98.4SYMay 5Code
Building Power Grid Models from Open Data: A Complete Pipeline from OpenStreetMap to Optimal Power FlowAndrea Britto, Thiago Spina, Weiwei Yang et al.
Access to realistic transmission grid models is essential for power systems research, yet detailed network data in the United States remains restricted under critical-infrastructure regulations. We present a pipeline that constructs complete, OPF-solvable transmission network models entirely from publicly available data. The five-stage pipeline (1) extracts power infrastructure from OpenStreetMap via a local Overpass API instance, (2) reconstructs bus-branch topology through voltage inference, line merging, and transformer detection, (3) estimates electrical parameters using voltage-class lookup tables calibrated with U.S. Energy Information Administration (EIA) plant-level data, (4) allocates hourly demand from EIA-930 to individual buses using US Census population as a spatial proxy, and (5) solves both DC and AC optimal power flow using PowerModels.jl with a progressive relaxation strategy that automatically loosens constraints on imprecise models. We validate the pipeline on all 48 contiguous US states and six multi-state regions, including the full Western (5,076 buses) and Eastern (21,697 buses) Interconnections. Of the 48 single-state models, 42 (88%) converge at the strictest relaxation level for AC-OPF at peak hour and 44 (92%) off-peak. Dispatch costs (median $22/MWh) and system losses (median 1.0%) are consistent with real wholesale-market outcomes. The pipeline relies exclusively on open data sources, enabling reproducible grid analysis without proprietary data. All 54 models (48 single-state and 6 multi-state) are publicly released at https://github.com/microsoft/GridSFM.
SYMar 16, 2023
Methodology for Capacity Credit Evaluation of Physical and Virtual Energy Storage in Decarbonized Power SystemNing Qi, Peng Li, Lin Cheng et al.
Energy storage (ES) and virtual energy storage (VES) are key components to realizing power system decarbonization. Although ES and VES have been proven to deliver various types of grid services, little work has so far provided a systematical framework for quantifying their adequacy contribution and credible capacity value while incorporating human and market behavior. Therefore, this manuscript proposed a novel evaluation framework to evaluate the capacity credit (CC) of ES and VES. To address the system capacity inadequacy and market behavior of storage, a two-stage coordinated dispatch is proposed to achieve the trade-off between day-ahead self-energy management of resources and efficient adjustment to real-time failures. And we further modeled the human behavior with storage operations and incorporate two types of decision-independent uncertainties (DIUs) (operate state and self-consumption) and one type of decision-dependent uncertainty (DDUs) (available capacity) into the proposed dispatch. Furthermore, novel reliability and CC indices (e.g., equivalent physical storage capacity (EPSC)) are introduced to evaluate the practical and theoretical adequacy contribution of ES and VES, as well as the ability to displace generation and physical storage while maintaining equivalent system adequacy. Exhaustive case studies based on the IEEE RTS-79 system and real-world data verify the significant consequence (10%-70% overestimated CC) of overlooking DIUs and DDUs in the previous works, while the proposed method outperforms other and can generate a credible and realistic result. Finally, we investigate key factors affecting the adequacy contribution of ES and VES, and reasonable suggestions are provided for better flexibility utilization of ES and VES in decarbonized power system.
CLFeb 6Code
SEMA: Simple yet Effective Learning for Multi-Turn Jailbreak AttacksMingqian Feng, Xiaodong Liu, Weiwei Yang et al.
Multi-turn jailbreaks capture the real threat model for safety-aligned chatbots, where single-turn attacks are merely a special case. Yet existing approaches break under exploration complexity and intent drift. We propose SEMA, a simple yet effective framework that trains a multi-turn attacker without relying on any existing strategies or external data. SEMA comprises two stages. Prefilling self-tuning enables usable rollouts by fine-tuning on non-refusal, well-structured, multi-turn adversarial prompts that are self-generated with a minimal prefix, thereby stabilizing subsequent learning. Reinforcement learning with intent-drift-aware reward trains the attacker to elicit valid multi-turn adversarial prompts while maintaining the same harmful objective. We anchor harmful intent in multi-turn jailbreaks via an intent-drift-aware reward that combines intent alignment, compliance risk, and level of detail. Our open-loop attack regime avoids dependence on victim feedback, unifies single- and multi-turn settings, and reduces exploration complexity. Across multiple datasets, victim models, and jailbreak judges, our method achieves state-of-the-art (SOTA) attack success rates (ASR), outperforming all single-turn baselines, manually scripted and template-driven multi-turn baselines, as well as our SFT (Supervised Fine-Tuning) and DPO (Direct Preference Optimization) variants. For instance, SEMA performs an average $80.1\%$ ASR@1 across three closed-source and open-source victim models on AdvBench, 33.9% over SOTA. The approach is compact, reproducible, and transfers across targets, providing a stronger and more realistic stress test for large language model (LLM) safety and enabling automatic redteaming to expose and localize failure modes. Our code is available at: https://github.com/fmmarkmq/SEMA.
