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  <front>
    <journal-meta />
    <article-meta>
      <title-group>
        <article-title>Challenge Problems in Developing a Neuro-Symbolic OODA Loop</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Alberto Speranzon</string-name>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Christian H. Debrunner</string-name>
          <xref ref-type="aff" rid="aff2">2</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>David Rosenbluth</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Mauricio Castillo-Effen</string-name>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Anthony R. Nowicki</string-name>
          <xref ref-type="aff" rid="aff2">2</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Kevin Alcedo</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Andrzej Banaszuk</string-name>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>Lockheed Martin Artificial Intelligence Center</institution>
          ,
          <country country="US">USA</country>
        </aff>
        <aff id="aff1">
          <label>1</label>
          <institution>Lockheed Martin, Advanced Technology Labs</institution>
          ,
          <country country="US">USA</country>
        </aff>
        <aff id="aff2">
          <label>2</label>
          <institution>Lockheed Martin</institution>
          ,
          <addr-line>Missiles and Fire Control</addr-line>
          ,
          <country country="US">USA</country>
        </aff>
      </contrib-group>
      <abstract>
        <p>In this paper, we analyze the role of Neuro-Symbolic (NS) methods within the standard Observe, Orient, Decide and Act (OODA) framework and discuss their associated opportunities and challenges. To ground the discussion, we consider the OODA loop applied to a wildland firefighting use case where mixed teams of autonomous agents and humans need to collaboratively work to contain and ultimately extinguish large-scale fires. NS methods are appealing as they enable the integration of symbolic knowledge coming, for example, from time-tested firefighting tactics and procedures encoded in training manuals. However, there are key challenges in capturing and integrating such information within NS pipelines, especially in a way that is scalable with respect to the number of procedures, dynamics of the environment, and regulations. The integration of such symbolic priors within a NS OODA loop will enable autonomous systems to generate highly expressive yet compressed representations (or abstractions) of the environment and other agents' state, actions, and intent. However, NS integration brings new challenges, such as, designing abstractions that are composable and transferable across complex tasks, deciding how to ground symbols to sensory data, and verifying their validity to ensure they lead to safe decisions. Symbolic abstractions also need to deal with the fact that sensory data is uncertain-like the behavior of the fire front (boundary, rate of spread, etc.). Furthermore, prior knowledge may be incomplete and inconsistent leading to representations that need to be capable of explicitly modelling and managing ambiguity. Addressing such challenge problems will not only advance the state-of-the-art in NS AI, but also concretely demonstrate the benefits of such methods within the autonomy domain.</p>
      </abstract>
      <kwd-group>
        <kwd>1 Autonomous systems</kwd>
        <kwd>Abstractions</kwd>
        <kwd>Decision Making</kwd>
        <kwd>Challenge Problems</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>1. Introduction</title>
      <p>
        In recent years, deep neural networks (DNNs) and embedded GPUs have significantly improved the
capabilities of an autonomous system across the full Observe, Orient, Decide and Act (OODA) loop [
        <xref ref-type="bibr" rid="ref1 ref2">1,
2</xref>
        ]. However, we are still far from achieving the level of robustness and reliability that we expect from
such systems. One of the key difficulties is that autonomous systems are generally deployed in
environments that are highly dynamic and uncertain where the actual state of the environment cannot be
directly observed but needs to be inferred. Neuro-symbolic techniques offer the promise to extend the
virtues of DNNs and, by incorporating symbolic techniques, to increase the autonomous systems ability
to deal with uncertainty and ambiguity. In this paper, we explore the opportunities offered by NSR to
enhance OODA loops, but also the challenges.
      </p>
      <p>Consider, for example, the wildland firefighting problem shown in Figure 1. In this type of complex
mission, there are many challenges in developing an understanding of the current and future state of the
fire supporting the generation of strategies and actions to effectively fight a wildland fire.</p>
      <p>As the figure shows, fires may be in various states, burning at different rates along challenging
terrains; winds and vegetation fuel the fires in a difficult to predict way and thick clouds of smoke make
fire front detection and overall flight arduous. Furthermore, risks to people and infrastructure make
decisions on how to tackle the fires difficult.</p>
      <p>Purely data-driven machine learning (ML) approaches may not be sufficient to tackle the challenges
of such missions. For example, we expect that deployed autonomous systems will: coordinate with
humans and follow specific set of tactics and guidelines, build and reason over large-scale
spatio-temporal models of the world, adapt online to new situations for which training data was not available
before the mission, and manage both uncertainty and ambiguity.</p>
      <p>
        Neuro-Symbolic (NS) methods provide a new framework to overcome some of the limitations of
purely data-driven ML approaches [
        <xref ref-type="bibr" rid="ref3 ref4">3, 4</xref>
        ], however, missions like the wildland firefighting expose new
challenges that need to be overcome to deploy safe and reliable NS OODA loops for autonomous
systems. In the next section, we highlight some of these challenges to further energize the community
towards the development of next generation of safe and intelligent autonomous systems.
