustness, and responsible deployment, and then using those principles to create methods that are more reliable, efficient, and inclusive.

• The National Science Foundation in the science and technology and other research and development sector is offering a public funding opportunity titled "Stimulating Collaborative Advances Leveraging Expertise in the Mathematical and Scientific Foundations of Deep Learning" and is now available to receive applicants.
• Interested and eligible applicants and submit their applications by referencing the CFDA number(s): 47.041, 47.049, 47.070, 47.075.
• This funding opportunity was created on Feb 13, 2021.
• Applicants must submit their applications by May 12, 2021. (Agency may still review applications by suitable applicants for the remaining/unused allocated funding in 2026.)
• Each selected applicant is eligible to receive up to $1,200,000.00 in funding.
• The number of recipients for this funding is limited to 20 candidate(s).
• Eligible applicants include: Others (see text field entitled Additional Information on Eligibility for clarification).

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