SPFeb 27, 2023
Approximately optimal domain adaptation with Fisher's Linear DiscriminantHayden S. Helm, Ashwin De Silva, Joshua T. Vogelstein et al.
We propose a class of models based on Fisher's Linear Discriminant (FLD) in the context of domain adaptation. The class is the convex combination of two hypotheses: i) an average hypothesis representing previously seen source tasks and ii) a hypothesis trained on a new target task. For a particular generative setting we derive the optimal convex combination of the two models under 0-1 loss, propose a computable approximation, and study the effect of various parameter settings on the relative risks between the optimal hypothesis, hypothesis i), and hypothesis ii). We demonstrate the effectiveness of the proposed optimal classifier in the context of EEG- and ECG-based classification settings and argue that the optimal classifier can be computed without access to direct information from any of the individual source tasks. We conclude by discussing further applications, limitations, and possible future directions.
89.7CRMay 26
Jailbreak susceptibility prediction and mitigation via the behavioral geometry of modelsHayden Helm, Xiaodong Liu, Weiwei Yang
Evaluating and mitigating a generative system's susceptibility to jailbreak attacks is critical to its safe deployment. Given the number of deployable systems, full per-configuration evaluation and optimization is impractical. In this paper, we formalize the behavioral geometry of a population of models that, by leveraging previously evaluated and defended models, supports both efficient susceptibility prediction and effective defense transfer across a population. We apply the framework to 79 models spanning 24 providers and to 100 system configurations of a single base model. Simple methods that use the behavioral geometry reach an AUPRC of $0.94$ for susceptibility detection with $\approx98\%$ fewer probes relative to a full evaluation. Using the behavioral geometry to select which model to transfer an optimized defense from outperforms same-provider assignment ($+2\%$, $p = 0.03$) at no additional probe cost, with a set of three models sufficient to cover the population. Results are robust to hyperparameter selection and judge.
LGNov 30, 2022
Efficient Reinforcement Learning Through Trajectory GenerationWenqi Cui, Linbin Huang, Weiwei Yang et al.
A key barrier to using reinforcement learning (RL) in many real-world applications is the requirement of a large number of system interactions to learn a good control policy. Off-policy and Offline RL methods have been proposed to reduce the number of interactions with the physical environment by learning control policies from historical data. However, their performances suffer from the lack of exploration and the distributional shifts in trajectories once controllers are updated. Moreover, most RL methods require that all states are directly observed, which is difficult to be attained in many settings. To overcome these challenges, we propose a trajectory generation algorithm, which adaptively generates new trajectories as if the system is being operated and explored under the updated control policies. Motivated by the fundamental lemma for linear systems, assuming sufficient excitation, we generate trajectories from linear combinations of historical trajectories. For linear feedback control, we prove that the algorithm generates trajectories with the exact distribution as if they are sampled from the real system using the updated control policy. In particular, the algorithm extends to systems where the states are not directly observed. Experiments show that the proposed method significantly reduces the number of sampled data needed for RL algorithms.
AISep 16, 2023
A Statistical Turing Test for Generative ModelsHayden Helm, Carey E. Priebe, Weiwei Yang
The emergence of human-like abilities of AI systems for content generation in domains such as text, audio, and vision has prompted the development of classifiers to determine whether content originated from a human or a machine. Implicit in these efforts is an assumption that the generation properties of a human are different from that of the machine. In this work, we provide a framework in the language of statistical pattern recognition that quantifies the difference between the distributions of human and machine-generated content conditioned on an evaluation context. We describe current methods in the context of the framework and demonstrate how to use the framework to evaluate the progression of generative models towards human-like capabilities, among many axes of analysis.
LGMay 28, 2022
Deep Learning with Label Noise: A Hierarchical ApproachLi Chen, Ningyuan Huang, Cong Mu et al.