      </p>
    </sec>
    <sec id="sec-2">
      <title>2. Challenges in Designing NS OODA Loops</title>
      <p>The challenges discussed in the following sections stem from the authors’ recent experience in
developing and integrating NS methods within autonomous systems. Not all of them are exclusive to
NSenabled autonomy.
2.1.</p>
    </sec>
    <sec id="sec-3">
      <title>Integration of Prior Knowledge</title>
      <p>NS methods enable the integration of symbolic priors during both the learning and inference. In
wildland firefighting, for example, symbolic priors can be a set of well-established tactics and
procedures when fighting fires (e.g., never attack an aggressive fire at the head or up-slope from an active
fire front) as well as priorities on how tactics should be selected (e.g., preservation of life being at the
highest priority). Symbolic knowledge also imposes requirements on the “Observe” and “Orient” parts
of the loop as certain types of specific features in the terrain, vegetation or land usage need to be detected
and characterized.</p>
      <p>
        Within the Decide portion of the loop, symbolic priors impact decisions as the autonomous systems
need to conform to procedures to both coordinate effectively with humans and for ethical and legal
reasons. ML methods, such as DNNs, require a lot of data to learn to recognize such complex behavioral
patterns and from there select the appropriate actions. NS methods such as [
        <xref ref-type="bibr" rid="ref5 ref6 ref7 ref8 ref9">5, 6, 7, 8, 9</xref>
        ], to name a few,
on the other hand provide ways to explicitly encode symbolic knowledge and constraints reducing the
amount of data required for training.
      </p>
      <p>However, at this stage there does not seem to exist well-established quantitative metrics that help
developers understand the tradeoff between data requirements, richness of symbolic priors and
performance of a NS system. In the application domain this is ultimately translating into development costs.</p>
      <p>For example, in the wildland firefighting setting, generating (or collecting) more data, and possibly
labeling the data, can be costly. Transforming firefighting procedures into ontologies and knowledge
graphs by ingesting, for example, procedure manuals that encode information in highly unstructured
forms, such as pictures and/or sketches can also very onerous.</p>
      <p>
        One of the key enablers of the success of supervised learning has been the availability of extremely
large sets of labelled data, typically released as benchmark data. Many existing NS methods (for
example, [
        <xref ref-type="bibr" rid="ref6">28, 6</xref>
        ]) are tested using large and well established deep learning datasets, but they are combined
with small- to medium-sized, hand-build knowledge bases that do not reflect the complexity of typical
applications such as the wildland fire fighting. This raises the question if the NS community should
consider the development of curated symbolic knowledge to be used to evaluate and compare NS
methods. This would enable researchers to, firstly, show the benefits of the methods and, secondly, provide
data to develop the metrics we mentioned earlier. Although ontologies and other sources of symbolic
knowledge are available, more efforts seem to be needed to “replicate” the advances in data curation
and distribution that have been, in many ways, behind the success demonstrated by statistical ML.
      </p>
      <p>
        The development of advanced Large Language Models (LLMs) [
        <xref ref-type="bibr" rid="ref10 ref11">10, 11</xref>
        ] may provide an opportunity
to speed up the creation of curated symbolic knowledge for robotics applications, as shown in some
recent work [
        <xref ref-type="bibr" rid="ref12 ref13">12, 13</xref>
        ]. The integration of LLMs within the NS framework is certainly a topic or future
research that we believe will have strong impacts within the autonomy/robotics communities.
      </p>
      <p>
        In the context of symbolic knowledge capture, there is a more fundamental question that we believe
should be pursued more aggressively. Generally, formal knowledge is encoded via description logics,
and this raises the question if this formalism is sufficient or even optimal for NS methods. Recent
developments [
        <xref ref-type="bibr" rid="ref14 ref5 ref7 ref8">5, 7, 8, 14</xref>
        ], and references therein, extend or propose new logics that leverage
manyvalued logics [
        <xref ref-type="bibr" rid="ref15">15</xref>
        ]. Although there are extensions of ontologies to many-values/fuzzy description logics
[
        <xref ref-type="bibr" rid="ref16 ref17">16, 17</xref>
        ], most of the available ontologies do not use such semantics.
2.2.
