While performing favourably on the independent and identically distributed (i.i.d.)

Inthis paper,weconsider various distributions forthenode coordinates inVRPs, followed which we randomly generate instances for both training and testing. Below we present details on how to generate those instances. Uniform distribution.Itconsiders uniformly distributed nodes. It considers multiple (nc) clusters, where we setnc = 3. Then, instead ofgathering allnodes towards the centroid inImplosion distribution, itmovesawaythose nodes from the circle (radiusRec =0.3) and explode them outside the circle, which follow the direction vector between the centroidϵe and the corresponding nodes.

Abstract--In recent years, deep reinforcement learning (DRL) has gained traction for solving the NP-hard traveling salesman problem (TSP). However, limited attention has been given to the close-enough TSP (CETSP), primarily due to the challenge introduced by its neighborhood-based visitation criterion, wherein a node is considered visited if the agent enters a compact neighborhood around it. In this work, we formulate a Markov decision process (MDP) for CETSP using a discretization scheme and propose a novel unified dual-decoder DRL (UD3RL) framework that separates decision-making into node selection and waypoint determination. Specifically, an adapted encoder is employed for effective feature extraction, followed by a node-decoder and a loc-decoder to handle the two sub-tasks, respectively. A k-nearest neighbors subgraph interaction strategy is further introduced to enhance spatial reasoning during location decoding. Furthermore, we customize the REINFORCE algorithm to train UD3RL as a unified model capable of generalizing across different problem sizes and varying neighborhood radius types (i.e., constant and random radii). Experimental results show that UD3RL outperforms conventional methods in both solution quality and runtime, while exhibiting strong generalization across problem scales, spatial distributions, and radius ranges, as well as robustness to dynamic environments. HE close-enough traveling salesman problem (CETSP) is a well-known variant of the classical traveling salesman problem (TSP) that preserves its NP-hard complexity [1].

We introduce logit-gap steering, a fast jailbreak framework that casts the refusal-affirmation gap of RLHF-aligned language models as a single pass over the vocabulary. A forward-computable score blends gap reduction with lightweight proxies for KL penalty and reward shift, allowing a "sort-sum-stop" sweep to complete in under a second and return a short suffix--two orders of magnitude fewer model calls than beam or gradient attacks. The same suffix generalises to unseen prompts and scales from 0.5 B to 70 B checkpoints, lifting one-shot attack success from baseline levels to 80-100 % while preserving topical coherence. Beyond efficiency, these suffixes expose sentence-boundary reward cliffs and other alignment artefacts, offering a lightweight probe into how safety tuning reshapes internal representations.

Calibrating verbalized probabilities presents a novel approach for reliably assessing and leveraging outputs from black-box Large Language Models (LLMs). Recent methods have demonstrated improved calibration by applying techniques like Platt scaling or temperature scaling to the confidence scores generated by LLMs. In this paper, we explore the calibration of verbalized probability distributions for discriminative tasks. First, we investigate the capability of LLMs to generate probability distributions over categorical labels. We theoretically and empirically identify the issue of re-softmax arising from the scaling of verbalized probabilities, and propose using the invert softmax trick to approximate the "logit" by inverting verbalized probabilities. Through extensive evaluation on three public datasets, we demonstrate: (1) the robust capability of LLMs in generating class distributions, and (2) the effectiveness of the invert softmax trick in estimating logits, which, in turn, facilitates post-calibration adjustments.

While in-context learning with large language models (LLMs) has shown impressive performance, we have discovered a unique miscalibration behavior where both correct and incorrect predictions are assigned the same level of confidence. We refer to this phenomenon as indiscriminate miscalibration. We found that traditional calibration metrics, such as Expected Calibrated Errors (ECEs), are unable to capture this behavior effectively. To address this issue, we propose new metrics to measure the severity of indiscriminate miscalibration. Additionally, we develop a novel in-context comparative inference method to alleviate miscalibrations and improve classification performance. Through extensive experiments on five datasets, we demonstrate that our proposed method can achieve more accurate and calibrated predictions compared to regular zero-shot and few-shot prompting.

We propose a self-supervised learning approach for solving the following constrained optimization task in log-linear models or Markov networks. Let $f$ and $g$ be two log-linear models defined over the sets $\mathbf{X}$ and $\mathbf{Y}$ of random variables respectively. Given an assignment $\mathbf{x}$ to all variables in $\mathbf{X}$ (evidence) and a real number $q$, the constrained most-probable explanation (CMPE) task seeks to find an assignment $\mathbf{y}$ to all variables in $\mathbf{Y}$ such that $f(\mathbf{x}, \mathbf{y})$ is maximized and $g(\mathbf{x}, \mathbf{y})\leq q$. In our proposed self-supervised approach, given assignments $\mathbf{x}$ to $\mathbf{X}$ (data), we train a deep neural network that learns to output near-optimal solutions to the CMPE problem without requiring access to any pre-computed solutions. The key idea in our approach is to use first principles and approximate inference methods for CMPE to derive novel loss functions that seek to push infeasible solutions towards feasible ones and feasible solutions towards optimal ones. We analyze the properties of our proposed method and experimentally demonstrate its efficacy on several benchmark problems.

One domain of interest is their use in algorithmic hiring, specifically in matching resumes with job categories. Yet, this introduces issues of bias on protected attributes like gender, race and maternity status. The seminal work of Bertrand & Mullainathan (2003) set the gold-standard for identifying hiring bias via field experiments where the response rate for identical resumes that differ only in protected attributes, e.g., racially suggestive names such as Emily or Lakisha, is compared. We replicate this experiment on state-of-art LLMs (GPT-3.5, Bard, Claude and Llama) to evaluate bias (or lack thereof) on gender, race, maternity status, pregnancy status, and political affiliation. We evaluate LLMs on two tasks: (1) matching resumes to job categories; and (2) summarizing resumes with employment relevant information. Overall, LLMs are robust across race and gender. They differ in their performance on pregnancy status and political affiliation. We use contrastive input decoding on open-source LLMs to uncover potential sources of bias.

Nearly all practical neural models for classification are trained using cross-entropy loss. Yet this ubiquitous choice is supported by little theoretical or empirical evidence. Recent work (Hui & Belkin, 2020) suggests that training using the (rescaled) square loss is often superior in terms of the classification accuracy. In this paper we propose the "squentropy" loss, which is the sum of two terms: the cross-entropy loss and the average square loss over the incorrect classes. We provide an extensive set of experiments on multi-class classification problems showing that the squentropy loss outperforms both the pure cross entropy and rescaled square losses in terms of the classification accuracy. We also demonstrate that it provides significantly better model calibration than either of these alternative losses and, furthermore, has less variance with respect to the random initialization. Additionally, in contrast to the square loss, squentropy loss can typically be trained using exactly the same optimization parameters, including the learning rate, as the standard cross-entropy loss, making it a true "plug-and-play" replacement. Finally, unlike the rescaled square loss, multiclass squentropy contains no parameters that need to be adjusted.