Computer networks are the foundation of modern digital infrastructure, facilitating global communication and data exchange. As demand for reliable high-bandwidth connectivity grows, advanced network modeling techniques become increasingly essential to optimize performance and predict network behavior. Traditional modeling methods, such as packet-level simulators and queueing theory, have notable limitations --either being computationally expensive or relying on restrictive assumptions that reduce accuracy. In this context, the deep learning-based RouteNet family of models has recently redefined network modeling by showing an unprecedented cost-performance trade-off. In this work, we revisit RouteNet's sophisticated design and uncover its hidden connection to Topological Deep Learning (TDL), an emerging field that models higher-order interactions beyond standard graph-based methods. We demonstrate that, although originally formulated as a heterogeneous Graph Neural Network, RouteNet serves as the first instantiation of a new form of TDL. More specifically, this paper presents OrdGCCN, a novel TDL framework that introduces the notion of ordered neighbors in arbitrary discrete topological spaces, and shows that RouteNet's architecture can be naturally described as an ordered topological neural network. To the best of our knowledge, this marks the first successful real-world application of state-of-the-art TDL principles --which we confirm through extensive testbed experiments--, laying the foundation for the next generation of ordered TDL-driven applications.

We examine an adaptive learning framework for nonatomic congestion games where the players' cost functions may be subject to exogenous fluctuations (e.g., due to disturbances in the network, variations in the traffic going through a link, etc.). In this setting, the popular multiplicative / exponential weights algorithm enjoys an O(1/ T) equilibrium convergence rate; however, this rate is suboptimal in static environments - i.e., when the network is not subject to randomness.

Graph Convolutional Networks (GCNs), aiming to obtain the representation of a node by aggregating its neighbors, have demonstrated great power in tackling various analytics tasks on graph (network) data. The remarkable performance of GCNs typically relies on the homophily assumption of networks, while such assumption cannot always be satisfied, since the heterophily or randomness are also widespread in real-world. This gives rise to one fundamental question: whether networks with different structural properties should adopt different propagation mechanisms?

Cryo-Electron Microscopy (Cryo-EM) is an important imaging method which allows high-resolution reconstruction of the 3D structures of biomolecules. It produces highly noisy 2D images by projecting a molecule's 3D density from random viewing directions. Because the projection directions are unknown, estimating the images' poses is necessary to perform the reconstruction. We focus on this task and study it under the group synchronization framework: if the relative poses of pairs of images can be approximated from the data, an estimation of the images' poses is given by the assignment which is most consistent with the relative ones. In particular, by studying the symmetries of cryo-EM, we show that relative poses in the group O(2) provide sufficient constraints to identify the images' poses, up to the molecule's chirality. With this in mind, we improve the existing multi-frequency vector diffusion maps (MFVDM) method: by using O(2) relative poses, our method not only predicts the similarity between the images' viewing directions but also recovers their poses. Hence, we can leverage all input images in a 3D reconstruction algorithm by initializing the poses with our estimation rather than just clustering and averaging the input images. We validate the recovery capabilities and robustness of our method on randomly generated synchronization graphs and a synthetic cryo-EM dataset.

While Distributed Machine Learning (DML) has been widely used to achieve decent performance, it is still challenging to take full advantage of data and devices distributed at multiple vantage points to adapt and learn; this is because the current linear aggregation paradigm cannot solve inter-model divergence caused by (1) heterogeneous learning data at different devices (i.e., non-IID data) and (2) in the case of time-varying communication links, the limited ability for devices to reconcile model divergence. In this paper, we present a non-linear class aggregation framework HyperPrism that leverages Kolmogorov Means to conduct distributed mirror descent with the averaging occurring within the mirror descent dual space; HyperPrism selects the degree for a Weighted Power Mean (WPM), a subset of the Kolmogorov Means, each round. Moreover, HyperPrism can adaptively choose different mapping for different layers of the local model with a dedicated hypernetwork per device, achieving automatic optimization of DML in high divergence settings. We perform rigorous analysis and experimental evaluations to demonstrate the effectiveness of adaptive, mirror-mapping DML. In particular, we extend the generalizability of existing related works and position them as special cases within HyperPrism. For practitioners, the strength of HyperPrism is in making feasible the possibility of distributed asynchronous training with minimal communication. Our experimental results show HyperPrism can improve the convergence speed up to 98.63% and scale well to more devices compared with the state-of-the-art, all with little additional computation overhead compared to traditional linear aggregation.

We present a new method for scaling automatic configuration of computer networks. The key idea is to relax the computationally hard search problem of finding a configuration that satisfies a given specification into an approximate objective amenable to learning-based techniques. Based on this idea, we train a neural algorithmic model which learns to generate configurations likely to (fully or partially) satisfy a given specification under existing routing protocols. By relaxing the rigid satisfaction guarantees, our approach (i) enables greater flexibility: it is protocol-agnostic, enables cross-protocol reasoning, and does not depend on hardcoded rules; and (ii) finds configurations for much larger computer networks than previously possible. Our learned synthesizer is up to 490 faster than state-of-the-art SMT-based methods, while producing configurations which on average satisfy more than 92% of the provided requirements.

Large Language models have demonstrated excellent domain-specific question-answering capabilities when finetuned with a particular dataset of that specific domain. However, fine-tuning the models requires a significant amount of training time and a considerable amount of hardware. In this work, we propose CARE (Customer Assistance and Response Engine), a lightweight model made by fine-tuning Phi3.5-mini on very minimal hardware and data, designed to handle queries primarily across three domains: telecommunications support, medical support, and banking support. For telecommunications and banking, the chatbot addresses issues and problems faced by customers regularly in the above-mentioned domains. In the medical domain, CARE provides preliminary support by offering basic diagnoses and medical suggestions that a user might take before consulting a healthcare professional. Since CARE is built on Phi3.5-mini, it can be used even on mobile devices, increasing its usability. Our research also shows that CARE performs relatively well on various medical benchmarks, indicating that it can be used to make basic medical suggestions.