Hirschberg's algorithm (1975) reduces the space complexity for the longest common subsequence problem from $O(N^2)$ to $O(N)$ via recursive midpoint bisection on a grid dynamic program (DP). We show that the underlying idea generalizes to a broad class of dynamic programs with local dependencies on directed acyclic graphs (DP DAGs). Modeling a DP as deterministic time evolution over a topologically ordered DAG with frontier width $ω$ and bounded in-degree, and assuming a max-type semiring with deterministic tie breaking, we prove that in a standard offline random-access model any such DP admits deterministic traceback in space $O(ω\log T + (\log T)^{O(1)})$ cells over a fixed finite alphabet, where $T$ is the number of states. Our construction replaces backward dynamic programs by forward-only recomputation and organizes the time order into a height-compressed recursion tree whose nodes expose small "middle frontiers'' across which every optimal path must pass. The framework yields near-optimal traceback bounds for asymmetric and banded sequence alignment, one-dimensional recurrences, and dynamic-programming formulations on graphs of bounded pathwidth. We also show that an $Ω(ω)$ space term (in bits) is unavoidable in forward single-pass models and discuss conjectured $\sqrt{T}$-type barriers in streaming settings, supporting the view that space-efficient traceback is a structural property of width-bounded DP DAGs rather than a peculiarity of grid-based algorithms.

Inverse medium scattering is an ill-posed, nonlinear wave-based imaging problem arising in medical imaging, remote sensing, and non-destructive testing. Machine learning (ML) methods offer increased inference speed and flexibility in capturing prior knowledge of imaging targets relative to classical optimization-based approaches; however, they perform poorly in regimes where the scattering behavior is highly nonlinear. A key limitation is that ML methods struggle to incorporate the physics governing the scattering process, which are typically inferred implicitly from the training data or loosely enforced via architectural design. In this paper, we present a method that endows a machine learning framework with explicit knowledge of problem physics, in the form of a differentiable solver representing the forward model. The proposed method progressively refines reconstructions of the scattering potential using measurements at increasing wave frequencies, following a classical strategy to stabilize recovery. Empirically, we find that our method provides high-quality reconstructions at a fraction of the computational or sampling costs of competing approaches.

This paper analyzes a fuzzy multiplex from a logical perspective in a way that has not been formalized so far. A fuzzy multiplex is a nested structure with inner nodes representing sub-system level agent traits and with outer nodes representing system agents; all while the ensemble is the system under consideration. Moreover, a mathematical framework is necessary to describe that structure which is formulated and then utilized. The system is firstly initialized using fuzzy set theory [2], inspired by Fuzzy Cognitive Maps [1]. Then a criterion that describes the structure is devised to implement a multiplex instead of a map [7] [8], and lastly system optimization is achieved. Furthermore, the theoretical context behind the multiplex is expounded in an attempt to establish a formal way of handling implications within a closed system using human intelligence. The paper is organized in sections following the reasoning process behind this unique idea. 1

We address the problem of Gaussian Process (GP) optimization in the presence of unknown and potentially varying adversarial perturbations. Unlike traditional robust optimization approaches that focus on maximizing performance under worst-case scenarios, we consider a robust satisficing objective, where the goal is to consistently achieve a predefined performance threshold $τ$, even under adversarial conditions. We propose two novel algorithms based on distinct formulations of robust satisficing, and show that they are instances of a general robust satisficing framework. Further, each algorithm offers different guarantees depending on the nature of the adversary. Specifically, we derive two regret bounds: one that is sublinear over time, assuming certain conditions on the adversary and the satisficing threshold $τ$, and another that scales with the perturbation magnitude but requires no assumptions on the adversary. Through extensive experiments, we demonstrate that our approach outperforms the established robust optimization methods in achieving the satisficing objective, particularly when the ambiguity set of the robust optimization framework is inaccurately specified.

We propose geodesic-based optimization methods on dually flat spaces, where the geometric structure of the parameter manifold is closely related to the form of the objective function. A primary application is maximum likelihood estimation in statistical models, especially exponential families, whose model manifolds are dually flat. We show that an m-geodesic update, which directly optimizes the log-likelihood, can theoretically reach the maximum likelihood estimator in a single step. In contrast, an e-geodesic update has a practical advantage in cases where the parameter space is geodesically complete, allowing optimization without explicitly handling parameter constraints. We establish the theoretical properties of the proposed methods and validate their effectiveness through numerical experiments.

We study online statistical inference for the solutions of stochastic optimization problems with equality and inequality constraints. Such problems are prevalent in statistics and machine learning, encompassing constrained $M$-estimation, physics-informed models, safe reinforcement learning, and algorithmic fairness. We develop a stochastic sequential quadratic programming (SSQP) method to solve these problems, where the step direction is computed by sequentially performing a quadratic approximation of the objective and a linear approximation of the constraints. Despite having access to unbiased estimates of population gradients, a key challenge in constrained stochastic problems lies in dealing with the bias in the step direction. As such, we apply a momentum-style gradient moving-average technique within SSQP to debias the step. We show that our method achieves global almost-sure convergence and exhibits local asymptotic normality with an optimal primal-dual limiting covariance matrix in the sense of Hájek and Le Cam. In addition, we provide a plug-in covariance matrix estimator for practical inference. To our knowledge, the proposed SSQP method is the first fully online method that attains primal-dual asymptotic minimax optimality without relying on projection operators onto the constraint set, which are generally intractable for nonlinear problems. Through extensive experiments on benchmark nonlinear problems, as well as on constrained generalized linear models and portfolio allocation problems using both synthetic and real data, we demonstrate superior performance of our method, showing that the method and its asymptotic behavior not only solve constrained stochastic problems efficiently but also provide valid and practical online inference in real-world applications.

