At the sNoise Research Laboratory (sNRL), we are pioneering the next generation of intelligent systems by operationalizing Fractional Calculus—the true mathematics of nature. We are developing the foundational technologies that will allow Artificial Intelligence, robotics, and complex control systems to operate with a new level of realism and precision.
Through our FSDSP toolboxes, sNRL is revolutionizing how fractional calculus is applied in digital signal processing and AI. We are developing user-friendly code libraries that integrate our patented algorithms into existing deep learning frameworks, while also creating our own custom solutions across various application, opening the door for everyone to harness the power of fractional calculus. These toolboxes make it easy for practitioners to adopt fractional calculus, enhancing model accuracy, convergence rates, and overall efficiency, particularly in agent-based systems. By driving innovation in the field, we are shaping the future of intelligent digital signal processing and AI systems, paving the way for groundbreaking advancements in this new digital age.
Today's AI is shackled by 17th-century Traditional Calculus, which functions like a ruler marked only with whole numbers governing its internal architecture.
What is the length of the paperclip?
Without fractional resolutions, one can only approximate the length of the paperclip.
For over three centuries, the profound potential of Fractional Calculus (FC) to model the intricate processes of nature has been recognized. However, its adoption has been historically limited by its immense computational complexity, leaving its power largely inaccessible for practical, real-world applications.
Traditional calculus, rooted in 17th-century methods, struggles to accurately model complex, non-linear systems, leading to oversimplifications and approximations. This creates significant barriers not only for AI but also for digital signal processing (DSP) and conventional control systems, which rely on outdated mathematical frameworks.
The limitations of traditional calculus hinder the ability to filter and clean noise from signals in DSP, affecting data transmission clarity. In control systems, they restrict responsiveness and stability, preventing quick recovery from disturbances. For AI, the absence of advanced mathematical tools means that pre-training optimization, inference reasoning, and decision-making processes remain less effective. As a result, decision-making processes are hindered, adaptability is compromised, and the full potential of these technologies remains unrealized.
21st-century Fractional Calculus (FC) with a near-infinite-fractional-resolution ruler and fully adjustable operators enhances the precision and accuracy of AI's internal architecture, mirroring how fractals revolutionized graphics.
What is the length of the paperclip?
With fractional resolutions, we can accurately measure the exact length of the paperclip at 1 9/16 of an inch.
sNRL has solved this long-standing challenge with the invention of our patented Fractional Scaling Digital Signal Processing (FSDSP). This modern computational framework is designed to harness the power of Fractional Calculus (FC) for the digital age, providing the foundational algorithms and building blocks necessary for advanced applications.
FSDSP enables complex calculations to be performed efficiently in the complex frequency domain, allowing for unprecedented control over any waveform or digital signal. This capability facilitates precise shaping of both magnitude and phase at any frequency, unlocking new possibilities for digital signal processing.
At sNRL, we are addressing the constraints of traditional calculus by leveraging our patented FC algorithms as a foundational platform technology. Our solutions integrate seamlessly into AI applications, DSP, and control systems, paving the way for enhanced adaptability, responsiveness, and overall performance. By utilizing FSDSP, we empower these technologies to overcome historical limitations, transforming decision-making processes and enabling the realization of their full potential.
FSDSP is not just an improvement; it establishes a new category of technology—an emerging interdisciplinary field at the intersection of applied mathematics, computer science, and engineering.
The applications for FSDSP are transformative, with the potential to fundamentally advance and "level up" numerous high-growth and critical sectors:
The foundational technology of FSDSP is protected by our robust portfolio of four issued U.S. utility patents (awarded between 2017 and 2020), securing its position as a unique and defensible innovation. These patents establish FSDSP as a platform technology, forming the building blocks for an emerging interdisciplinary field that seamlessly links various applications—from simple digital signal processing (DSP) to complex artificial intelligence (AI) systems.
Our intellectual property strategy not only safeguards our proprietary algorithms and methodologies but also reinforces our commitment to advancing the fields of digital signal processing, fractional-order control systems, and AI. By protecting these core technologies, we maintain a competitive edge in a rapidly evolving landscape, positioning ourselves to lead and level up entire industries through transformative applications across high-growth sectors.
Fractional calculus can provide a more accurate representation of complex systems by capturing long-term dependencies and memory effects in data, while deep learning excels at learning complex patterns and representations. By incorporating AI techniques, such as deep learning, into the modeling and analysis process powered by fractional calculus, we can develop more accurate and robust models for complex systems. Deep learning can learn the underlying patterns and relationships in the data and adaptively adjust the fractional calculus models to better capture and provide a more accurate representation the underlying dynamics of the system, especially when dealing with non-integer order and fractal-like behavior.
Fractional calculus is well-suited for analyzing and modeling time series data with long-term dependencies. Deep learning, particularly recurrent neural networks (RNNs), can effectively capture temporal dependencies in sequential data. By integrating fractional calculus with RNNs or other deep learning architectures, we can develop more powerful models for time series analysis, forecasting, and anomaly detection. This can have applications in finance, weather prediction, health monitoring, and more.
Fractional calculus can be used to describe and control systems with fractional order dynamics, while deep learning can optimize complex functions and learn control policies. By combining the two, deep reinforcement learning or evolutionary algorithms can learn control policies that optimize system performance, while fractional calculus can provide a more accurate representation of the system's dynamics to develop intelligent control strategies that actively adapt to the fractional order characteristics of the system. This can lead to improved control performance and optimization in various domains, such as robotics, autonomous systems, and process control.
Fractional calculus can capture long-term dependencies and memory effects in time series data. By combining AI techniques, such as deep learning or recurrent neural networks, with fractional calculus, we can develop predictive models that can forecast future behavior more accurately. This can have applications in areas like financial forecasting, weather prediction, or stock market analysis.
Deep learning can be used to learn fractional calculus operators directly from data. Instead of relying on predefined fractional order operators, deep learning algorithms can learn the fractional derivatives or integrals directly from the available data. This data-driven approach can be particularly useful when dealing with complex or noisy data where the underlying fractional order behavior is not well-known or easily defined.
Fractional calculus can help in detecting anomalies or abnormal behavior in complex systems. By integrating AI algorithms, such as anomaly detection or pattern recognition, with fractional calculus, we can develop intelligent systems that can identify and diagnose faults or anomalies in real-time. This can be valuable in areas like fault detection in industrial processes, cybersecurity, or medical diagnosis.
Imagine having the ability to forecast financial trends with unprecedented accuracy, detect anomalies in complex industrial processes, or optimize control strategies for autonomous systems. With sNRL, these possibilities become a reality.
We are already making waves in various industries, from geophysics to healthcare, where our solutions have delivered remarkable results. Now, we are seeking strategic partnerships and investments to scale our operations and expand our reach.