Deep neural networks are susceptible to label noise. Existing methods to improve robustness, such as meta-learning and regularization, usually require significant change to the network architecture or careful tuning of the optimization procedure. In this work, we propose a simple hierarchical approach that incorporates a label hierarchy when training the deep learning models. Our approach requires no change of the network architecture or the optimization procedure. We investigate our hierarchical network through a wide range of simulated and real datasets and various label noise types. Our hierarchical approach improves upon regular deep neural networks in learning with label noise. Combining our hierarchical approach with pre-trained models achieves state-of-the-art performance in real-world noisy datasets.
CLOct 24, 2024Code
Iterative Self-Tuning LLMs for Enhanced Jailbreaking CapabilitiesChung-En Sun, Xiaodong Liu, Weiwei Yang et al.
Recent research has shown that Large Language Models (LLMs) are vulnerable to automated jailbreak attacks, where adversarial suffixes crafted by algorithms appended to harmful queries bypass safety alignment and trigger unintended responses. Current methods for generating these suffixes are computationally expensive and have low Attack Success Rates (ASR), especially against well-aligned models like Llama2 and Llama3. To overcome these limitations, we introduce ADV-LLM, an iterative self-tuning process that crafts adversarial LLMs with enhanced jailbreak ability. Our framework significantly reduces the computational cost of generating adversarial suffixes while achieving nearly 100\% ASR on various open-source LLMs. Moreover, it exhibits strong attack transferability to closed-source models, achieving 99\% ASR on GPT-3.5 and 49\% ASR on GPT-4, despite being optimized solely on Llama3. Beyond improving jailbreak ability, ADV-LLM provides valuable insights for future safety alignment research through its ability to generate large datasets for studying LLM safety. Our code is available at: https://github.com/SunChungEn/ADV-LLM
CLMar 13, 2025Code
NeurIPS 2023 LLM Efficiency Fine-tuning CompetitionMark Saroufim, Yotam Perlitz, Leshem Choshen et al.
Our analysis of the NeurIPS 2023 large language model (LLM) fine-tuning competition revealed the following trend: top-performing models exhibit significant overfitting on benchmark datasets, mirroring the broader issue of benchmark overfitting on popular leaderboards and that data curation is essential in order to get a high performing LLM. The competition, which consisted of two stages - an open evaluation stage with publicly available tasks and a closed evaluation stage with unseen tasks - allowed us to assess the generalizability of fine-tuned LLMs. Our results highlight the limitations of current benchmark-based evaluation schemes for generative models and demonstrate the need for more robust evaluation methods. Notably, the winning submissions utilized standard open-source libraries and focused primarily on data curation. To facilitate further research and promote reproducibility, we release all competition entries, Docker files, and evaluation infrastructure, providing a valuable resource for the community to explore fine-tuning, overfitting, and reproducibility in LLMs.
AIJan 30
Statistical Estimation of Adversarial Risk in Large Language Models under Best-of-N SamplingMingqian Feng, Xiaodong Liu, Weiwei Yang et al.
Large Language Models (LLMs) are typically evaluated for safety under single-shot or low-budget adversarial prompting, which underestimates real-world risk. In practice, attackers can exploit large-scale parallel sampling to repeatedly probe a model until a harmful response is produced. While recent work shows that attack success increases with repeated sampling, principled methods for predicting large-scale adversarial risk remain limited. We propose a scaling-aware Best-of-N estimation of risk, SABER, for modeling jailbreak vulnerability under Best-of-N sampling. We model sample-level success probabilities using a Beta distribution, the conjugate prior of the Bernoulli distribution, and derive an analytic scaling law that enables reliable extrapolation of large-N attack success rates from small-budget measurements. Using only n=100 samples, our anchored estimator predicts ASR@1000 with a mean absolute error of 1.66, compared to 12.04 for the baseline, which is an 86.2% reduction in estimation error. Our results reveal heterogeneous risk scaling profiles and show that models appearing robust under standard evaluation can experience rapid nonlinear risk amplification under parallel adversarial pressure. This work provides a low-cost, scalable methodology for realistic LLM safety assessment. We will release our code and evaluation scripts upon publication to future research.
CLOct 31, 2024Code
Interpretable Next-token Prediction via the Generalized Induction HeadEunji Kim, Sriya Mantena, Weiwei Yang et al.
