Events & Conferences
Low-precision arithmetic makes robot localization more efficient
Simultaneous localization and mapping (SLAM) is the core technology of autonomous mobile robots. It involves simultaneously building a map of the robot’s environment and finding the robot’s location within that map.
SLAM is computationally intensive, and deploying it on resource-constrained robots — such as consumer household robots — generally requires techniques for making computations more tractable.
One such technique is the use of low-precision floating-point arithmetic, or reducing the number of bits used to represent numbers with decimal points. The technique is popular in deep learning, where halving the number of bits (from the standard 32 to 16) can double computational efficiency with little effect on accuracy.
But applying low-precision arithmetic to SLAM is more complicated. Where deep-learning-based classification models are discrete-valued, SLAM involves solving a nonlinear optimization problem with continuous-valued functions, which require higher accuracy.
At Amazon, we’ve tackled this problem by designing a novel mixed-precision solver, which combines 64-bit (fp64), 32-bit (fp32), and 16-bit (fp16) precisions for nonlinear optimization problems in the SLAM algorithm. This innovation paves the way for faster and greener on-device navigation.
General framework
A SLAM algorithm has two key components: visual odometry and loop closure. Visual odometry gives real-time estimates of the robot’s pose, or its orientation and location on the map, based on the most recent observations. When the robot recognizes that it has arrived at a place that it previously visited, it closes the loop by globally correcting its map and its location estimate.
Both visual odometry and loop closure involve solving nonlinear optimization problems — bundle adjustment (BA) and pose graph optimization (PGO), respectively. To solve them efficiently, SLAM systems typically use approximate methods that recast them as sequences of linearized optimization problems. If the goal is to find the pose estimate x, then each linear problem minimizes the linearized error function, which is the sum of the current error function and its first-order correction. The first-order correction is the product of the Jacobian, which is the matrix of the function’s first-order derivatives, and the update to the pose estimation. The linear problems are typically solved through factorization, using either Cholesky or QR methods. The solution of each linearized optimization problem is the update for the current pose estimate.
The general procedure is to start with the current approximation of x, compute the error function and the Jacobian, solve a linear optimization problem, and update x accordingly, repeating the process until certain stopping criteria are met. At each iteration, the value of the error function is known as the residual, since it’s the residual error left over from the previous iteration.
The most expensive computations in the nonlinear optimizations for both BA and PGO are the computation of the Jacobian (about 15% of the optimization time) and the solution of the linear problem (about 60%). Simply solving either problem at half-precision (fp16) from beginning to end will result in lower accuracy and sometimes numerical instability.
To mitigate these difficulties, we regularize and scale the matrices to avoid overflow and rank deficiency. The rank deficiency occurs when columns of the Jacobian are linearly dependent. Through careful experiments, we further identified the computations to be done at precision higher than fp16 and proposed a mixed-precision nonlinear optimization solver.
We found that, to match the accuracy of the solution in pure double-precision, the following two components have to be computed in precision higher than fp16:
- The residual must be evaluated in single or higher precision;
- The update of x, which is a six-degree position-angle update, must be done in double precision.
Although this general optimization framework applies to both BA and PGO, the details vary across the two applications, because of the different structures and properties of the matrices in the linear problems. We thus propose two mixed-precision solving strategies for the relevant linear systems.
Visual odometry
For visual odometry, people traditionally use filter-based methods, which can suffer from large linearization error. Nonlinear optimization-based methods have become more popular in recent years. These methods estimate the position and orientation of the robot by minimizing an error function, which is the difference between the re-projection of landmarks and their observation in the image frame. This procedure is called bundle adjustment because we are adjusting a bundle of light rays to match the projection with the observation.
BA-based visual odometry operates over a sliding window that contains a fixed number of (key) frames. On average, a new key frame comes at 10Hz. The challenge is to solve the BA problem within a given time budget. One popular way to do this is to solve the normal equation that is the equivalent of the linearized optimization problem; this involves the approximation of the Hessian matrix, or the matrix of second-order derivatives of the residual.
The BA problem involves two sets of unknown state variables: one indicates the robot’s pose and the other indicates the landmark location. One way to reduce the computational burden of the BA problem is to marginalize the constraints between camera poses and landmarks and focus on the camera poses first. In the SLAM community, this procedure is known as Schur elimination or landmark marginalization.
