arXiv subjects

Amir Leshem

Publications and source records attributed to Amir Leshem.

At least 19 recordsLinked to original sources

arXiv2026

Fast Synergetic Simulation to Study Slow Evolution of Soliton Patterns in Optical Resonators

Complex patterns in physical and biological systems often emerge through slow collective dynamics governed by a small number of key variables. In nonlinear optical resonators, dissipative Kerr solitons provide an important example, where interactions between well-separated solitons can evolve over timescales far longer than the characteristic loss and gain timescales. Direct numerical simulation of these dynamics is challenging because stiffness forces conventional methods to resolve many rapidly damped degrees-of-freedom with very small time steps. We present a numerical scheme, the synergetic method, that eliminates these rapidly damped degrees-of-freedom and retains the slowly evolving modes, enabling time steps many orders of magnitude larger than those used in conventional approaches. Applied to soliton molecules in driven Kerr cavities, the method achieves speedups of $10^3$ to $10^5$ while capturing dynamics on laboratory timescales. We use it to model the full interaction dynamics of a three-soliton molecule and the evolution of an eight-soliton molecule. The approach provides an efficient framework for studying slow pattern formation in nonlinear systems with widely separated timescales.

nlin.PS↗

arXiv2026

Sequential-Innovation Reducibility and the Innovation Spectrum

Sequential prediction naturally induces an innovation sequence consisting of the prediction errors produced by a causal predictor. We use the collection of all such innovation sequences to define the \emph{innovation spectrum} of an individual binary sequence and, from it, a new reducibility based on sequential information extraction. We show that this reducibility refines truth-table reducibility while exhibiting a fundamentally different geometry. The degree structure decomposes into two canonical regions: a truth-table spine, whose induced order is isomorphic to the truth-table degrees, and a complementary reservoir-immune region, consisting of sequences from which no infinite computable predictable reservoir can be extracted. We establish bridge constructions connecting the two regions, prove that reservoir immunity is preserved under sequential innovation, and show that the Martin--L\"of-random degrees form a proper downward-closed substructure inside the reservoir-immune region. These results reveal a new geometric organization of individual sequences based on causal predictability rather than classical oracle computation.

math.LO↗

arXiv2026

Universal Individual-Sequence Prediction with a Primitive-Recursive Superpredictor

We study sequential prediction of individual binary sequences under zero-one loss. No computable master can compete on every sequence with all total computable predictors. We therefore consider rational-valued primitive-recursive forecasters, a broad syntactically enumerable class containing finite-state, context-based, and Prediction by Partial Matching (PPM) rules. We construct a computable probabilistic predictor with an explicit sublinear regret bound relative to every primitive-recursive forecaster on every individual sequence. We further prove that the PPM predictor is primitive recursive. Consequently, our predictor attains the infinite-past Bayes error on every Martin-L\"of random realization of every computable stationary ergodic binary source. This optimality extends to finitely many independent such sources interleaved according to an arbitrary primitive-recursive schedule. Finally, we establish strict separations from finite-state prediction and from every fixed primitive-recursive predictor. keywords: Universal prediction, individual sequences, prediction with expert advice, primitive recursive functions, Kolmogorov complexity, PPM.

cs.IT↗

arXiv2026

Constrained Multi-Objective Reinforcement Learning with Max-Min Criterion

Multi-Objective Reinforcement Learning (MORL) extends standard RL by optimizing policies with respect to multiple, often conflicting, objectives. While max-min MORL has emerged as an effective approach for promoting fairness, its applicability remains limited, particularly when constraints must be incorporated. In this paper, we propose a MORL framework that integrates the max-min criterion with explicit constraint satisfaction. We establish a theoretical foundation for the proposed framework and validate the resulting algorithm through convergence analysis and experiments in tabular settings. We further demonstrate the practical relevance of our approach in simulated building thermal control, multi-objective locomotion control, and greenhouse-gas-emission-aware traffic management. Across these domains, our method effectively balances fairness and constraint satisfaction in multi-objective decision-making.

cs.LG↗

arXiv2026

Computability Limits of Sequential Hypothesis Testing

Sequential hypothesis testing asks for decision rules that update as data arrive. A natural goal is \emph{eventual correctness}: the rule may change its mind early on, but it should make only finitely many wrong decisions almost surely. Starting from Cover's theorem, which guarantees such behavior for membership in a countable set of candidate means, we ask a sharper question: \emph{which sets actually admit computable sequential decision procedures with finitely many errors?} We answer this optimally by giving a complete characterization both necessary and sufficient of the subsets of $\Q$ that admit a computable finite-error sequential membership test. We further extend the characterization to any \emph{effectively presented} countable family of real means, exactly the setting in which Cover's identification rule can be implemented computably. Beyond the technical boundary, the results clarify within a precise probabilistic setting what it can mean for inquiry to ``converge to the truth,'' and they formalize a limit to which empirical methods can be expected to succeed when only eventual stabilization (rather than fixed-time guarantees) is demanded. keywords: Cover's theorem, sequential decision procedures, finite error learning, limit computability, $\Delta^0_2$ sets.

