Large Vision-Language Models (LVLMs) exhibit powerful reasoning capabilities but suffer sophisticated jailbreak vulnerabilities. Fundamentally, aligning LVLMs is not just a safety challenge but a problem of economic efficiency. Current alignment methods struggle with the trade-off between safety, utility, and operational costs. Critically, a focus solely on final outputs (process-blindness) wastes significant computational budget on unsafe deliberation. This flaw allows harmful reasoning to be disguised with benign justifications, thereby circumventing simple additive safety scores. To address this, we propose EcoAlign, an inference-time framework that reframes alignment as an economically rational search by treating the LVLM as a boundedly rational agent. EcoAlign incrementally expands a thought graph and scores actions using a forward-looking function (analogous to net present value) that dynamically weighs expected safety, utility, and cost against the remaining budget. To prevent deception, path safety is enforced via the weakest-link principle. Extensive experiments across 3 closed-source and 2 open-source models on 6 datasets show that EcoAlign matches or surpasses state-of-the-art safety and utility at a lower computational cost, thereby offering a principled, economical pathway to robust LVLM alignment.

This article reviews modern optimization methods for training neural networks with an emphasis on efficiency and scale. We present state-of-the-art optimization algorithms under a unified algorithmic template that highlights the importance of adapting to the structures in the problem. We then cover how to make these algorithms agnostic to the scale of the problem. Our exposition is intended as an introduction for both practitioners and researchers who wish to be involved in these exciting new developments.

Many tasks in machine learning can be described as or reduced to learning a probability distribution given a finite set of samples. A common approach is to minimize a statistical divergence between the (empirical) data distribution and a parameterized distribution, e.g., a normalizing flow (NF) or an energy-based model (EBM). In this context, the forward KL divergence is a ubiquitous due to its tractability, though its asymmetry may prevent capturing some properties of the target distribution. Symmetric alternatives involve brittle min-max formulations and adversarial training (e.g., generative adversarial networks) or evaluating the reverse KL divergence, as is the case for the symmetric Jeffreys divergence, which is challenging to compute from samples. This work sets out to develop a new approach to minimize the Jeffreys divergence. To do so, it uses a proxy model whose goal is not only to fit the data, but also to assist in optimizing the Jeffreys divergence of the main model. This joint training task is formulated as a constrained optimization problem to obtain a practical algorithm that adapts the models priorities throughout training. We illustrate how this framework can be used to combine the advantages of NFs and EBMs in tasks such as density estimation, image generation, and simulation-based inference.

Predictive coding (PC) replaces global backpropagation with local optimization over weights and activations. We show that linear PC networks admit a natural formulation as cellular sheaves: the sheaf coboundary maps activations to edge-wise prediction errors, and PC inference is diffusion under the sheaf Laplacian. Sheaf cohomology then characterizes irreducible error patterns that inference cannot remove. We analyze recurrent topologies where feedback loops create internal contradictions, introducing prediction errors unrelated to supervision. Using a Hodge decomposition, we determine when these contradictions cause learning to stall. The sheaf formalism provides both diagnostic tools for identifying problematic network configurations and design principles for effective weight initialization for recurrent PC networks.

Model merging combines expert models for multitask performance but faces challenges from parameter interference. This has sparked recent interest in controllable model merging, giving users the ability to explicitly balance performance trade-offs. Existing approaches employ a compile-then-query paradigm, performing a costly offline multi-objective optimization to enable fast, preference-aware model generation. This offline stage typically involves iterative search or dedicated training, with complexity that grows exponentially with the number of tasks. To overcome these limitations, we shift the perspective from parameter-space optimization to a direct correction of the model's final representation. Our approach models this correction as an optimal linear transformation, yielding a closed-form solution that replaces the entire offline optimization process with a single-step, architecture-agnostic computation. This solution directly incorporates user preferences, allowing a Pareto-optimal model to be generated on-the-fly with complexity that scales linearly with the number of tasks. Experimental results show our method generates a superior Pareto front with more precise preference alignment and drastically reduced computational cost.

We study a Stackelberg variant of the classical Most Vital Links problem, modeled as a one-round adversarial game between an attacker and a defender. The attacker strategically removes up to $k$ edges from a flow network to maximally disrupt flow between a source $s$ and a sink $t$, after which the defender optimally reroutes the remaining flow. To capture this attacker--defender interaction, we introduce a new mathematical model of discounted cuts, in which the cost of a cut is evaluated by excluding its $k$ most expensive edges. This model generalizes the Most Vital Links problem and uncovers novel algorithmic and complexity-theoretic properties. We develop a unified algorithmic framework for analyzing various forms of discounted cut problems, including minimizing or maximizing the cost of a cut under discount mechanisms that exclude either the $k$ most expensive or the $k$ cheapest edges. While most variants are NP-complete on general graphs, our main result establishes polynomial-time solvability for all discounted cut problems in our framework when the input is restricted to bounded-genus graphs, a relevant class that includes many real-world networks such as transportation and infrastructure networks. With this work, we aim to open collaborative bridges between artificial intelligence, algorithmic game theory, and operations research.