This marginalization step can greatly reduce the size of the linear system that needs to be solved. For a 50-frame BA problem, the Jacobian matrix is usually of the size 5,500 x 1,000, and the Hessian is of size 1,000 x 1,000. Decoupling constraints reduces the size of the linear system to 300 x 300, small enough to be solved with direct or iterative solvers. However, this strategy requires both the formulation of the Hessian matrix and a partial-elimination step, which are expensive to employ in practice.
Our mixed-precision linear solver, which mixes single and half-precision, is based on the conjugate gradient normal-equation residual (CGNR) method, which is an iterative method directly applied to the linear-optimization problem without explicit formulation of the Hessian.
As in the general framework, a naïve casting of all computations to half-precision will result in lower accuracy. In our experiments, we found that if we compute matrix-vector products in half-precision and all other operations in single precision, we will maintain the overall accuracy of the SLAM pipeline.
The matrix-vector products, which are the major computation in CGNR iterations, usually account for 83% of the computing cost, in terms of number of floating-point operations. That means that, if run on NVIDIA V100 GPUs, the mixed-precision solver could save at least 41% solving time compared to the single-precision linear solver.
Loop closure
In the SLAM pipeline, the local pose estimates from VO usually exhibit large drift, especially in the long run. Loop closure corrects this drift.
For a real-world mapping estimate, without LC correction, the average trajectory error could be at the order of 0.1 meter, which is not acceptable in practice. This error is reduced to 10-4 meters after applying LC corrections.
| ATE w/o LC (m) | ATE with LC (m) | |
| Max | 4.03E-01 | 5.83E-04 |
| 99% | 2.65E-01 | 5.71E-04 |
| 90% | 2.00E-01 | 5.57E-04 |
| Mean | 9.72E-02 | 3.19E-04 |
The LC adjustment involves solving a global PGO problem. Like the BA problem, it is a nonlinear optimization problem and can be solved within the same mixed-precision framework. But the linear systems arising from PGO problems are much larger and sparser than those of the BA problem.
As more and more loops are closed, the problem size could grow from several hundreds of poses to several thousands of poses. If we measure the size of a matrix by the number of its rows, during loop closure, the size could grow from the order of 100 to the order of 10,000. Directly solving sparse matrices of this size in double precision is challenging, especially considering the time and computation constraints of on-device applications. For a real-world trajectory estimation, the solving time for the PGO problem could grow up to eight seconds with full CPU usage.
This results in a different strategy for designing a mixed-precision solver for PGO problems. Due to the sparsity of the Jacobian matrix, our mixed-precision method is still based on the iterative CGNR method. But to accelerate the convergence of the CGNR iterations, we apply a static incomplete Cholesky preconditioner in each iteration. Cholesky factorization decomposes a symmetric linear system into a product of two triangular matrices, meaning that all of their nonzero values are concentrated on one side of a diagonal across the matrix. This decomposition step is expensive, so we do it only once for the whole problem. The computational cost is mostly dominated by the application of the preconditioner, which involves solving two triangular systems. In our timing analysis, this step consumes around 50% of the computation in each linear solving.
To accelerate the optimization, instead of computing matrix-vector products in half-precision, we solve the triangular system in half-precision, keeping all other operations in single precision. With this mixed-precision solver, we could almost match the accuracy of the full-precision solver while reducing computing time by 26% on average.
Our results across both the VO and LC applications show that because of the high-efficiency and low-energy nature of half-precision arithmetic, mixed-precision solvers could make on-device SLAM faster and greener.
Acknowledgments
The following contributed equally to this work: Tong Qin, applied scientist, Amazon Hardware; Sankalp Dayal, applied-science manager, Hardware; Joydeep Biswas, software development engineer, Amazon Devices; Varada Gopalakrishnan, vice president and distinguished engineer, Hardware; Adam Fineberg, senior principal engineer, Devices; Rahul Bakshi, senior manager of software, machine learning, and mobility, Hardware.
Have you ever worked is legacy code? Are you curious what it takes to modernize systems at a massive scale?
Pascal Hartig is joined on the latest Meta Tech Podcast by Elaine and Buping, two software engineers working on a bold project to rewrite the decades-old C code in one of Meta’s core messaging libraries in Rust. It’s an ambitious effort that will transform a central messaging library that is shared across Messenger, Facebook, Instagram, and Meta’s AR/VR platforms.