      </p>
    </sec>
    <sec id="sec-4">
      <title>Development of Abstractions</title>
      <p>Symbols represent concepts ranging from objects and classes to tasks and plans or from beliefs to
properties and strategies. To apply symbolic knowledge, a NS system must be able to ground a symbol,
i.e., associate it (possibly probabilistically) with real world observations or with combinations of other
related symbols. Often symbols are arranged hierarchically (e.g., in an ontology) to represent concepts
at many levels of abstraction, so we refer to the association of symbols with real world observations or
with combinations of other related symbols as an abstraction. Hierarchical abstractions occur naturally
in the OODA loop, where “Observe” creates symbols representing objects in the environment, “Orient”
groups these observed objects and relates them to each other and to higher level concepts through a rich
set of relationships, “Decide” plans actions based on the hierarchical plans and goals of the agents and
symbolic representations, and “Act” carries out the actions in context of the observed objects and agents
and the expected plans and goals of the agents. Prior knowledge generally defines abstractions, but
common sense and efficient reasoning requires an ability to fluidly relate existing abstractions to each
other, to refine them based on context, and to create new abstractions for new situations. Abstractions
should have, at a minimum, the following characteristics:
1) Utility: the abstraction should be compositional, modular, and reusable/transferable (ideally
across applications and domains). Reusability may require adaptation of the abstraction to new
domains/contexts.
2) Interpretability: the abstractions should be defined in terms of existing abstractions/symbols
and observations in a way that humans can understand and such that it is easy to determine
whether a given abstraction is applicable in a given context.</p>
      <p>In the firefighting domain, abstractions within the “Orient” part of the OODA loop will be designed
to support the efficient prediction of wildfire behavior from the fire’s current state, the fuel
characteristics, the topography, and the weather, and to characterize the risk to structures and human life in
planning the firefighting effort.</p>
      <p>Within “Decide”, the abstractions will likely need to align with the hierarchical organization of the
command structure. At the top is the Incident Commander (IC) who makes both tactical and strategic
decisions about how to best fight the fire that has both a long-term and short-term effect. At the lower
layers, the abstractions will capture tactics and actions other agents, both autonomous and humans, are
going to take to carry out the IC decisions.</p>
      <p>
        Although human experts, field manuals and fire behavior models [
        <xref ref-type="bibr" rid="ref18">18</xref>
        ] can guide the development of
abstractions, as noted in Section 2.1, it can be difficult to translate these into the appropriate symbolic
knowledge base that an autonomous system can both learn from and reason on.
      </p>
      <p>A key challenge to take advantage of NS methods in developing next generation OODA loops is on
developing theoretical and computational methods for generating and adapting abstractions across the
elements of the loop as well as measuring their utility and interpretability. Each of these characteristics
is critical to ensure consistency of the symbolic representations across abstractions, the management of
uncertainty and ambiguities (see Section 2.3) and to support reasoning. We believe that such
abstractions should be designed to ensure transferability across problem instances/types and scalable to large
number of heterogenous systems.
2.3.</p>
    </sec>
    <sec id="sec-5">
      <title>Uncertainty and Ambiguity</title>
      <p>
        Although integration of probabilistic models, to consider, e.g., sources of uncertainty, have been
considered in the context of NS methods [
        <xref ref-type="bibr" rid="ref19 ref20">19, 20</xref>
        ], there are other uncertainty and ambiguity
considerations that are unique to NS architectures we would like to highlight. The symbolic abstraction process
transforms vector space neural representations to symbolic ones. Since this is a mapping from
continuous space to a discrete space, it is necessarily lossy. It is useful to think of this process as a vector
quantization which will necessarily introduce quantization error/uncertainty and quantization noise
[
        <xref ref-type="bibr" rid="ref21">21</xref>
        ]. Uncertainty can be quantitatively characterized in terms of a distortion function which quantifies
the cost of replacing a specific element of a set with a symbol. Vector quantization algorithms optimize
a rate-distortion to maximize the coding rate/efficiently while minimizing the distortion.
      </p>
      <p>
        Although, we believe it is appealing to consider information theoretic approaches to study
quantization tradeoffs, in the context of autonomous systems using NS components, the choice of symbols is
not just a “bottom-up” process, from continuous to discrete domains, but also a “top-down” process as
the symbols have associated semantics that depend on the mission, external knowledge encoded in
ontologies and, potentially, the need to be interpretable by humans. In the firefighting setting, if we
require autonomous systems to coordinate with humans, it seems highly desirable to have symbolic
representations that match humans’ representations. Although there is initial work in developing
interpretable symbolic NS world models for autonomous systems [
        <xref ref-type="bibr" rid="ref22">22, 23</xref>
        ], more research seems to be
necessary to better understand the tradeoffs between human interpretability, efficiency, and distortion of
symbolic representations.