While large transformer models excel in predictive performance, their lack of interpretability restricts their usefulness in high-stakes domains. To remedy this, we propose the Generalized Induction-Head Model (GIM), an interpretable model for next-token prediction inspired by the observation of "induction heads" in LLMs. GIM is a retrieval-based module that identifies similar sequences in the input context by combining exact n-gram matching and fuzzy matching based on a neural similarity metric. We evaluate GIM in two settings: language modeling and fMRI response prediction. In language modeling, GIM improves next-token prediction by up to 25%p over interpretable baselines, significantly narrowing the gap with black-box LLMs. In an fMRI setting, GIM improves neural response prediction by 20% and offers insights into the language selectivity of the brain. GIM represents a significant step toward uniting interpretability and performance across domains. The code is available at https://github.com/ejkim47/generalized-induction-head.
83.6AIMay 5
Agentic-imodels: Evolving agentic interpretability tools via autoresearchChandan Singh, Yan Shuo Tan, Weijia Xu et al.
Agentic data science (ADS) systems are rapidly improving their capability to autonomously analyze, fit, and interpret data, potentially moving towards a future where agents conduct the vast majority of data-science work. However, current ADS systems use statistical tools designed to be interpretable by humans, rather than interpretable by agents. To address this, we introduce Agentic-imodels, an agentic autoresearch loop that evolves data-science tools designed to be interpretable by agents. Specifically, it develops a library of scikit-learn-compatible regressors for tabular data that are optimized for both predictive performance and a novel LLM-based interpretability metric. The metric measures a suite of LLM-graded tests that probe whether a fitted model's string representation is "simulatable" by an LLM, i.e. whether the LLM can answer questions about the model's behavior by reading its string output alone. We find that the evolved models jointly improve predictive performance and agent-facing interpretability, generalizing to new datasets and new interpretability tests. Furthermore, these evolved models improve downstream end-to-end ADS, increasing performance for Copilot CLI, Claude Code, and Codex on the BLADE benchmark by up to 73%
61.4CLMay 3
MultiBreak: A Scalable and Diverse Multi-turn Jailbreak Benchmark for Evaluating LLM SafetyJialin Song, Xiaodong Liu, Weiwei Yang et al.
We present MultiBreak, a scalable and diverse multi-turn jailbreak benchmark to evaluate large language model (LLM) safety. Multi-turn jailbreaks mimic natural conversational settings, making them easier to bypass safety-aligned LLM than single-turn jailbreaks. Existing multi-turn benchmarks are limited in size or rely heavily on templates, which restrict their diversity. To address this gap, we unify a wide range of harmful jailbreak intents, and introduce an active learning pipeline for expanding high-quality multi-turn adversarial prompts, where a generator is iteratively fine-tuned to produce stronger attack candidates, guided by uncertainty-based refinement. Our MultiBreak includes 10,389 multi-turn adversarial prompts, spans 2,665 distinct harmful intents, and covers the most diverse set of topics to date. Empirical evaluation shows that our benchmark achieves up to a 54.0 and 34.6 higher attack success rate (ASR)} than the second-best dataset on DeepSeek-R1-7B and GPT-4.1-mini, respectively. More importantly, safety evaluations suggest that diverse attack categories uncover fine-grained LLM vulnerabilities}, and categories that appear benign under single-turn can exhibit substantially higher adversarial effectiveness in multi-turn scenarios. These findings highlight persistent vulnerabilities of LLMs under realistic adversarial settings and establish MultiBreak as a scalable resource for advancing LLM safety.
CRDec 15, 2023
Binary Code Summarization: Benchmarking ChatGPT/GPT-4 and Other Large Language ModelsXin Jin, Jonathan Larson, Weiwei Yang et al.
Binary code summarization, while invaluable for understanding code semantics, is challenging due to its labor-intensive nature. This study delves into the potential of large language models (LLMs) for binary code comprehension. To this end, we present BinSum, a comprehensive benchmark and dataset of over 557K binary functions and introduce a novel method for prompt synthesis and optimization. To more accurately gauge LLM performance, we also propose a new semantic similarity metric that surpasses traditional exact-match approaches. Our extensive evaluation of prominent LLMs, including ChatGPT, GPT-4, Llama 2, and Code Llama, reveals 10 pivotal insights. This evaluation generates 4 billion inference tokens, incurred a total expense of 11,418 US dollars and 873 NVIDIA A100 GPU hours. Our findings highlight both the transformative potential of LLMs in this field and the challenges yet to be overcome.