They discuss taking on a project of this scope – even without a background in Rust, how they’re approaching it, and what it means to optimize for ‘developer happiness.’
Download or listen to the episode below:
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The Meta Tech Podcast is a podcast, brought to you by Meta, where we highlight the work Meta’s engineers are doing at every level – from low-level frameworks to end-user features.
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Amazon Research Awards (ARA) provides unrestricted funds and AWS Promotional Credits to academic researchers investigating various research topics in multiple disciplines. This cycle, ARA received many excellent research proposals from across the world and today is publicly announcing 73 award recipients who represent 46 universities in 10 countries.
This announcement includes awards funded under five call for proposals during the fall 2024 cycle: AI for Information Security, Automated Reasoning, AWS AI, AWS Cryptography, and Sustainability. Proposals were reviewed for the quality of their scientific content and their potential to impact both the research community and society. Additionally, Amazon encourages the publication of research results, presentations of research at Amazon offices worldwide, and the release of related code under open-source licenses.
Recipients have access to more than 700 Amazon public datasets and can utilize AWS AI/ML services and tools through their AWS Promotional Credits. Recipients also are assigned an Amazon research contact who offers consultation and advice, along with opportunities to participate in Amazon events and training sessions.
“Automated Reasoning is an important area of research for Amazon, with potential applications across various features and applications to help improve security, reliability, and performance for our customers. Through the ARA program, we collaborate with leading academic researchers to explore challenges in this field,” said Robert Jones, senior principal scientist with the Cloud Automated Reasoning Group. “We were again impressed by the exceptional response to our Automated Reasoning call for proposals this year, receiving numerous high-quality submissions. Congratulations to the recipients! We’re excited to support their work and partner with them as they develop new science and technology in this important area.”
“At Amazon, we believe that solving the world’s toughest sustainability challenges benefits from both breakthrough scientific research and open and bold collaboration. Through programs like the Amazon Research Awards program, we aim to support academic research that could contribute to our understanding of these complex issues,” said Kommy Weldemariam, Director of Science and Innovation Sustainability. “The selected proposals represent innovative projects that we hope will help advance knowledge in this field, potentially benefiting customers, communities, and the environment.”
ARA funds proposals throughout the year in a variety of research areas. Applicants are encouraged to visit the ARA call for proposals page for more information or send an email to be notified of future open calls.
The tables below list, in alphabetical order by last name, fall 2024 cycle call-for-proposal recipients, sorted by research area.
AI for Information Security
| Recipient | University | Research title |
| Christopher Amato | Northeastern University | Multi-Agent Reinforcement Learning Cyber Defense for Securing Cloud Computing Platforms |
| Bernd Bischl | Ludwig Maximilian University of Munich | Improving Generative and Foundation Models Reliability via Uncertainty-awareness |
| Shiqing Ma | University Of Massachusetts Amherst | LLM and Domain Adaptation for Attack Detection |
| Alina Oprea | Northeastern University | Multi-Agent Reinforcement Learning Cyber Defense for Securing Cloud Computing Platforms |
| Roberto Perdisci | University of Georgia | ContextADBench: A Comprehensive Benchmark Suite for Contextual Anomaly Detection |
Automated Reasoning
| Recipient | University | Research title |
| Nada Amin | Harvard University | LLM-Augmented Semi-Automated Proofs for Interactive Verification |
| Suguman Bansal | Georgia Institute of Technology | Certified Inductive Generalization in Reinforcement Learning |
| Ioana Boureanu | University of Surrey | Phoebe+: An Automated-Reasoning Tool for Provable Privacy in Cryptographic Systems |
