You are here

Neural Collapse for Responsible Artificial Intelligence in Directed Energy


OUSD (R&E) CRITICAL TECHNOLOGY AREA(S): Trusted AI and Autonomy; Advanced Computing and Software; Directed Energy (DE)


The technology within this topic is restricted under the International Traffic in Arms Regulation (ITAR), 22 CFR Parts 120-130, which controls the export and import of defense-related material and services, including export of sensitive technical data, or the Export Administration Regulation (EAR), 15 CFR Parts 730-774, which controls dual use items. Offerors must disclose any proposed use of foreign nationals (FNs), their country(ies) of origin, the type of visa or work permit possessed, and the statement of work (SOW) tasks intended for accomplishment by the FN(s) in accordance with the Announcement. Offerors are advised foreign nationals proposed to perform on this topic may be restricted due to the technical data under US Export Control Laws.



To develop theoretical foundations necessary to support and sustain Artificial Intelligence technologies within Directed Energy.



Modern neural network-based machine learning techniques achieve high performance, at the cost of limited explainability and understandability through their black box structure. As described in a recent Defense strategy [1] and directive [2] Defense Artificial Intelligence systems in general require a level of trust incompatible with state-of-the art machine learning systems. A recent executive order [3] further demonstrates the need for trustworthy Artificial Intelligence systems.



AFRL/RD is interested in investigating solutions that address the described black box incompatibility for Directed Energy-specific target acquisition and tracking problems. Specific problems might include acquisition of small, unmanned aircraft, cruise missiles, small ground-based targets, and anti-aircraft missiles. If successful, compatibility will have impact to both AFRL/RD and other Directed Energy organizations, with strong potential for generalization to other Department of Defense weapons and commercial applications such as medical diagnostic systems (e.g. the Food and Drug Administration's oncology diagnostics program [4].) The compatibility will enable trust and proliferation of predictive artificial intelligence-based decision-making systems, enabling the Warfighter to automate tasks and achieve well-understood behaviors.


Main Goal:

To understand neural network technology, beyond traditional black box models towards fully explainable, mathematically understood models, enabling Defense users to implement trusted artificial intelligence systems.


  1. (Basic Research) Study fundamentals of neural networks to enable deeper understanding in terms of neural network performance, performance bounds, and limitations, and achieve neural network explainability.
  2. (Applied Research) Understand neural network fundamentals and their applicability to Directed Energy problems. Achieve compatibility with Defense strategies and directives [1] [2].



Reports in Powerpoint and text-based manuscript formats.


A software package including material necessary to understand and reproduce SBIR results.


DESCRIPTION: Recent research has demonstrated a neural network training phenomenon, Double Descent [5]. Here, sufficiently large predictive classification networks can train beyond the overfitting regime and achieve lower local minimum test loss, approaching the global minimum. Later, it was shown that double descent-achieving networks can collapse, or converge, to a structure with well-defined mathematical properties [6]. This is called Neural Collapse, and its study has recently been an active research field regarding its implications on performance, optimality, robustness, and other traits.


AFRL/RD has interest in the Neural Collapse phenomenon because conclusions derived from its study may generalize across all neural networks achieving Neural Collapse. More specifically, recent research has investigated Neural Collapse for traits such as optimality [7], training success [8], transfer learning [9], and robustness [10]. While the state-of-the-art is not fully peer reviewed, success in these lines of research could lead to explainability and trust in a technology that has traditionally been considered a black box, achieving the objective of the STTR.


To meet the objective, potential tasks in several research directions are described below. These tasks are open ended, and comprehensive results are not expected before Phase III. Further related tasks in support of the goals may be proposed due to the fast-paced nature of the research area.


Applied Research (Export Controlled):

  1. Demonstrate that networks trained on Directed Energy datasets such as CLIPS, in applications such target acquisition of small, unmanned aircraft, can achieve Double Descent and Neural Collapse.
  2. Validation of recent research (References 7-10) with regards to correctness and applicability of Neural Collapse to the Directed Energy dataset.
  3. Quantify generalizability of Neural Collapse across different Directed Energy application datasets and sensors. Understand Neural Collapse robustness to specific sensor, noise, and scenario types.


