The Colored Points Traveling Salesman Problem (Colored Points TSP) is introduced in this work as a novel variation of the traditional Traveling Salesman Problem (TSP) in which the set of points is partitioned into multiple classes, each of which is represented by a distinct color (or label). The goal is to find a minimum cost cycle $C$ that visits all the colors and only makes each one appears once. This issue has various applications in the fields of transportation, goods distribution network, postal network, inspection, insurance, banking, etc. By reducing the traditional TSP to it, we can demonstrate that Colored Points TSP is NP-hard. Here, we offer a $\frac{2\pi r}{3}$-approximation algorithm to solve this issue, where $r$ denotes the radius of the points' smallest color-spanning circle. The algorithm has been implemented, executed on random datasets, and compared against the brute force method.
Deep Reinforcement Learning is widely used for aligning Large Language Models (LLM) with human preference. However, the conventional reward modelling has predominantly depended on human annotations provided by a select cohort of individuals. Such dependence may unintentionally result in models that are skewed to reflect the inclinations of these annotators, thereby failing to represent the expectations of the wider population adequately. In this paper, we introduce the Distributional Preference Reward Model (DPRM), a simple yet effective framework to align large language models with a diverse set of human preferences. To this end, we characterize the preferences by a beta distribution, which can dynamically adapt to fluctuations in preference trends. On top of that, we design an optimal-transportation-based loss to calibrate DPRM to align with the preference distribution. Finally, the expected reward is utilized to fine-tune an LLM policy to generate responses favoured by the population. Our experiments show that DPRM significantly enhances the alignment of LLMs with population preference, yielding more accurate, unbiased, and contextually appropriate responses.
A Bernoulli factory is an algorithmic procedure for exact sampling of certain random variables having only Bernoulli access to their parameters. Bernoulli access to a parameter $p \in [0,1]$ means the algorithm does not know $p$, but has sample access to independent draws of a Bernoulli random variable with mean equal to $p$. In this paper, we study the problem of Bernoulli factories for polytopes: given Bernoulli access to a vector $x\in P$ for a given polytope $P\subset [0,1]^n$, output a randomized vertex such that the expected value of the $i$-th coordinate is \emph{exactly} equal to $x_i$. For example, for the special case of the perfect matching polytope, one is given Bernoulli access to the entries of a doubly stochastic matrix $[x_{ij}]$ and asked to sample a matching such that the probability of each edge $(i,j)$ be present in the matching is exactly equal to $x_{ij}$. We show that a polytope $P$ admits a Bernoulli factory if and and only if $P$ is the intersection of $[0,1]^n$ with an affine subspace. Our construction is based on an algebraic formulation of the problem, involving identifying a family of Bernstein polynomials (one per vertex) that satisfy a certain algebraic identity on $P$. The main technical tool behind our construction is a connection between these polynomials and the geometry of zonotope tilings. We apply these results to construct an explicit factory for the perfect matching polytope. The resulting factory is deeply connected to the combinatorial enumeration of arborescences and may be of independent interest. For the $k$-uniform matroid polytope, we recover a sampling procedure known in statistics as Sampford sampling.
In this paper, we present QueryWarp, a novel framework for temporally coherent human motion video translation. Existing diffusion-based video editing approaches that rely solely on key and value tokens to ensure temporal consistency, which scarifies the preservation of local and structural regions. In contrast, we aim to consider complementary query priors by constructing the temporal correlations among query tokens from different frames. Initially, we extract appearance flows from source poses to capture continuous human foreground motion. Subsequently, during the denoising process of the diffusion model, we employ appearance flows to warp the previous frame's query token, aligning it with the current frame's query. This query warping imposes explicit constraints on the outputs of self-attention layers, effectively guaranteeing temporally coherent translation. We perform experiments on various human motion video translation tasks, and the results demonstrate that our QueryWarp framework surpasses state-of-the-art methods both qualitatively and quantitatively.
While Language Models (LMs) are the workhorses of NLP, their interplay with structured knowledge graphs (KGs) is still actively researched. Current methods for encoding such graphs typically either (i) linearize them for embedding with LMs -- which underutilize structural information, or (ii) use Graph Neural Networks (GNNs) to preserve the graph structure -- but GNNs cannot represent text features as well as pretrained LMs. In our work we introduce a novel LM type, the Graph Language Model (GLM), that integrates the strengths of both approaches and mitigates their weaknesses. The GLM parameters are initialized from a pretrained LM to enhance understanding of individual graph concepts and triplets. Simultaneously, we design the GLM's architecture to incorporate graph biases, thereby promoting effective knowledge distribution within the graph. This enables GLMs to process graphs, texts, and interleaved inputs of both. Empirical evaluations on relation classification tasks show that GLM embeddings surpass both LM- and GNN-based baselines in supervised and zero-shot setting, demonstrating their versatility.
This paper gives an overview of Software Defined Optical Networks or SDONs and how they can be implemented. It traces the evolution of Optical networks upto GMPLS and traces the idea of SDN and builds upto OpenFlow. The paper explores the need for SDONs and explains what a SDON solution could look like, including the hardware. It also seeks to explain how OpenFlow could be used as a part of this solution to overcome the limitations of GMPLS.