| Omar Haider Chowdhury | Stony Brook University | Restricter: An Automatic Tool for Authoring Amazon Cedar Access Control Policies with the Principle of Least Privilege |
| Stefan Ciobaca | Alexandru Ioan Cuza University | An Interactive Proof Mode for Dafny |
| João Ferreira | INESC-ID | Polyglot Automated Program Repair for Infrastructure as Code |
| Sicun Gao | University Of California, San Diego | Monte Carlo Trees with Conflict Models for Proof Search |
| Mirco Giacobbe | University of Birmingham | Neural Software Verification |
| Tobias Grosser | University of Cambridge | Synthesis-based Symbolic BitVector Simplification for Lean |
| Ronghui Gu | Columbia University | Scaling Formal Verification of Security Properties for Unmodified System Software |
| Alexey Ignatiev | Monash University | Huub: Next-Gen Lazy Clause Generation |
| Kenneth McMillan | University of Texas At Austin | Synthesis of Auxiliary Variables and Invariants for Distributed Protocol Verification |
| Alexandra Mendes | University of Porto | Overcoming Barriers to the Adoption of Verification-Aware Languages |
| Jason Nieh | Columbia University | Scaling Formal Verification of Security Properties for Unmodified System Software |
| Rohan Padhye | Carnegie Mellon University | Automated Synthesis and Evaluation of Property-Based Tests |
| Nadia Polikarpova | University Of California, San Diego | Discovering and Proving Critical System Properties with LLMs |
| Fortunat Rajaona | University of Surrey | Phoebe+: An Automated-Reasoning Tool for Provable Privacy in Cryptographic Systems |
| Subhajit Roy | Indian Institute of Technology Kanpur | Theorem Proving Modulo LLM |
| Gagandeep Singh | University of Illinois At Urbana–Champaign | Trustworthy LLM Systems using Formal Contracts |
| Scott Stoller | Stony Brook University | Restricter: An Automatic Tool for Authoring Amazon Cedar Access Control Policies with the Principle of Least Privilege |
| Peter Stuckey | Monash University | Huub: Next-Gen Lazy Clause Generation |
| Yulei Sui | University of New South Wales | Path-Sensitive Typestate Analysis through Sparse Abstract Execution |
| Nikos Vasilakis | Brown University | Semantics-Driven Static Analysis for the Unix/Linux Shell |
| Ping Wang | Stevens Institute of Technology | Leveraging Large Language Models for Reasoning Augmented Searching on Domain-specific NoSQL Database |
| John Wawrzynek | University of California, Berkeley | GPU-Accelerated High-Throughput SAT Sampling |
AWS AI
| Recipient | University | Research title |
| Panagiotis Adamopoulos | Emory University | Generative AI solutions for The Spillover Effect of Fraudulent Reviews on Product Recommendations |
| Vikram Adve | University of Illinois at Urbana–Champaign | Fellini: Differentiable ML Compiler for Full-Graph Optimization for LLM Models |
| Frances Arnold | California Institute of Technology | Closed-loop Generative Machine Learning for De Novo Enzyme Discovery and Optimization |
| Yonatan Bisk | Carnegie Mellon University | Useful, Safe, and Robust Multiturn Interactions with LLMs |
| Shiyu Chang | University of California, Santa Barbara | Cut the Crap: Advancing the Efficient Communication of Multi-Agent Systems via Spatial-Temporal Topology Design and KV Cache Sharing |
| Yuxin Chen | University of Pennsylvania | Provable Acceleration of Diffusion Models for Modern Generative AI |
| Tianlong Chen | University of North Carolina at Chapel Hill | Cut the Crap: Advancing the Efficient Communication of Multi-Agent Systems via Spatial-Temporal Topology Design and KV Cache Sharing |
| Mingyu Ding | University of North Carolina at Chapel Hill | Aligning Long Videos and Language as Long-Horizon World Models |
| Nikhil Garg | Cornell University | Market Design for Responsible Multi-agent LLMs |
| Jessica Hullman | Northwestern University | Human-Aligned Uncertainty Quantification in High Dimensions |
| Christopher Jermaine | Rice University | Fast, Trusted AI Using the EINSUMMABLE Compiler |
| Yunzhu Li | Columbia University | Physics-Informed Foundation Models Through Embodied Interactions |
| Pattie Maes | Massachusetts Institute of Technology | Understanding How LLM Agents Deviate from Human Choices |
| Sasa Misailovic | University of Illinois at Urbana–Champaign | Fellini: Differentiable ML Compiler for Full-Graph Optimization for LLM Models |