SPFeb 25, 2022
Mental State Classification Using Multi-graph FeaturesGuodong Chen, Hayden S. Helm, Kate Lytvynets et al.
We consider the problem of extracting features from passive, multi-channel electroencephalogram (EEG) devices for downstream inference tasks related to high-level mental states such as stress and cognitive load. Our proposed method leverages recently developed multi-graph tools and applies them to the time series of graphs implied by the statistical dependence structure (e.g., correlation) amongst the multiple sensors. We compare the effectiveness of the proposed features to traditional band power-based features in the context of three classification experiments and find that the two feature sets offer complementary predictive information. We conclude by showing that the importance of particular channels and pairs of channels for classification when using the proposed features is neuroscientifically valid.
LGJan 19, 2022
Prospective Learning: Principled Extrapolation to the FutureAshwin De Silva, Rahul Ramesh, Lyle Ungar et al.
Learning is a process which can update decision rules, based on past experience, such that future performance improves. Traditionally, machine learning is often evaluated under the assumption that the future will be identical to the past in distribution or change adversarially. But these assumptions can be either too optimistic or pessimistic for many problems in the real world. Real world scenarios evolve over multiple spatiotemporal scales with partially predictable dynamics. Here we reformulate the learning problem to one that centers around this idea of dynamic futures that are partially learnable. We conjecture that certain sequences of tasks are not retrospectively learnable (in which the data distribution is fixed), but are prospectively learnable (in which distributions may be dynamic), suggesting that prospective learning is more difficult in kind than retrospective learning. We argue that prospective learning more accurately characterizes many real world problems that (1) currently stymie existing artificial intelligence solutions and/or (2) lack adequate explanations for how natural intelligences solve them. Thus, studying prospective learning will lead to deeper insights and solutions to currently vexing challenges in both natural and artificial intelligences.
LGJun 23, 2021
Leveraging semantically similar queries for ranking via combining representationsHayden S. Helm, Marah Abdin, Benjamin D. Pedigo et al.
In modern ranking problems, different and disparate representations of the items to be ranked are often available. It is sensible, then, to try to combine these representations to improve ranking. Indeed, learning to rank via combining representations is both principled and practical for learning a ranking function for a particular query. In extremely data-scarce settings, however, the amount of labeled data available for a particular query can lead to a highly variable and ineffective ranking function. One way to mitigate the effect of the small amount of data is to leverage information from semantically similar queries. Indeed, as we demonstrate in simulation settings and real data examples, when semantically similar queries are available it is possible to gainfully use them when ranking with respect to a particular query. We describe and explore this phenomenon in the context of the bias-variance trade off and apply it to the data-scarce settings of a Bing navigational graph and the Drosophila larva connectome.
LGMar 16, 2021
Learning without gradient descent encoded by the dynamics of a neurobiological modelVivek Kurien George, Vikash Morar, Weiwei Yang et al.
The success of state-of-the-art machine learning is essentially all based on different variations of gradient descent algorithms that minimize some version of a cost or loss function. A fundamental limitation, however, is the need to train these systems in either supervised or unsupervised ways by exposing them to typically large numbers of training examples. Here, we introduce a fundamentally novel conceptual approach to machine learning that takes advantage of a neurobiologically derived model of dynamic signaling, constrained by the geometric structure of a network. We show that MNIST images can be uniquely encoded and classified by the dynamics of geometric networks with nearly state-of-the-art accuracy in an unsupervised way, and without the need for any training.
MLFeb 20, 2021
Inducing a hierarchy for multi-class classification problemsHayden S. Helm, Weiwei Yang, Sujeeth Bharadwaj et al.
In applications where categorical labels follow a natural hierarchy, classification methods that exploit the label structure often outperform those that do not. Un-fortunately, the majority of classification datasets do not come pre-equipped with a hierarchical structure and classical flat classifiers must be employed. In this paper, we investigate a class of methods that induce a hierarchy that can similarly improve classification performance over flat classifiers. The class of methods follows the structure of first clustering the conditional distributions and subsequently using a hierarchical classifier with the induced hierarchy. We demonstrate the effectiveness of the class of methods both for discovering a latent hierarchy and for improving accuracy in principled simulation settings and three real data applications.
MLNov 12, 2020
A partition-based similarity for classification distributionsHayden S. Helm, Ronak D. Mehta, Brandon Duderstadt et al.