      </p>
      <p>A different, but related, important aspect in the design of a NS OODA loop is the need to ensure that
symbol groundings do not conflict across the components of an OODA loop. The use of different
complex sensors (e.g., EO/IR cameras, LIDARs, etc.) within the “Observe” and the generation of multiple
abstractions in “Orient” to tradeoff computation complexity and accuracy, combined with the fact that
the world is only partially observable, can lead to situations where symbolic representations are
inconsistent. We believe that NS OODA loops will require new approaches to represent and reason under
such uncertainty and ambiguity without sacrificing reliability and assurability, see also Section 2.4.
2.4.</p>
    </sec>
    <sec id="sec-6">
      <title>Assurance of NS Systems</title>
      <p>The deployment of OODA loop solutions to safety critical domains, such as wildland firefighting
require demonstrably correct, reliable, and safe behavior in all foreseeable situations. In regulated
industries users need explainability, transparency, and auditability of the system’s behavior [24]. We call
this the assurance challenge. Assured systems aim to satisfy four Overarching Properties (OAs) listed
below [25]:
• Intent: The system's defined intended behavior must be correct and complete with respect
•
•
•
to the desired behavior.</p>
      <p>Correctness: The implementation must be correct with respect to its defined intended
behavior under foreseeable operating conditions.</p>
      <p>Innocuity: Any part of the implementation that is not required by the defined intended
behavior must not have unacceptable impact.</p>
      <p>Operation: The system must possess mechanisms for addressing correctness or intent
deficiencies and for mitigating unacceptable impacts manifested during operation.</p>
      <p>
        The verification of a system is meant to establish whether OODA components satisfy the four OAs
via objective evidence, thus providing confidence that a system has been “built right”. The symbolic
interfaces and knowledge representations afforded by NS techniques, compared to DNN based
approaches, enable that possibility. For instance, Logic Tensor Networks (LTN) [
        <xref ref-type="bibr" rid="ref5">5</xref>
        ], are suitable for
implementing multiple forms of NS classification, as required for a variety of “Observe”, and “Orient”
functions, as well as reasoning and query-answering, required by “Decision” functions. As LTNs
implement a first-order language, Real Logic, the associated semantics enable the formal specification
(Intent OA) and verification (Correctness OA) of NS OODA functions expressed in the Real Logic
language. Furthermore, LTN-endowed NS components could also use its symbolic knowledge
representation to monitor whether the actual operating conditions differ from those assumed during design
and development. This enables the autonomous system to identify possible unsafe states and trigger
fail-safe behaviors (Operation OA). LTNs represent just one category of verifiable NS structures.
Logical Neural Networks [
        <xref ref-type="bibr" rid="ref8">8</xref>
        ], Neural Tensor Networks [26], Tensor Product Representations [27], and
Abductive Learning [29] offer similar opportunities for verification, both offline and online.
      </p>
      <p>Although the assurance of NS OODA loops can take advantage of explicit symbolic representations
these may be still learned from combination of data and explicit knowledge.</p>
      <p>Learned NS functions implies the presence of uncertainty and ambiguity, as mentioned before, that
not only needs to be managed but also treated as an assurance gap. Seeding learning by injecting
symbolic priors may accelerate learning but also introduces grounding boundary discrepancies, in other
words, a discordance between real world objects and their representations. Furthermore, the validity of
learned symbols and their symbolic relations are highly dependent on the quality, quantity, and
relevance of the input and training data, and thus connected to the challenges in Section 2.1 and 2.2. More
generally, we believe that the connections and interfaces between the symbolic and the sub-symbolic
components of NS systems need to be better understood from an assurance perspective and, likely, new
mitigation approaches need to be developed to provide strong safety guarantees.</p>
    </sec>
    <sec id="sec-7">
      <title>3. Conclusions</title>
      <p>NS methods can greatly improve the way we design and deploy autonomous systems in complex
missions. The opportunity to incorporate prior symbolic knowledge, integrate deep learning with
symbolic representations and reasoning, provide interpretability and enable formal analysis are huge
advantages compared to approaches that completely rely on statistical machine learning. There are,
however, challenges that we need to overcome to design next generation of NS based autonomous systems.
In this paper we have listed a few challenges related to the tradeoff between data requirements and
symbolic knowledge in training NS architectures, the development of composable symbolic abstraction
for reasoning and the need of formalize methods for managing uncertainty and ambiguity in these novel
architectures. We believe that autonomous systems/robotics can be a great application domain to drive
the development of new theoretical and computational advances in NS learning and reasoning.
Specifically, we have also introduced a rich problem domain, wildland firefighting, that provides the research
community with a strong and concrete motivating example where we believe NS methods can make an
important contribution and impact.</p>
    </sec>
    <sec id="sec-8">
      <title>4. References</title>
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