cs.IT↗

arXiv2026

Metastability-Containing Turing Machines

Metastability is a spurious mode of operation in digital signals, where an electrical signal fails to settle into a stable state within a specified time, leading to uncertainty and potentially failing downstream hardware. A system that computes the closure over all possibilities, given an uncertain input, is called a Metastability-containing system. While prior work has addressed metastability-containing systems in the context of combinational and clocked circuits, state machines, and logic formulas, its implications for general-purpose computation remain largely unexplored. In this work, we study the metastability-containing systems within an abstract computational model: The Turing Machine. This approach allows us to investigate the computational limits and capabilities of Turing Machines operating under uncertain inputs. Specifically, we prove that in general the metastable closure of a Turing Machine is non-computable. Then we discuss cases where the meta-stable closure is computable: For EXPTIME problems, we prove that resolving even a single uncertain bit is EXPTIME-complete. In contrast, we prove that for polynomial time problems, the meta-stable closure is polynomial time computable for a logarithmic number of uncertain bits, but coNP-complete, when the number of undefined inputs is arbitrary. Finally, we describe a hardware-realizable Universal Turning Machine that computes the metastable closure of any given bounded-time Turing Machine with at most an exponential blowup in time.

cs.CC↗

arXiv2026

Creating a digital poet

Can a machine write good poetry? Any positive answer raises fundamental questions about the nature and value of art. We report a seven-month poetry workshop in which a large language model was shaped into a digital poet through iterative in-context expert feedback, without retraining. Across sessions, the model developed a distinctive style and a coherent corpus, supported by quantitative and qualitative analyses, and it produced a pen name and author image. In a blinded authorship test with 50 humanities students and graduates (three AI poems and three poems by well-known poets each), judgments were at chance: human poems were labeled human 54% of the time and AI poems 52%, with 95% confidence intervals including 50%. After the workshop, a commercial publisher released a poetry collection authored by the model. These results show that workshop-style prompting can support long-horizon creative shaping and renew debates on creativity and authorship.

cs.AI↗

arXiv2025

Multi-Objective Reinforcement Learning with Max-Min Criterion: A Game-Theoretic Approach

In this paper, we propose a provably convergent and practical framework for multi-objective reinforcement learning with max-min criterion. From a game-theoretic perspective, we reformulate max-min multi-objective reinforcement learning as a two-player zero-sum regularized continuous game and introduce an efficient algorithm based on mirror descent. Our approach simplifies the policy update while ensuring global last-iterate convergence. We provide a comprehensive theoretical analysis on our algorithm, including iteration complexity under both exact and approximate policy evaluations, as well as sample complexity bounds. To further enhance performance, we modify the proposed algorithm with adaptive regularization. Our experiments demonstrate the convergence behavior of the proposed algorithm in tabular settings, and our implementation for deep reinforcement learning significantly outperforms previous baselines in many MORL environments.

cs.LG↗

arXiv2025

Dynamics of interacting cavity solitons

We derive the equations governing the motion of Kerr solitons in pair waveforms. Recent experiments in microresonators have studied a variety of interaction effects in multisoliton waveforms, including collisions and formation of soliton molecules and crystals. Here we analyze the effective interaction that arises from the coupling of soliton-tail overlap nonlinearity with global soliton variables associated with the breaking of translation symmetry. The interaction is either purely repulsive, or alternates between attraction and repulsion, according to whether the decay of soliton tails is monotone or oscillatory. In the latter case, stable fixed points of the effective dynamical system signify stable soliton molecule configuration, but the exponential weakening of the interaction with increasing inter-soliton separation may prevent the molecule from forming in experimentally accessible time scales. Our theory becomes asymptotically exact in the large-separation limit, and we verify the theoretical calculations using soliton trajectories extracted from direct numerical solutions of the wave equation.

nlin.PS↗

arXiv2024

The Max-Min Formulation of Multi-Objective Reinforcement Learning: From Theory to a Model-Free Algorithm