Herein we define a measure of similarity between classification distributions that is both principled from the perspective of statistical pattern recognition and useful from the perspective of machine learning practitioners. In particular, we propose a novel similarity on classification distributions, dubbed task similarity, that quantifies how an optimally-transformed optimal representation for a source distribution performs when applied to inference related to a target distribution. The definition of task similarity allows for natural definitions of adversarial and orthogonal distributions. We highlight limiting properties of representations induced by (universally) consistent decision rules and demonstrate in simulation that an empirical estimate of task similarity is a function of the decision rule deployed for inference. We demonstrate that for a given target distribution, both transfer efficiency and semantic similarity of candidate source distributions correlate with empirical task similarity.
LGMay 20, 2020
Distance-based Positive and Unlabeled Learning for RankingHayden S. Helm, Amitabh Basu, Avanti Athreya et al.
Learning to rank -- producing a ranked list of items specific to a query and with respect to a set of supervisory items -- is a problem of general interest. The setting we consider is one in which no analytic description of what constitutes a good ranking is available. Instead, we have a collection of representations and supervisory information consisting of a (target item, interesting items set) pair. We demonstrate analytically, in simulation, and in real data examples that learning to rank via combining representations using an integer linear program is effective when the supervision is as light as "these few items are similar to your item of interest." While this nomination task is quite general, for specificity we present our methodology from the perspective of vertex nomination in graphs. The methodology described herein is model agnostic.
HCMay 12, 2020
Design of a Privacy-Preserving Data Platform for Collaboration Against Human TraffickingDarren Edge, Weiwei Yang, Kate Lytvynets et al.
Case records on victims of human trafficking are highly sensitive, yet the ability to share such data is critical to evidence-based practice and policy development across government, business, and civil society. We present new methods to anonymize, publish, and explore such data, implemented as a pipeline generating three artifacts: (1) synthetic data mitigating the privacy risk that published attribute combinations might be linked to known individuals or groups; (2) aggregate data mitigating the utility risk that synthetic data might misrepresent statistics needed for official reporting; and (3) visual analytics interfaces to both datasets mitigating the accessibility risk that privacy mechanisms or analysis tools might not be understandable and usable by all stakeholders. We present our work as a design study motivated by the goal of transforming how the world's largest database of identified victims is made available for global collaboration against human trafficking.
AIApr 27, 2020
Simple Lifelong Learning MachinesJayanta Dey, Joshua T. Vogelstein, Hayden S. Helm et al.
In lifelong learning, data are used to improve performance not only on the present task, but also on past and future (unencountered) tasks. While typical transfer learning algorithms can improve performance on future tasks, their performance on prior tasks degrades upon learning new tasks (called forgetting). Many recent approaches for continual or lifelong learning have attempted to maintain performance on old tasks given new tasks. But striving to avoid forgetting sets the goal unnecessarily low. The goal of lifelong learning should be to use data to improve performance on both future tasks (forward transfer) and past tasks (backward transfer). In this paper, we show that a simple approach -- representation ensembling -- demonstrates both forward and backward transfer in a variety of simulated and benchmark data scenarios, including tabular, vision (CIFAR-100, 5-dataset, Split Mini-Imagenet, and Food1k), and speech (spoken digit), in contrast to various reference algorithms, which typically failed to transfer either forward or backward, or both. Moreover, our proposed approach can flexibly operate with or without a computational budget.
ITJan 6, 2014
When Does Relay Transmission Give a More Secure Connection in Wireless Ad Hoc Networks?Chunxiao Cai, Yueming Cai, Xiangyun Zhou et al.
Relay transmission can enhance coverage and throughput, while it can be vulnerable to eavesdropping attacks due to the additional transmission of the source message at the relay. Thus, whether or not one should use relay transmission for secure communication is an interesting and important problem. In this paper, we consider the transmission of a confidential message from a source to a destination in a decentralized wireless network in the presence of randomly distributed eavesdroppers. The source-destination pair can be potentially assisted by randomly distributed relays. For an arbitrary relay, we derive exact expressions of secure connection probability for both colluding and non-colluding eavesdroppers. We further obtain lower bound expressions on the secure connection probability, which are accurate when the eavesdropper density is small. By utilizing these lower bound expressions, we propose a relay selection strategy to improve the secure connection probability. By analytically comparing the secure connection probability for direct transmission and relay transmission, we address the important problem of whether or not to relay and discuss the condition for relay transmission in terms of the relay density and source-destination distance. These analytical results are accurate in the small eavesdropper density regime.