Practical Foundations

(Technical Bases)

Mathematical Modeling, Control Theory, and Multi-Agent Systems: Development of advanced AI platforms based on cutting-edge theoretical research, including complex adaptive systems, stochastic processes, and distributed cooperative algorithms.
Soft Robotics x AI: Integrating clinical AI with research inspired by soft robotics, which features flexible physical interfaces.

(Applied Foundations)

- Medical Field: Creating on-site systems where healthcare professionals, patients, devices, and AI collaborate in real time.
- Distributed Autonomous Intelligence:Enabling self-evolving and self-decision-making AI in closed environments.
- Social Infrastructure: Implementing environments—such as cities, local governments, and disaster response domains—where the field itself possesses knowledge and the ability to make decisions.

Federated Autonomous Knowledge AI Network

Empowered by a Self-evolving Field Intelligence Platform
This study proposes a new approach that treats the medical environment as a “field,” and formalizes each healthcare worker and patient present within it as a “quantum”-like entity.
Each “quantum” behaves dynamically within the field according to its own state function and transition probabilities, and as local interactions accumulate, collective order (emergence) is dynamically generated across the entire environment.
Our distributed autonomous AI system precisely measures and records such state transitions and local interactions of these “quanta” in real time, and quantitatively analyzes and visualizes the resulting macroscopic phenomena―such as workflow optimization, coordinated behavior, and risk events―that emerge as aggregates of microscopic dynamics.
Furthermore, based on these insights, we implement feedback control to the field, building a next-generation medical intelligence infrastructure that simultaneously achieves optimization of individual (micro) behavior and formation of collective (macro) order throughout the environment.

Technology and Intellectual Assets

Our intellectual assets include proprietary algorithms, software, and methodologies developed through extensive research and development. These assets are protected by patents and copyrights, ensuring our competitive advantage and enabling us to continue investing in innovation.

• Medical Code Generation Technology： Encodes clinical actions and decisions as internal symbolic sequences.
  $$\mathrm{Code}(l_n) = \phi(c_t, h_t) \in \mathcal{L}$$
  where $l_n$ is the logic of clinical practice, $c_t$ is the context, and $h_t$ is the history.
  
  
• State Transition Management:： Structures behavioral progression and environmental changes into interpretable flows.
  $$P(s_{t+1} | s_t, a_t) = \frac{\exp\left(-\|f(s_t, a_t) - s_{t+1}\|^2\right)}{Z}$$
• Voice/Contactless UI： Enables interaction with information while minimizing disruption to field behavior.
  $$u_t = \psi(x_t, \theta), \quad \text{with } \psi \text{ minimizing } \nabla_{x_t} \mathrm{Disruption}(x)$$
• Automated Code Generation： Generates auxiliary logic at runtime based on environmental information.
  $$\pi_{\mathrm{gen}}(t) = g(F_t, C_t, \Delta_t)$$

Many of the core technologies we have developed are patented or published both in Japan and internationally, including:

• - Autonomous distributed AI supporting the evolution of field intelligence
• - AI platforms that automatically generate and share knowledge across various fields
• - Optimization of AI based on real-world input and feedback

We aim to contribute to new research, industry collaboration, and the advancement of society as a whole through active utilization of our intellectual property.

Mathematics-Driven Robotics with Original Devices
The original medical devices developed by VRI are based on a multi-agent system design philosophy, which physically and logically integrates human-machine interactions.


Distributed Autonomous AI
Our vision for a distributed autonomous AI platform is one in which each device and AI agent operates as a node within a network, dynamically sharing and optimizing knowledge and information.
This comprehensive system is supported by the following three mathematical frameworks:


Stochastic Fields and Graph Theory:
Each device or agent forms part of a network as a node defined by graph theory. These nodes transition dynamically through a probabilistic field within the state space, self-organizing and optimizing information sharing for their respective environments.


Mathematical Mapping in Similarity Spaces:
Multidimensional data—including patient records, electronic health records, and literature—are projected into high-dimensional spaces such as Hilbert spaces or metric spaces. By applying distance functions and kernel methods, similar cases and relevant knowledge can be dynamically compared and retrieved, enabling the delivery of required insights and optimal actions in real time.


Non-Invasive Interfaces and Data Collection:
Through original devices and non-invasive protocols, our system connects with hospital infrastructure, mobile devices, and a variety of sensors, enabling secure and real-time integration and processing of medical data. This approach minimizes operational burden while supporting the advanced circulation and implementation of knowledge.


Implementation: Collaborative Systems of Distributed Autonomous AI and Robotics
In real-world settings such as medical care and social infrastructure, a diverse array of devices and agents must collaborate—each acting autonomously—while collectively achieving order and the evolution of knowledge.
To support such complex coordination, we base our development on mathematical frameworks such as multi-agent systems, graph theory, stochastic fields, and metric spaces, and are committed to designing and implementing "evolving AI at the front lines" and "robotics capable of flexibly responding to situational demands."