The interpretation of Chest X-ray is an important diagnostic issue in clinical practice and especially in the resource-limited setting where the shortage of radiologists plays a role in delayed diagnosis and poor patient outcomes. Although the original CheXNet architecture has shown potential in automated analysis of chest radiographs, DenseNet-121 backbone is computationally inefficient and poorly single-label classifier. To eliminate such shortcomings, we suggest a better classification framework of chest disease that relies on EfficientNetV2-M and incorporates superior training approaches such as Automatic Mixed Precision training, AdamW, Cosine Annealing learning rate scheduling, and Exponential Moving Average regularization. We prepared a dataset of 18,080 chest X-ray images of three source materials of high authority and representing five key clinically significant disease categories which included Cardiomegaly, COVID-19, Normal, Pneumonia, and Tuberculosis. To achieve statistical reliability and reproducibility, nine independent experimental runs were run. The suggested architecture showed significant gains with mean test accuracy of 96.45 percent compared to 95.30 percent at baseline (p less than 0.001) and macro-averaged F1-score increased to 91.08 percent (p less than 0.001). Critical infectious diseases showed near-perfect classification performance with COVID-19 detection having 99.95 percent accuracy and Tuberculosis detection having 99.97 percent accuracy. Although 6.8 times more parameters are included, the training time was reduced by 11.4 percent and performance stability was increased by 22.7 percent. This framework presents itself as a decision-support tool that can be used to respond to a pandemic, screen tuberculosis, and assess thoracic disease regularly in various healthcare facilities.

Role-playing agents (RPAs) must simultaneously master many conflicting skills -- following multi-turn instructions, exhibiting domain knowledge, and adopting a consistent linguistic style. Existing work either relies on supervised fine-tuning (SFT) that over-fits surface cues and yields low diversity, or applies reinforcement learning (RL) that fails to learn multiple dimensions for comprehensive RPA optimization. We present MOA (Multi-Objective Alignment), a reinforcement-learning framework that enables multi-dimensional, fine-grained rubric optimization for general RPAs. MOA introduces a novel multi-objective optimization strategy that trains simultaneously on multiple fine-grained rubrics to boost optimization performance. Besides, to address the issues of model output diversity and quality, we have also employed thought-augmented rollout with off-policy guidance. Extensive experiments on challenging benchmarks such as PersonaGym and RoleMRC show that MOA enables an 8B model to match or even outperform strong baselines such as GPT-4o and Claude across numerous dimensions. This demonstrates the great potential of MOA in building RPAs that can simultaneously meet the demands of role knowledge, persona style, diverse scenarios, and complex multi-turn conversations.

Abstract--Semantic Communication (SC) combined with V e-hicular edge computing (VEC) provides an efficient edge task processing paradigm for Internet of V ehicles (IoV). Focusing on highway scenarios, this paper proposes a Tripartite Cooperative Semantic Communication (TCSC) framework, which enables V e-hicle Users (VUs) to perform semantic task offloading via V ehicle-to-Infrastructure (V2I) and V ehicle-to-V ehicle (V2V) communications. Considering task latency and the number of semantic symbols, the framework constructs a Mixed-Integer Nonlinear Programming (MINLP) problem, which is transformed into two subproblems. First, we innovatively propose a multi-agent proximal policy optimization task offloading optimization method based on parametric distribution noise (MAPPO-PDN) to solve the optimization problem of the number of semantic symbols; second, linear programming (LP) is used to solve offloading ratio. Simulations show that performance of this scheme is superior to that of other algorithms.

AI tasks differ in complexity and are best addressed with different computation strategies (e.g., combinations of models and decoding methods). Hence, an effective routing system that maps tasks to the appropriate strategies is crucial. Most prior methods build the routing framework by training a single model across all strategies, which demands full retraining whenever new strategies appear and leads to high overhead. Prior models also typically use a single input representation, limiting their ability to capture the full complexity of the routing problem and leading to sub-optimal routing decisions. To address these gaps, we propose CONCUR, a continual routing framework that supports both constrained and unconstrained routing (i.e., routing with or without a budget). Our modular design trains a separate predictor model for each strategy, enabling seamless incorporation of new strategies with low additional training cost. Experiments on both in-distribution and out-of-distribution, knowledge-and reasoning-intensive tasks show that our method outperforms the best single strategy and strong existing routing techniques with higher end-to-end accuracy and lower inference cost in both continual and non-continual settings, while also reducing training cost in the continual setting. AI tasks vary in difficulty, and thus are optimally served by different computation strategies, such as selecting appropriate models (small or large language models) and decoding methods (with or without chain-of-thought reasoning (Wei et al., 2022)).