Information Theory/Optimality Basic Research (Not Export Controlled):

  1. Using techniques such as Task Specific Information [11] to calculate quantitative optimal detector/classifier task performance, show that a Neural Collapsed network quantitatively approaches this performance value.
  2. If such optimal performance is demonstrated, investigate implications derived from optimality including bounded network outputs and network robustness.
  3. Quantify the degree of neural collapse in a network and relate this value as a function to quantified task performance.


Neural Collapse Behavior/Limitations Basic Research (Not Export Controlled):

  1. Neural Collapse represents an end state; a neural network converges to the state but may never fully reach collapse. In addition, multiple layers in the network may reach an intermediate collapsed state [8, 12]. Define and justify what is quantitatively meant when a network should be declared to be in a collapsed state, and the implications in this declaration.
  2. A network needs to be sufficiently large and have sufficient training to reach Neural Collapse. Quantify requirements that define when a network is capable of/qualified to reach a double descent/neural collapse state.
  3. Quantify the resource costs and performance benefits associated with Neural Collapse. Are there performance benefits (Quantified with ROC/Precision and Recall/Confusion Matrix) associated with reaching Neural Collapse, and are there additional training/testing/inference/other costs associated with operating in a Neural Collapse state?


Results are expected through a software package, as well as in written form including reports and presentation, with likely submission to the DTIC database. Publication through conferences, articles, and press release is encouraged.



  1. Downselect imaging datasets for training a neural network-based detection system, including Defense/Directed Energy datasets and public, popular datasets. Successfully demonstrate Neural Collapse behavior on Directed Energy target datasets to demonstrate application, as well as popular public datasets, through network training and transfer learning.
  2. Identify promising Neural Collapse research tasks for Phase II and conduct preliminary research demonstrating potential value in this tasking.



  1. Neural collapse is confirmed as a phenomenon affecting neural networks and confirmed as relevant to Directed Energy applications.
  2. Delivery of a software package demonstrating existence of the Neural Collapse phenomenon. The package should contain source code, build scripts and instructions, a software dependency list including acquisition and installation instructions, dataset acquisition instructions, and software documentation including structural and functional descriptions.



  1. Establish plans including statement of work, work breakdown, and software development documents for specific tasks to complete in Phase II, either from the Project Description, or self-developed.
  2. Establish relationships and collaborations with interested Directed Energy and Defense partners



  1. Complete, demonstrate, and report on basic and applied research efforts to further project goals.



  1. Basic Research: Inform the Applied Research effort and report on and publish results from task completion.
  1. Applied Research: Demonstrate that Neural Collapse
  2. Delivery of software package demonstrating the specifically researched Neural Collapse phenomenon. The package should contain source code, build scripts and instructions, a software dependency list including acquisition and installation instructions, dataset acquisition instructions, and software documentation including structural and functional descriptions.



  1. Demonstrate that Neural Collapse may have a significant impact on Directed Energy applications as well as broader detection/classification applications.







  1. Conduct statistical analysis using effort-specific data recordings from either a Directed Energy testbed such as BC TRAIL or a laboratory setup, demonstrating discovered Neural Collapse implications as applied to Directed Energy systems. These implications might include robustness, optimality or transferability, as discussed in the Project Description.



  1. 1)Demonstration of Neural Collapse and its implications as a TRL-5 capability. If successful, this demonstration will enable integration with DE imaging systems and AI subsystems.



  1. Successful Integration of Neural Collapse concepts into DE AI system development, enabling compliance with orders, strategies, and regulations mandating trustworthy AI.



  1. DoD Responsible AI Working Council, “DoD Responsible Artificial Intelligence Strategy and Implementation Pathway,” June 21, 2022
  2. DoD Directive 3000.09, “Autonomy in Weapons Systems”, January 25, 2023
  3. Biden, Joseph R. "Executive Order on the Safe, Secure, and Trustworthy Development and Use of Artificial Intelligence." (2023)


KEYWORDS: Machine Learning; Artificial Intelligence; Applied Mathematics; System Performance; Directed Energy; Computer Vision; Image Processing

US Flag An Official Website of the United States Government