In this paper, we consider multi-objective reinforcement learning, which arises in many real-world problems with multiple optimization goals. We approach the problem with a max-min framework focusing on fairness among the multiple goals and develop a relevant theory and a practical model-free algorithm under the max-min framework. The developed theory provides a theoretical advance in multi-objective reinforcement learning, and the proposed algorithm demonstrates a notable performance improvement over existing baseline methods.

cs.LG↗

arXiv2024

Two-Stage Resource Allocation in Reconfigurable Intelligent Surface Assisted Hybrid Networks via Multi-Player Bandits

This paper considers a resource allocation problem where several Internet-of-Things (IoT) devices send data to a base station (BS) with or without the help of the reconfigurable intelligent surface (RIS) assisted cellular network. The objective is to maximize the sum rate of all IoT devices by finding the optimal RIS and spreading factor (SF) for each device. Since these IoT devices lack prior information on the RISs or the channel state information (CSI), a distributed resource allocation framework with low complexity and learning features is required to achieve this goal. Therefore, we model this problem as a two-stage multi-player multi-armed bandit (MPMAB) framework to learn the optimal RIS and SF sequentially. Then, we put forth an exploration and exploitation boosting (E2Boost) algorithm to solve this two-stage MPMAB problem by combining the $ε$-greedy algorithm, Thompson sampling (TS) algorithm, and non-cooperation game method. We derive an upper regret bound for the proposed algorithm, i.e., $\mathcal{O}(\log^{1+δ}_2 T)$, increasing logarithmically with the time horizon $T$. Numerical results show that the E2Boost algorithm has the best performance among the existing methods and exhibits a fast convergence rate. More importantly, the proposed algorithm is not sensitive to the number of combinations of the RISs and SFs thanks to the two-stage allocation mechanism, which can benefit high-density networks.

eess.SP↗

arXiv2024

Medium Access Control protocol for Collaborative Spectrum Learning in Wireless Networks

In recent years there is a growing effort to provide learning algorithms for spectrum collaboration. In this paper we present a medium access control protocol which allows spectrum collaboration with minimal regret and high spectral efficiency in highly loaded networks. We present a fully-distributed algorithm for spectrum collaboration in congested ad-hoc networks. The algorithm jointly solves both the channel allocation and access scheduling problems. We prove that the algorithm has an optimal logarithmic regret. Based on the algorithm we provide a medium access control protocol which allows distributed implementation of the algorithm in ad-hoc networks. The protocol utilizes single-channel opportunistic carrier sensing to carry out a low-complexity distributed auction in time and frequency. We also discuss practical implementation issues such as bounded frame size and speed of convergence. Computer simulations comparing the algorithm to state-of-the-art distributed medium access control protocols show the significant advantage of the proposed scheme.

cs.NI↗

arXiv2024

Mitigating Data Injection Attacks on Federated Learning

Federated learning is a technique that allows multiple entities to collaboratively train models using their data without compromising data privacy. However, despite its advantages, federated learning can be susceptible to false data injection attacks. In these scenarios, a malicious entity with control over specific agents in the network can manipulate the learning process, leading to a suboptimal model. Consequently, addressing these data injection attacks presents a significant research challenge in federated learning systems. In this paper, we propose a novel technique to detect and mitigate data injection attacks on federated learning systems. Our mitigation method is a local scheme, performed during a single instance of training by the coordinating node, allowing the mitigation during the convergence of the algorithm. Whenever an agent is suspected to be an attacker, its data will be ignored for a certain period, this decision will often be re-evaluated. We prove that with probability 1, after a finite time, all attackers will be ignored while the probability of ignoring a trustful agent becomes 0, provided that there is a majority of truthful agents. Simulations show that when the coordinating node detects and isolates all the attackers, the model recovers and converges to the truthful model.

cs.LG↗

arXiv2023

Nonlinear Self-Calibrated Spectrometer with Single GeSe-InSe Heterojunction Device

Optical spectroscopy the measurement of electromagnetic spectra is fundamental to various scientific domains and serves as the building block of numerous technologies. Computational spectrometry is an emerging field that employs an array of photodetectors with different spectral responses or a single photodetector device with tunable spectral response, in conjunction with numerical algorithms, for spectroscopic measurements. Compact single photodetectors made from layered materials are particularly attractive, since they eliminate the need for bulky mechanical and optical components used in traditional spectrometers and can easily be engineered as heterostructures to optimize device performance. However, compact tunable photodetectors are typically nonlinear devices and this adds complexity to extracting optical spectra from the device response. Here, we report on the training of an artificial neural network (ANN) to recover the full nonlinear spectral photoresponse of a nonlinear problem of high dimensionality of a single GeSe-InSe p-n heterojunction device. We demonstrate the functionality of a calibrated spectrometer in the spectral range of 400-1100 nm, with a small device footprint of ~25X25 micrometers, and we achieve a mean reconstruction error of 0.0002 for the power-spectrum at a spectral resolution of 0.35 nm. Using our device, we demonstrate a solution to metamerism, an apparent matching of colors with different power spectral distributions, which is a fundamental problem in optical imaging.

