Lech Szymanski, Brendan McCane, Michael Albert
We show that the number of unique function mappings in a neural network hypothesis space is inversely proportional to $\prod_lU_l!$, where $U_{l}$ is the number of neurons in the hidden layer $l$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
In this paper we analyze, evaluate, and improve the performance of training Random Forest (RF) models on modern CPU architectures. An exact, state-of-the-art binary decision tree building algorithm is used as the basis of this study. Firstly, we investigate the trade-offs between using different tree building algorithms, namely breadth-first-search (BFS) and depth-search-first (DFS). We design a novel, dynamic, hybrid BFS-DFS algorithm and demonstrate that it performs better than both BFS and DFS, and is more robust in the presence of workloads with different characteristics. Secondly, we iden…
Impact of Data Breadth and Depth on Performance of Siamese Neural Network Model: Experiments with Three Keystroke Dynamic Datasets
本研究通过三个公开击键数据集实验，探究数据广度与深度对孪生神经网络性能的影响，发现增加广度可提升模型捕捉受试者间差异的能力，深度影响则依数据集类型而异，为行为生物识别模型训练和身份验证系统设计提供参考。
Breadth Beats Depth: Improving GCG-Based Jailbreak Optimization with Breadth-Oriented Suffix Search
该研究针对GCG越狱优化易忽视后缀空间具前景区域的问题，提出即插即用框架BOSS，采用广度导向后缀搜索，提升攻击成功率并缩短优化时间。
Growing a Neural Network in Breadth, Depth, and Time
提出在循环卷积神经网络中定义广度、深度和时间的可微成本，通过反向传播联合优化任务误差和资源成本，发现三者可相互权衡，且模型使用的时间与人类反应时间相关。
Depth-Breadth Synergy in RLVR: Unlocking LLM Reasoning Gains with Adaptive Exploration
本文提出DARS方法，通过自适应探索提升LLM推理能力，发现扩大批量大小能显著提升Pass@1指标，同时结合DARS-Breadth方法实现深度与广度的协同增益。
Compute Allocation for Self-Evolving LLMs: From Depth-Breadth to Multi-Armed Bandits
针对LLM引导的进化搜索中固定预算的LLM调用分配问题，提出基于多臂老虎机的BaSE方法，通过跨并行轨迹分配调用，平均适应度提升12.3%。
Autonomous Knowledge Graph Exploration with Adaptive Breadth-Depth Retrieval
本文提出ARK工具，通过全局词搜索和邻域探索平衡知识图谱的广度与深度检索，提升多跳遍历效率，在STaRK上达到59.1%的平均Hit@1和67.4的平均MRR，优于其他方法。
Beyond Pass@k: Breadth-Depth Metrics for Reasoning Boundaries
针对大k值下Pass@k指标可能高估离散答案任务推理能力的问题，提出带可靠性阈值的Cover@tau指标，发现其会改变RLVR模型的相对排名，为评估推理边界提供新视角。
Deep versus Broad Technology Search and the Timing of Innovation Impact
本研究探讨深度与广度技术搜索对创新影响时间点的影响，发现深度搜索在初期有高影响但后期回报下降，而广度搜索虽初期阻力大但能带来更广泛的长期影响。
Do Neural Operators Forget Geometry? The Forgetting Hypothesis in Deep Operator Learning
本文研究了神经算子在不规则几何上性能下降的原因，提出几何遗忘假设，并引入轻量级几何记忆注入机制以缓解遗忘问题，揭示几何保留是结构需求而非设计选择。
We present, GeniePath, a scalable approach for learning adaptive receptive fields of neural networks defined on permutation invariant graph data. In GeniePath, we propose an adaptive path layer consists of two complementary functions designed for breadth and depth exploration respectively, where the former learns the importance of different sized neighborhoods, while the latter extracts and filters signals aggregated from neighbors of different hops away. Our method works in both transductive and inductive settings, and extensive experiments compared with competitive methods show that our appr…
Several recent works have shown separation results between deep neural networks, and hypothesis classes with inferior approximation capacity such as shallow networks or kernel classes. On the other hand, the fact that deep networks can efficiently express a target function does not mean that this target function can be learned efficiently by deep neural networks. In this work we study the intricate connection between learnability and approximation capacity. We show that learnability with deep networks of a target function depends on the ability of simpler classes to approximate the target. Spe…
Absolute abstraction: a renormalisation group approach
本文提出通过重整化群方法，利用数据广度和深度增强神经网络的抽象能力，最终达到绝对抽象的层次特征模型。
The strong lottery ticket hypothesis has highlighted the potential for training deep neural networks by pruning, which has inspired interesting practical and theoretical insights into how neural networks can represent functions. For networks with ReLU activation functions, it has been proven that a target network with depth $L$ can be approximated by the subnetwork of a randomly initialized neural network that has double the target's depth $2L$ and is wider by a logarithmic factor. We show that a depth $L+1$ network is sufficient. This result indicates that we can expect to find lottery ticket…
Graph Neural Networks (GNNs) are a powerful representational tool for solving problems on graph-structured inputs. In almost all cases so far, however, they have been applied to directly recovering a final solution from raw inputs, without explicit guidance on how to structure their problem-solving. Here, instead, we focus on learning in the space of algorithms: we train several state-of-the-art GNN architectures to imitate individual steps of classical graph algorithms, parallel (breadth-first search, Bellman-Ford) as well as sequential (Prim's algorithm). As graph algorithms usually rely on …
Neural inductive program synthesis is a task generating instructions that can produce desired outputs from given inputs. In this paper, we focus on the generation of a chunk of assembly code that can be executed to match a state change inside the CPU and RAM. We develop a neural program synthesis algorithm, AutoAssemblet, learned via self-learning reinforcement learning that explores the large code space efficiently. Policy networks and value networks are learned to reduce the breadth and depth of the Monte Carlo Tree Search, resulting in better synthesis performance. We also propose an effect…
Revisiting the Platonic Representation Hypothesis: An Aristotelian View
针对神经网络表征收敛于统一统计模型的柏拉图式假说，本文发现现有相似性度量受网络规模混淆，提出基于置换的零校准框架，揭示全局谱收敛在校准后消失，而局部邻域相似性（非距离）仍跨模态一致，据此提出亚里士多德式表征假说。
We prove several hardness results for training depth-2 neural networks with the ReLU activation function; these networks are simply weighted sums (that may include negative coefficients) of ReLUs. Our goal is to output a depth-2 neural network that minimizes the square loss with respect to a given training set. We prove that this problem is NP-hard already for a network with a single ReLU. We also prove NP-hardness for outputting a weighted sum of $k$ ReLUs minimizing the squared error (for $k>1$) even in the realizable setting (i.e., when the labels are consistent with an unknown depth-2 ReLU…
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。