Despite the recent advances in the field of computational Schrodinger Bridges (SB), most existing SB solvers are still heavy-weighted and require complex optimization of several neural networks. It turns out that there is no principal solver which plays the role of simple-yet-effective baseline for SB just like, e.g., $k$-means method in clustering, logistic regression in classification or Sinkhorn algorithm in discrete optimal transport. We address this issue and propose a novel fast and simple SB solver. Our development is a smart combination of two ideas which recently appeared in the field: (a) parameterization of the Schrodinger potentials with sum-exp quadratic functions and (b) viewing the log-Schrodinger potentials as the energy functions. We show that combined together these ideas yield a lightweight, simulation-free and theoretically justified SB solver with a simple straightforward optimization objective. As a result, it allows solving SB in moderate dimensions in a matter of minutes on CPU without a painful hyperparameter selection. Our light solver resembles the Gaussian mixture model which is widely used for density estimation. Inspired by this similarity, we also prove an important theoretical result showing that our light solver is a universal approximator of SBs. The code for the LightSB solver can be found at //github.com/ngushchin/LightSB
Interactive Natural Language Processing (iNLP) has emerged as a novel paradigm within the field of NLP, aimed at addressing limitations in existing frameworks while aligning with the ultimate goals of artificial intelligence. This paradigm considers language models as agents capable of observing, acting, and receiving feedback iteratively from external entities. Specifically, language models in this context can: (1) interact with humans for better understanding and addressing user needs, personalizing responses, aligning with human values, and improving the overall user experience; (2) interact with knowledge bases for enriching language representations with factual knowledge, enhancing the contextual relevance of responses, and dynamically leveraging external information to generate more accurate and informed responses; (3) interact with models and tools for effectively decomposing and addressing complex tasks, leveraging specialized expertise for specific subtasks, and fostering the simulation of social behaviors; and (4) interact with environments for learning grounded representations of language, and effectively tackling embodied tasks such as reasoning, planning, and decision-making in response to environmental observations. This paper offers a comprehensive survey of iNLP, starting by proposing a unified definition and framework of the concept. We then provide a systematic classification of iNLP, dissecting its various components, including interactive objects, interaction interfaces, and interaction methods. We proceed to delve into the evaluation methodologies used in the field, explore its diverse applications, scrutinize its ethical and safety issues, and discuss prospective research directions. This survey serves as an entry point for researchers who are interested in this rapidly evolving area and offers a broad view of the current landscape and future trajectory of iNLP.
Recently, a considerable literature has grown up around the theme of Graph Convolutional Network (GCN). How to effectively leverage the rich structural information in complex graphs, such as knowledge graphs with heterogeneous types of entities and relations, is a primary open challenge in the field. Most GCN methods are either restricted to graphs with a homogeneous type of edges (e.g., citation links only), or focusing on representation learning for nodes only instead of jointly propagating and updating the embeddings of both nodes and edges for target-driven objectives. This paper addresses these limitations by proposing a novel framework, namely the Knowledge Embedding based Graph Convolutional Network (KE-GCN), which combines the power of GCNs in graph-based belief propagation and the strengths of advanced knowledge embedding (a.k.a. knowledge graph embedding) methods, and goes beyond. Our theoretical analysis shows that KE-GCN offers an elegant unification of several well-known GCN methods as specific cases, with a new perspective of graph convolution. Experimental results on benchmark datasets show the advantageous performance of KE-GCN over strong baseline methods in the tasks of knowledge graph alignment and entity classification.
Adversarial attack is a technique for deceiving Machine Learning (ML) models, which provides a way to evaluate the adversarial robustness. In practice, attack algorithms are artificially selected and tuned by human experts to break a ML system. However, manual selection of attackers tends to be sub-optimal, leading to a mistakenly assessment of model security. In this paper, a new procedure called Composite Adversarial Attack (CAA) is proposed for automatically searching the best combination of attack algorithms and their hyper-parameters from a candidate pool of \textbf{32 base attackers}. We design a search space where attack policy is represented as an attacking sequence, i.e., the output of the previous attacker is used as the initialization input for successors. Multi-objective NSGA-II genetic algorithm is adopted for finding the strongest attack policy with minimum complexity. The experimental result shows CAA beats 10 top attackers on 11 diverse defenses with less elapsed time (\textbf{6 $\times$ faster than AutoAttack}), and achieves the new state-of-the-art on $l_{\infty}$, $l_{2}$ and unrestricted adversarial attacks.
In this paper, we propose Latent Relation Language Models (LRLMs), a class of language models that parameterizes the joint distribution over the words in a document and the entities that occur therein via knowledge graph relations. This model has a number of attractive properties: it not only improves language modeling performance, but is also able to annotate the posterior probability of entity spans for a given text through relations. Experiments demonstrate empirical improvements over both a word-based baseline language model and a previous approach that incorporates knowledge graph information. Qualitative analysis further demonstrates the proposed model's ability to learn to predict appropriate relations in context.