physics.app-ph↗

arXiv2023

Random Access Protocols for Cell-Free Wireless Network Exploiting Statistical Behavior of THz Signal Propagation

The current body of research on terahertz (THz) wireless communications predominantly focuses on its application for single-user backhaul/fronthaul connectivity at sub-THz frequencies. First, we develop a generalized statistical model for signal propagation at THz frequencies encompassing physical layer impairments, including random path-loss with Gamma distribution for the molecular absorption coefficient, short-term fading characterized by the $α$-$η$-$κ$-$μ$ distribution, antenna misalignment errors, and transceiver hardware impairments. Next, we propose random access protocols for a cell-free wireless network, ensuring successful transmission for multiple users with limited delay and energy loss, exploiting the combined effect of random atmospheric absorption, non-linearity of fading, hardware impairments, and antenna misalignment errors. We consider two schemes: a fixed transmission probability (FTP) scheme where the transmission probability (TP) of each user is updated at the beginning of the data transmission and an adaptive transmission probability (ATP) scheme where the TP is updated with each successful reception of the data. We analyze the performance of both protocols using delay, energy consumption, and outage probability with scaling laws for the transmission of a data frame consisting of a single packet from users at a predefined quality of service (QoS).

cs.IT↗

arXiv2023

Near-Optimal Privacy-Preserving Learning for Max-Min Fair Multi-Agent Bandits

We study fair multi-agent multi-armed bandit learning under collision-only coordination. Agents cannot communicate explicitly during learning and observe only their own rewards and whether collisions occur when several agents access the same arm. The goal is to learn a max-min fair allocation while keeping each agent's reward samples and empirical reward estimates local. We propose a fully distributed algorithm for bounded rewards with unknown support, achieving regret $O\!\left(N^3 f(\log T)\log T\right)$, where $f$ is any nondecreasing diverging function satisfying $f(k-1)/f(k)\to 1$. The algorithm combines distributed agent ordering, cumulative round-robin exploration, endpoint-revalidated warm-started bisection, and a collision-based distributed auction for threshold-feasibility tests. Unlike leader-based optimal algorithms, no agent collects the reward observations, empirical estimates, or preferences of the others. Thus, the protocol preserves reward privacy in the operational sense of avoiding reward sharing, while coordinating only through collision outcomes. Compared with previous privacy-preserving algorithms for max--min fair bandits, which have exponential dependence on the number of agents, our method achieves polynomial $N^3$ dependence while retaining near-logarithmic dependence on $T$. The analysis uses concentration of cumulative empirical estimates and stability of endpoint-revalidated bisection. Simulations confirm the predicted scaling with horizon, number of agents, and max--min gap across representative numerical settings.

cs.LG↗

arXiv2022

Joint Scheduling and Resource Allocation for Packets with Deadlines and Priorities

Cellular networks provide communication for different applications. Some applications have strict and very short latency requirements, while others require high bandwidth with varying priorities. The challenge of satisfying the requirements grows in congested traffic where some packets might miss their deadlines. Unfortunately, we prove that the problem is NP-Hard. To overcome this, we propose a new scheduling policy for packets with multiple priorities, latency requirements, and strict deadlines. To alleviate the complexity, our solution incorporates a novel time domain relaxation solved by linear programming. Simulation results show that this method outperforms existing scheduling strategies.

cs.NI↗

arXiv2022

Communication Efficient Distributed Learning over Wireless Channels

Vertical distributed learning exploits the local features collected by multiple learning workers to form a better global model. However, the exchange of data between the workers and the model aggregator for parameter training incurs a heavy communication burden, especially when the learning system is built upon capacity-constrained wireless networks. In this paper, we propose a novel hierarchical distributed learning framework, where each worker separately learns a low-dimensional embedding of their local observed data. Then, they perform communication efficient distributed max-pooling for efficiently transmitting the synthesized input to the aggregator. For data exchange over a shared wireless channel, we propose an opportunistic carrier sensing-based protocol to implement the max-pooling operation for the output data from all the learning workers. Our simulation experiments show that the proposed learning framework is able to achieve almost the same model accuracy as the learning model using the concatenation of all the raw outputs from the learning workers, while requiring a communication load that is independent of the number of workers.

cs.NI↗