| Kristina Monakhova | Cornell University | Trustworthy extreme imaging for science using interpretable uncertainty quantification |
| Todd Mowry | Carnegie Mellon University | Efficient LLM Serving on Trainium via Kernel Generation |
| Min-hwan Oh | Seoul National University | Mutually Beneficial Interplay Between Selection Fairness and Context Diversity in Contextual Bandits |
| Patrick Rebeschini | University of Oxford | Optimal Regularization for LLM Alignment |
| Jose Renau | University of California, Santa Cruz | Verification Constrained Hardware Optimization using Intelligent Design Agentic Programming |
| Vilma Todri | Emory University | Generative AI solutions for The Spillover Effect of Fraudulent Reviews on Product Recommendations |
| Aravindan Vijayaraghavan | Northwestern University | Human-Aligned Uncertainty Quantification in High Dimensions |
| Wei Yang | University of Texas at Dallas | Optimizing RISC-V Compilers with RISC-LLM and Syntax Parsing |
| Huaxiu Yao | University of North Carolina at Chapel Hill | Aligning Long Videos and Language as Long-Horizon World Models |
| Amy Zhang | University of Washington | Tools for Governing AI Agent Autonomy |
| Ruqi Zhang | Purdue University | Efficient Test-time Alignment for Large Language Models and Large Multimodal Models |
| Zheng Zhang | Rutgers University-New Brunswick | AlphaQC: An AI-powered Quantum Circuit Optimizer and Denoiser |
AWS Cryptography
| Recipient | University | Research title |
| Alexandra Boldyreva | Georgia Institute of Technology | Quantifying Information Leakage in Searchable Encryption Protocols |
| Maria Eichlseder | Graz University of Technology, Austria | SALAD – Systematic Analysis of Lightweight Ascon-based Designs |
| Venkatesan Guruswami | University of California, Berkeley | Obfuscation, Proof Systems, and Secure Computation: A Research Program on Cryptography at the Simons Institute for the Theory of Computing |
| Joseph Jaeger | Georgia Institute of Technology | Analyzing Chat Encryption for Group Messaging |
| Aayush Jain | Carnegie Mellon | Large Scale Multiparty Silent Preprocessing for MPC from LPN |
| Huijia Lin | University of Washington | Large Scale Multiparty Silent Preprocessing for MPC from LPN |
| Hamed Nemati | KTH Royal Institute of Technology | Trustworthy Automatic Verification of Side-Channel Countermeasures for Binary Cryptographic Programs using the HoIBA libary |
| Karl Palmskog | KTH Royal Institute of Technology | Trustworthy Automatic Verification of Side-Channel Countermeasures for Binary Cryptographic Programs using the HoIBA libary |
| Chris Peikert | University of Michigan, Ann Arbor | Practical Third-Generation FHE and Bootstrapping |
| Dimitrios Skarlatos | Carnegie Mellon University | Scale-Out FHE LLMs on GPUs |
| Vinod Vaikuntanathan | Massachusetts Institute of Technology | Can Quantum Computers (Really) Factor? |
| Daniel Wichs | Northeastern University | Obfuscation, Proof Systems, and Secure Computation: A Research Program on Cryptography at the Simons Institute for the Theory of Computing |
| David Wu | University Of Texas At Austin | Fast Private Information Retrieval and More using Homomorphic Encryption |
Sustainability
| Recipient | University | Research title |
| Meeyoung Cha | Max Planck Institute | Forest-Blossom (Flossom): A New Framework for Sustaining Forest Biodiversity Through Outcome-Driven Remote Sensing Monitoring |
| Jingrui He | University of Illinois at Urbana–Champaign | Foundation Model Enabled Earth’s Ecosystem Monitoring |
| Pedro Lopes | University of Chicago | AI-powered Tools that Enable Engineers to Make & Re-make Sustainable Hardware |
| Cheng Yaw Low | Max Planck Institute | Forest-Blossom (Flossom): A New Framework for Sustaining Forest Biodiversity Through Outcome-Driven Remote Sensing Monitoring |
AI safety is a priority at Amazon. Our investment in safe, transparent, and responsible AI (RAI) includes collaboration with the global community and policymakers. We are members of and collaborate with organizations such as the Frontier Model Forum, the Partnership on AI, and other forums organized by government agencies such as the National Institute of Standards and Technology (NIST). Consistent with Amazon’s endorsement of the Korea Frontier AI Safety Commitments, we published our Frontier Model Safety Framework earlier this year.
