arXiv subjects

Roy Siegelmann

Publications and source records attributed to Roy Siegelmann.

4 recordsLinked to original sources

arXiv2026

Stability Analysis and Data-driven Verification via Recurrent Lyapunov Functions

Lyapunov's direct method is a cornerstone of stability and control, but it hinges on finding a Lyapunov function, a task demanding ingenuity or computation. A key difficulty is that every sub-level set of the function must be forward invariant, coupling its geometry to the system's trajectories. We relax this by replacing invariance with recurrence: a set is recurrent if every trajectory starting in it returns within a finite time. This yields the notion of a Recurrent Lyapunov Function (RLF), whose sub-level sets need only be recurrent. We show that, under mild conditions, RLFs guarantee stability, and we introduce stronger notions yielding asymptotic and exponential stability. We also give norm-based converse theorems: under the corresponding stability conditions, any norm is an RLF for their practical versions. We then develop GPU-based algorithms that certify (practical) stability from trajectory data alone, without a Lyapunov function. Certifying stability up to an $\varepsilon$-neighborhood needs only $O(\log(1/\varepsilon))$ trajectory evaluations, with constants growing as the certified decay rate nears the true one, exposing an intrinsic performance-cost trade-off.

math.OC↗

arXiv2026

Overcoming Valid Action Suppression in Unmasked Policy Gradient Algorithms

In reinforcement learning environments with state-dependent action validity, action masking consistently outperforms penalty-based handling of invalid actions, yet existing theory only shows that masking preserves the policy gradient theorem. We identify a distinct failure mode of unmasked training: it systematically suppresses valid actions at states the agent has not yet visited. This occurs because gradients pushing down invalid actions at visited states propagate through shared network parameters to unvisited states where those actions are valid. We prove that for softmax policies with shared features, when an action is invalid at visited states but valid at an unvisited state $s^*$, the probability $π(a \mid s^*)$ is bounded by exponential decay due to parameter sharing and the zero-sum identity of softmax logits. This bound reveals that entropy regularization trades off between protecting valid actions and sample efficiency, a tradeoff that masking eliminates. We validate empirically that deep networks exhibit the feature alignment condition required for suppression, and experiments on Craftax, Craftax-Classic, and MiniHack confirm the predicted exponential suppression and demonstrate that feasibility classification enables deployment without oracle masks.

cs.LG↗

arXiv2025

Data-driven Practical Stabilization of Nonlinear Systems via Chain Policies: Sample Complexity and Incremental Learning

We propose a method for data-driven practical stabilization of nonlinear systems with provable guarantees, based on the concept of Nonparametric Chain Policies (NCPs). The approach employs a normalized nearest-neighbor rule to assign, at each state, a finite-duration control signal derived from stored data, after which the process repeats. Unlike recent works that model the system as linear, polynomial, or polynomial fraction, we only assume the system to be locally Lipschitz. Our analysis builds on the framework of Recurrent Lyapunov Functions (RLFs), which enable data-driven certification of practical stability using standard norm functions instead of requiring the explicit construction of a classical Lyapunov function. To extend this framework, we introduce the concept of Recurrent Control Lyapunov Functions (R-CLFs), which can certify the existence of an NCP that practically stabilizes an arbitrarily small c-neighborhood of an equilibrium point. We also provide an explicit sample complexity guarantee of O((3/rho)^d log(R/c)) number of trajectories, where R is the domain radius, d the state dimension, and rho a system-dependent constant. The proposed Chain Policies are nonparametric, thus allowing new verified data to be readily incorporated into the policy to either improve convergence rate or enlarge the certified region. Numerical experiments illustrate and validate these properties.

eess.SY↗

arXiv2023

Meta-Analytic Operation of Threshold-independent Filtering (MOTiF) Reveals Sub-threshold Genomic Robustness in Trisomy

Trisomy, a form of aneuploidy wherein the cell possesses an additional copy of a specific chromosome, exhibits a high correlation with cancer. Studies from across different hosts, cell-lines, and labs into the cellular effects induced by aneuploidy have conflicted, ranging from small, chaotic global changes to large instances of either overexpression or underexpression throughout the trisomic chromosome. We ascertained that conflicting findings may be correct but miss the overarching ground truth due to careless use of thresholds. To correct this deficiency, we introduce the Meta-analytic Operation of Threshold-independent Filtering (MOTiF) method, which begins by providing a panoramic view of all thresholds, transforms the data to eliminate the effects accounted for by known mechanisms, and then reconstructs an explanation of the mechanisms that underly the difference between the baseline and the uncharacterized effects observed. As a proof of concept, we applied MOTiF to human colonic epithelial cells, discovering a uniform decrease in gene expression levels throughout the genome, which while significant, is beneath most common thresholds. Using Hi-C data we identified the structural correlate, wherein the physical genomic architecture condenses, compactifying in a uniform, genome-wide manner, which we hypothesize is a robustness mechanism counteracting the addition of a chromosome. We were able to decompose the gene expression alterations into three overlapping mechanisms: the raw chromosome content, the genomic compartmentalization, and the global structural condensation. While further studies must be conducted to corroborate the hypothesized robustness mechanism, MOTiF presents a useful meta-analytic tool in the realm of gene expression and beyond.

q-bio.QM↗