Searches are conducted to find missing persons and/or objects given uncertain information, imperfect observers and large search areas in Search and Rescue (SAR). In many scenarios, such as Maritime SAR, expected survival times are short and optimal search could increase the likelihood of success. This optimization problem is complex for nontrivial problems given its probabilistic nature. Stochastic optimization methods search large problems by nondeterministically sampling the space to reduce the effective size of the problem. This has been used in SAR planning to search otherwise intractably large problems but the stochastic nature provides no formal guarantees on the quality of solutions found in finite time. This paper instead presents $\rm{A}^{\rm{SAR}}$, an $\varepsilon$-optimal search algorithm for SAR planning. It calculates a heuristic to bound the search space and uses graph-search methods to find solutions that are formally guaranteed to be within a user-specified factor, $\varepsilon$, of the optimal solution. It finds better solutions faster than existing optimization approaches in operational simulations. It is also demonstrated with a real-world field trial on Lake Ontario, Canada, where it was used to locate a drifting manikin in only 150s.

Many real-world decision-making problems involve optimizing multiple objectives simultaneously, rendering the selection of the most preferred solution a non-trivial problem: All Pareto optimal solutions are viable candidates, and it is typically up to a decision maker to select one for implementation based on their subjective preferences. To reduce the cognitive load on the decision maker, previous work has introduced the Pareto pruning problem, where the goal is to compute a fixed-size subset of Pareto optimal solutions that best represent the full set, as evaluated by a given quality measure. Reframing Pareto pruning as a multiwinner voting problem, we conduct an axiomatic analysis of existing quality measures, uncovering several unintuitive behaviors. Motivated by these findings, we introduce a new measure, directed coverage. We also analyze the computational complexity of optimizing various quality measures, identifying previously unknown boundaries between tractable and intractable cases depending on the number and structure of the objectives. Finally, we present an experimental evaluation, demonstrating that the choice of quality measure has a decisive impact on the characteristics of the selected set of solutions and that our proposed measure performs competitively or even favorably across a range of settings.

Effective airfoil geometry optimization requires exploring a diverse range of designs using as few design variables as possible. This study introduces AirDbM, a Design-by-Morphing (DbM) approach specialized for airfoil optimization that systematically reduces design-space dimensionality. AirDbM selects an optimal set of 12 baseline airfoils from the UIUC airfoil database, which contains over 1,600 shapes, by sequentially adding the baseline that most increases the design capacity. With these baselines, AirDbM reconstructs 99 % of the database with a mean absolute error below 0.005, which matches the performance of a previous DbM approach that used more baselines. In multi-objective aerodynamic optimization, AirDbM demonstrates rapid convergence and achieves a Pareto front with a greater hypervolume than that of the previous larger-baseline study, where new Pareto-optimal solutions are discovered with enhanced lift-to-drag ratios at moderate stall tolerances. Furthermore, AirDbM demonstrates outstanding adaptability for reinforcement learning (RL) agents in generating airfoil geometry when compared to conventional airfoil parameterization methods, implying the broader potential of DbM in machine learning-driven design.

Large-scale transformer models have emerged as a powerful tool for semantic communication systems, enabling edge devices to extract rich representations for robust inference across noisy wireless channels. However, their substantial computational demands remain a major barrier to practical deployment in resource-constrained 6G networks. In this paper, we present a training-free framework for adaptive token merging in pretrained vision transformers to jointly reduce inference time and transmission resource usage. We formulate the selection of per-layer merging proportions as a multi-objective optimization problem to balance accuracy and computational cost. We employ Gaussian process-based Bayesian optimization to construct a Pareto frontier of optimal configurations, enabling flexible runtime adaptation to dynamic application requirements and channel conditions. Extensive experiments demonstrate that our method consistently outperforms other baselines and achieves significant reductions in floating-point operations while maintaining competitive accuracy across a wide range of signal-to-noise ratio (SNR) conditions. Additional results highlight the effectiveness of adaptive policies that adjust merging aggressiveness in response to channel quality, providing a practical mechanism to trade off latency and semantic fidelity on demand. These findings establish a scalable and efficient approach for deploying transformer-based semantic communication in future edge intelligence systems.