Large language models (LLMs) often experience language confusion, which is the unintended mixing of languages during text generation. Current solutions to this problem either necessitate model retraining or cannot differentiate between harmful confusion and acceptable code-switching. This paper introduces the Language Confusion Gate (LCG), a lightweight, plug-in solution that filters tokens during decoding without altering the base LLM. The LCG is trained using norm-adjusted self-distillation to predict appropriate language families and apply masking only when needed. Our method is based on the findings that language confusion is infrequent, correct-language tokens are usually among the top predictions, and output token embedding norms are larger for high-resource languages, which biases sampling. When evaluated across various models, including Qwen3, GPT-OSS, Gemma3, Llama3.1, LCG decreases language confusion significantly, often by an order of magnitude, without negatively impacting task performance. Code is available at https://github.com/collinzrj/language_confusion_gate.

We thank the reviewers for their detailed and constructive comments, especially during these unprecedented times. Our algorithm isn't designed to compete (or However, in our new experiment in Fig. B we achieve close to D-SGD We will add to the paper an experiment with 4 different models. Reference data can be synthetic and then it is easy to obtain (as in co-regularization, see R1's comment). We now explain that in detail. The graphs in this work were randomly drawn for a given maximum number of degrees per node.

Causal dynamics learning has recently emerged as a promising approach to enhancing robustness in reinforcement learning (RL). Typically, the goal is to build a dynamics model that makes predictions based on the causal relationships among the entities. Despite the fact that causal connections often manifest only under certain contexts, existing approaches overlook such fine-grained relationships and lack a detailed understanding of the dynamics. In this work, we propose a novel dynamics model that infers fine-grained causal structures and employs them for prediction, leading to improved robustness in RL. The key idea is to jointly learn the dynamics model with a discrete latent variable that quantizes the state-action space into subgroups. This leads to recognizing meaningful context that displays sparse dependencies, where causal structures are learned for each subgroup throughout the training. Experimental results demonstrate the robustness of our method to unseen states and locally spurious correlations in downstream tasks where fine-grained causal reasoning is crucial. We further illustrate the effectiveness of our subgroup-based approach with quantization in discovering fine-grained causal relationships compared to prior methods.

Freight forwarding plays a crucial role in facilitating global trade and logistics. However, as the freight forwarding market is extremely fragmented, freight forwarders often face the issue of not being able to fill the available shipping capacity. This recurrent issue motivates the creation of various freight forwarding networks that aim at exchanging capacities and demands so that the resource utilization of individual freight forwarders can be maximized. In this paper, we focus on how to design such a collaborative network based on collaborative game theory, with the Shapley value representing a fair scheme for profit sharing. Noting that the exact computation of Shapley values is intractable for large-scale real-world scenarios, we incorporate the observation that collaboration among two forwarders is only possible if their service routes and demands overlap. This leads to a new class of collaborative games called the Locally Collaborative Games (LCGs), where agents can only collaborate with their neighbors. We propose an efficient approach to compute Shapley values for LCGs, and numerically demonstrate that our approach significantly outperforms the state-of-the-art approach for a wide variety of network structures.

Risk and sparsity requirements often need to be enforced simultaneously in many applications, e.g., in portfolio optimization, assortment planning, and treatment planning. Properly balancing these potentially conflicting requirements entails the formulation of functional constrained optimization with either convex or nonconvex objectives. In this paper, we focus on projection-free methods that can generate a sparse trajectory for solving these challenging functional constrained optimization problems. Specifically, for the convex setting, we propose a Level Conditional Gradient (LCG) method, which leverages a level-set framework to update the approximation of the optimal value and an inner conditional gradient oracle (CGO) for solving mini-max subproblems. We show that the method achieves $\mathcal{O}\big(\frac{1}{\epsilon^2}\log\frac{1}{\epsilon}\big)$ iteration complexity for solving both smooth and nonsmooth cases without dependency on a possibly large size of optimal dual Lagrange multiplier. For the nonconvex setting, we introduce the Level Inexact Proximal Point (IPP-LCG) method and the Direct Nonconvex Conditional Gradient (DNCG) method. The first approach taps into the advantage of LCG by transforming the problem into a series of convex subproblems and exhibits an $\mathcal{O}\big(\frac{1}{\epsilon^3}\log\frac{1}{\epsilon}\big)$ iteration complexity for finding an ($\epsilon,\epsilon$)-KKT point. The DNCG is the first single-loop projection-free method, with iteration complexity bounded by $\mathcal{O}\big(1/\epsilon^4\big)$ for computing a so-called $\epsilon$-Wolfe point. We demonstrate the effectiveness of LCG, IPP-LCG and DNCG by devising formulations and conducting numerical experiments on two risk averse sparse optimization applications: a portfolio selection problem with and without cardinality requirement, and a radiation therapy planning problem in healthcare.