arXiv subjects

Joshua Shay Kricheli

Publications and source records attributed to Joshua Shay Kricheli.

6 recordsLinked to original sources

arXiv2026

Differential Games for Compositional Handling of Competing Control Tasks

We introduce a novel Divide and Conquer control design methodology leveraging differential games in single-agent, multi-objective dynamical systems. The proposed framework associates each control objective with a virtual input and establishes a non-cooperative, finite or infinite horizon differential game among representative players. Each player optimizes a distinct virtual cost function tailored to its specific goal, the full system state, and the other virtual inputs, while accounting for the remaining players' optimal policies. By establishing a Nash Equilibrium for this game, we synthesize a composite controller that achieves a stable balance across competing objectives, providing control engineers with an intuitive and modular framework for parameter re-tuning throughout the design cycle. We provide formal mathematical derivations for both continuous-time and discrete-time dynamical systems, targeting large-scale single-agent applications where complex, dynamically conflicting control objectives make global weighting intractable. To demonstrate the methodology, we developed an open-source Python package implementing a novel numerical algorithm for solving Coupled Algebraic Riccati Equations arising in infinite-horizon differential games. We evaluate the approach on two benchmark case studies: an inverted pendulum on a cart and a non-linear hierarchically controlled quadrotor. The resulting closed-loop performance is compared against the classical Linear Quadratic Regulator (LQR) across various transient and steady-state control metrics, demonstrating superior trajectory tracking and robust multi-objective regulation.

cs.MA↗

arXiv2026

VLC Fusion: Vision-Language Conditioned Sensor Fusion for Robust Object Detection

Although fusing multiple sensor modalities can enhance object detection performance, existing fusion approaches often overlook subtle variations in environmental conditions and sensor inputs. As a result, they struggle to adaptively weight each modality under such variations. To address this challenge, we introduce Vision-Language Conditioned Fusion (VLC Fusion), a novel fusion framework that leverages a Vision-Language Model (VLM) to condition the fusion process on nuanced environmental cues. By capturing high-level environmental context such as darkness, rain, and camera blurring, the VLM guides the model to dynamically adjust modality weights based on the current scene, ensuring robustness against environmental shifts. We evaluate VLC Fusion on real-world autonomous driving and military target detection datasets that include image, LIDAR, and mid-wave infrared modalities. Our experiments show that VLC Fusion consistently outperforms conventional fusion baselines, achieving improved detection accuracy in both seen and unseen scenarios.

cs.CV↗

arXiv2026

Tokens-per-Parameter Coverage Is Critical for Robust LLM Scaling Law Extrapolation

Neural scaling laws approximate a language model's loss as a power-law function of parameter count $N$ and token count $D$. Following Chinchilla-style compute-optimal training, many studies fit scaling laws from runs performed under a fixed tokens-per-parameter (TPP) ratio $k$ and set $D = kN$. We show that this collinear design, combined with the empirically common near-equality of the exponents governing $N$ and $D$, induces an inherent ill-conditioning in the Gauss-Newton least-squares problem: the condition number of the design grows as the inverse square of the gap between the $N$ and $D$-exponents. The scale coefficients become practically unidentifiable, with confidence intervals inflating by an order of magnitude or more, yielding a ``sloppy'' model whose extrapolations degrade sharply off the training ray. We prove this for four scaling-law formalisms and derive a closed-form TPP-diversity threshold that is necessary and sufficient for well-conditioned estimation. Empirically, non-collinear designs outperform collinear ones on held-out splits with a 97.3\% win rate across four laws, five corpora, multiple floating point precision modes. We further show the degeneracy is rooted in Jacobian geometry and is not an artifact of the loss function: any smooth estimation objective whose curvature involves the Jacobian inherits the same ill-conditioning.

cs.LG↗

arXiv2026

Consistency-based Abductive Reasoning over Perceptual Errors of Multiple Pre-trained Models in Novel Environments

The deployment of pre-trained perception models in novel environments often leads to performance degradation due to distributional shifts. Although recent artificial intelligence approaches for metacognition use logical rules to characterize and filter model errors, improving precision often comes at the cost of reduced recall. This paper addresses the hypothesis that leveraging multiple pre-trained models can mitigate this recall reduction. We formulate the challenge of identifying and managing conflicting predictions from various models as a consistency-based abduction problem, building on the idea of abductive learning (ABL) but applying it to test-time instead of training. The input predictions and the learned error detection rules derived from each model are encoded in a logic program. We then seek an abductive explanation--a subset of model predictions--that maximizes prediction coverage while ensuring the rate of logical inconsistencies (derived from domain constraints) remains below a specified threshold. We propose two algorithms for this knowledge representation task: an exact method based on Integer Programming (IP) and an efficient Heuristic Search (HS). Through extensive experiments on a simulated aerial imagery dataset featuring controlled, complex distributional shifts, we demonstrate that our abduction-based framework outperforms individual models and standard ensemble baselines, achieving, for instance, average relative improvements of approximately 13.6\% in F1-score and 16.6\% in accuracy across 15 diverse test datasets when compared to the best individual model. Our results validate the use of consistency-based abduction as an effective mechanism to robustly integrate knowledge from multiple imperfect models in challenging, novel scenarios.

cs.AI↗

arXiv2025

Error Detection and Constraint Recovery in Hierarchical Multi-Label Classification without Prior Knowledge

Recent advances in Hierarchical Multi-label Classification (HMC), particularly neurosymbolic-based approaches, have demonstrated improved consistency and accuracy by enforcing constraints on a neural model during training. However, such work assumes the existence of such constraints a-priori. In this paper, we relax this strong assumption and present an approach based on Error Detection Rules (EDR) that allow for learning explainable rules about the failure modes of machine learning models. We show that these rules are not only effective in detecting when a machine learning classifier has made an error but also can be leveraged as constraints for HMC, thereby allowing the recovery of explainable constraints even if they are not provided. We show that our approach is effective in detecting machine learning errors and recovering constraints, is noise tolerant, and can function as a source of knowledge for neurosymbolic models on multiple datasets, including a newly introduced military vehicle recognition dataset.

cs.LG↗

arXiv2025

SNIC bifurcation and its Application to MEMS

This project focuses on a method to extract a frequency comb in mechanical means, for general interest and numerous practical applications in MEMS. The method of execution is the implementation of a beam that is exhibiting non-linear dynamics that is perturbed and analyzed for its transverse vibrations. The perturbation is an external harmonic driver with a chosen small amplitude and frequency (which is slightly detuned from the beam eigenfrequency), that when engaged with the unperturbed beam oscillations, causes it reach a state of "injection pulling" - an effect that occurs when one harmonic oscillator is coupled with a second one and causes it to oscillate in a frequency near its own. This causes the beam to reach SNIC bifurcation, rendering a frequency comb as desired. Theoretical analysis showed that the problem can be modelled using a non-linear equation of the beam, that translates to a form of the non-linear Duffing equation. While a solution to the dynamics function of the beam is hard to obtain in practice due to mathematical difficulties, a slow evolution model is suggested that is composed of functions of a amplitude and phase. Using several additional mathematical assumptions, the amplitude is seen to be related to the phase, while the phase equation solution is seen to be of the form of Adler's equation. These assumptions ultimately reduce the entire behaviour of the beam to a relatively simple solution to the Adler equation, which has a known analytical solution. Computerized numerical simulations are run on it to check the results and compare them to the theory and desired outcome. The results agreed with the theory and produce the expected frequency comb, showing the assumptions to be valid in extracting the comb.

physics.class-ph↗