arXiv subjects

Sota Yoshihara

Publications and source records attributed to Sota Yoshihara.

4 recordsLinked to original sources

arXiv2026

Dynamical Systems in Elliptical Pursuit and Evasion

This paper investigates the difference between the circular and elliptical cases in one-on-one pursuit and evasion problems. Using the simultaneous differential equation derived by Barton and Eliezer, we derive a dynamical system based on the assumption that the shape of the pursuer's trajectory is unaffected by the evader's speed. The dynamical system involves the angular difference between the velocity vectors of the players and their separation distance. When the evader orbits a circle, the dynamical system is autonomous with an asymptotically stable equilibrium point. By contrast, if the evader orbits an ellipse, the dynamical system becomes non-autonomous and lacks an equilibrium point. To handle the singularity at capture, we reformulate the system using a complex variable that includes information about the logarithmic distance and the angular difference. We establish two main results: when the pursuer is faster than the evader, the pursuer captures the evader in finite time, and we derive an explicit upper bound for the capture time; when the pursuer is slower, the system possesses a unique periodic solution to which all trajectories converge globally and asymptotically.

math.OC↗

arXiv2025

Enhancing AI System Resiliency: Formulation and Guarantee for LSTM Resilience Based on Control Theory

This paper proposes a novel theoretical framework for guaranteeing and evaluating the resilience of long short-term memory (LSTM) networks in control systems. We introduce "recovery time" as a new metric of resilience in order to quantify the time required for an LSTM to return to its normal state after anomalous inputs. By mathematically refining incremental input-to-state stability ($δ$ISS) theory for LSTM, we derive a practical data-independent upper bound on recovery time. This upper bound gives us resilience-aware training. Experimental validation on simple models demonstrates the effectiveness of our resilience estimation and control methods, enhancing a foundation for rigorous quality assurance in safety-critical AI applications.

cs.AI↗

arXiv2024

Elliptical Pursuit and Evasion -Extended Version-

Many studies on one-on-one pursuit-evasion problems have shown that formulas about the pursuer's trajectory can be solved by supposing three conditions. First, the evader follows specific figures. Second, the pursuer's velocity vector always points toward the evader's position. Third, the ratio of their respective speed remains constant. However, previous studies often assumed that the evader moves at a steady speed. This study aims to investigate how changes in the evader's speed affect the pursuer's trajectory. We hypothesized that the pursuer's trajectory would remain unchanged. First, the pursuer's trajectories were obtained from three scenarios where the evader orbits an ellipse with different speeds and angular velocities. These trajectories coincided. Second, changes in the evader's speed correspond to changes in the evader's trajectory parameters. Replacing the evader's parameter is proven to be replacing the pursuer's parameter. It is shown that replacing the evader's parameter is equivalent to replacing the pursuer's parameter. Consequently, the shape of the pursuer's trajectory is unaffected by the evader's speed; only the speed ratio matters in the game. This version includes additional sections on the dynamical system that were not present in the original version. If the evader's speed is always one, a dynamical system can be derived from the three conditions of pursuit and evasion. When the evader orbits a circle, this dynamical system is autonomous and has an asymptotically stable equilibrium point. However, when the evader orbits an ellipse, the dynamical system becomes non-autonomous, and the solution trajectory converges to a closed curve. Additionally, we present a second-order nonlinear differential equation describing the angular difference between the velocity vectors of both players.

math.OC↗

arXiv2024

Spike Accumulation Forwarding for Effective Training of Spiking Neural Networks

In this article, we propose a new paradigm for training spiking neural networks (SNNs), spike accumulation forwarding (SAF). It is known that SNNs are energy-efficient but difficult to train. Consequently, many researchers have proposed various methods to solve this problem, among which online training through time (OTTT) is a method that allows inferring at each time step while suppressing the memory cost. However, to compute efficiently on GPUs, OTTT requires operations with spike trains and weighted summation of spike trains during forwarding. In addition, OTTT has shown a relationship with the Spike Representation, an alternative training method, though theoretical agreement with Spike Representation has yet to be proven. Our proposed method can solve these problems; namely, SAF can halve the number of operations during the forward process, and it can be theoretically proven that SAF is consistent with the Spike Representation and OTTT, respectively. Furthermore, we confirmed the above contents through experiments and showed that it is possible to reduce memory and training time while maintaining accuracy.

cs.NE↗