During the development of the Nova Premier model, we conducted a comprehensive evaluation to assess its performance and safety. This included testing on both internal and public benchmarks and internal/automated and third-party red-teaming exercises. Once the final model was ready, we prioritized obtaining unbiased, third-party evaluations of the model’s robustness against RAI controls. In this post, we outline the key findings from these evaluations, demonstrating the strength of our testing approach and Amazon Premier’s standing as a safe model. Specifically, we cover our evaluations with two third-party evaluators: PRISM AI and ActiveFence.
Evaluation of Nova Premier against PRISM AI
PRISM Eval’s Behavior Elicitation Tool (BET) dynamically and systematically stress-tests AI models’ safety guardrails. The methodology focuses on measuring how many adversarial attempts (steps) it takes to get a model to generate harmful content across several key risk dimensions. The central metric is “steps to elicit” — the number of increasingly sophisticated prompting attempts required before a model generates an inappropriate response. A higher number of steps indicates stronger safety measures, as the model is more resistant to manipulation. The PRISM risk dimensions (inspired by the MLCommons AI Safety Benchmarks) include CBRNE weapons, violent crimes, non-violent crimes, defamation, and hate, amongst several others.
Using the BET Eval tool and its V1.0 metric, which is tailored toward non-reasoning models, we compared the recently released Nova models (Pro and Premier) to the latest models in the same class: Claude (3.5 v2 and 3.7 non-reasoning) and Llama4 Maverick, all available through Amazon Bedrock. PRISM BET conducts black-box evaluations (where model developers don’t have access to the test prompts) of models integrated with their API. The evaluation conducted with BET Eval MAX, PRISM’s most comprehensive/aggressive testing suite, revealed significant variations in safety against malicious instructions. Nova models demonstrated superior overall safety performance, with an average of 43 steps for Premier and 52 steps for Pro, compared to 37.7 for Claude 3.5 v2 and fewer than 12 steps for other models in the comparison set (namely, 9.9 for Claude3.7, 11.5 for Claude 3.7 thinking, and 6.5 for Maverick). This higher step count suggests that on average, Nova’s safety guardrails are more sophisticated and harder to circumvent through adversarial prompting. The figure below presents the number of steps per harm category evaluated through BET Eval MAX.
The PRISM evaluation provides valuable insights into the relative safety of different Amazon Bedrock models. Nova’s strong performance, particularly in hate speech and defamation resistance, represents meaningful progress in AI safety. However, the results also highlight the ongoing challenge of building truly robust safety measures into AI systems. As the field continues to evolve, frameworks like BET will play an increasingly important role in benchmarking and improving AI safety. As a part of this collaboration Nicolas Miailhe, CEO of PRISM Eval, said, “It’s incredibly rewarding for us to see Nova outperforming strong baselines using the BET Eval MAX; our aim is to build a long-term partnership toward safer-by-design models and to make BET available to various model providers.” Organizations deploying AI systems should carefully consider these safety metrics when selecting models for their applications.
Manual red teaming with ActiveFence
The AI safety & security company ActiveFence benchmarked Nova Premier on Bedrock on prompts distributed across Amazon’s eight core RAI categories. ActiveFence also evaluated Claude 3.7 (non-reasoning mode) and GPT 4.1 API on the same set. The flag rate on Nova Premier was lower than that on the other two models, indicating that Nova Premier is the safest of the three.
| Model | 3P Flag Rate [↓ is better] |
| Nova Premier | 12.0% |
| Sonnet 3.7 (non-reasoning) | 20.6% |
| GPT4.1 API | 22.4% |
“Our role is to think like an adversary but act in service of safety,” said Guy Paltieli from ActiveFence. “By conducting a blind stress test of Nova Premier under realistic threat scenarios, we helped evaluate its security posture in support of Amazon’s broader responsible-AI goals, ensuring the model could be deployed with greater confidence.”
These evaluations conducted with PRISM and ActiveFence give us confidence in the strength of our guardrails and our ability to protect our customers’ safety when they use our models. While these evaluations demonstrate strong safety performance, we recognize that AI safety is an ongoing challenge requiring continuous improvement. These assessments represent a point-in-time snapshot, and we remain committed to regular testing and enhancement of our safety measures. No AI system can guarantee perfect safety in all scenarios, which is why we maintain monitoring and response systems after deployment.
Acknowledgments: Vincent Ponzo, Elyssa Vincent
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