Ordinary Differential Equations (ODEs) are widely used in physics, chemistry, and biology to model dynamic systems, including reaction kinetics, population dynamics, and biological processes. In this work, we integrate GPU-accelerated ODE solvers into the open-source DeepChem framework, making these tools easily accessible. These solvers support multiple numerical methods and are fully differentiable, enabling easy integration into more complex differentiable programs. We demonstrate the capabilities of our implementation through experiments on Lotka-Volterra predator-prey dynamics, pharmacokinetic compartment models, neural ODEs, and solving PDEs using reaction-diffusion equations. Our solvers achieved high accuracy with mean squared errors ranging from $10^{-4}$ to $10^{-6}$ and showed scalability in solving large systems with up to 100 compartments.

In both 2016 and 2018, a census of the highly-endangered Grevy's zebra population was enabled by the Great Grevy's Rally (GGR), a citizen science event that produces population estimates via expert and algorithmic curation of volunteer-captured images. A complementary, scalable, and long-term Grevy's population monitoring approach involves deploying camera trap networks. However, in both scenarios, a substantial majority of zebra images are not usable for individual identification due to poor in-the-wild imaging conditions; camera trap images in particular present high rates of occlusion and high spatio-temporal similarity within image bursts. Our proposed filtering pipeline incorporates animal detection, species identification, viewpoint estimation, quality evaluation, and temporal subsampling to obtain individual crops suitable for re-ID, which are subsequently curated by the LCA decision management algorithm. Our method processed images taken during GGR-16 and GGR-18 in Meru County, Kenya, into 4,142 highly-comparable annotations, requiring only 120 contrastive human decisions to produce a population estimate within 4.6% of the ground-truth count. Our method also efficiently processed 8.9M unlabeled camera trap images from 70 cameras at the Mpala Research Centre in Laikipia County, Kenya over two years into 685 encounters of 173 individuals, requiring only 331 contrastive human decisions.

Link prediction is a fundamental problem in graph data. In its most realistic setting, the problem consists of predicting missing or future links between random pairs of nodes from the set of disconnected pairs. Graph Neural Networks (GNNs) have become the predominant framework for link prediction. GNN-based methods treat link prediction as a binary classification problem and handle the extreme class imbalance -- real graphs are very sparse -- by sampling (uniformly at random) a balanced number of disconnected pairs not only for training but also for evaluation. However, we show that the reported performance of GNNs for link prediction in the balanced setting does not translate to the more realistic imbalanced setting and that simpler topology-based approaches are often better at handling sparsity. These findings motivate Gelato, a similarity-based link-prediction method that applies (1) graph learning based on node attributes to enhance a topological heuristic, (2) a ranking loss for addressing class imbalance, and (3) a negative sampling scheme that efficiently selects hard training pairs via graph partitioning. Experiments show that Gelato outperforms existing GNN-based alternatives.

We propose a novel framework to remove transient objects from input videos for 3D scene reconstruction using Gaussian Splatting. Our framework consists of the following steps. In the first step, we propose an unsupervised training strategy for a classification network to distinguish between transient objects and static scene parts based on their different training behavior inside the 3D Gaussian Splatting reconstruction. In the second step, we improve the boundary quality and stability of the detected transients by combining our results from the first step with an off-the-shelf segmentation method. We also propose a simple and effective strategy to track objects in the input video forward and backward in time. Our results show an improvement over the current state of the art in existing sparsely captured datasets and significant improvements in a newly proposed densely captured (video) dataset. More results and code are available at https://transient-3dgs.github.io.

We propose three completely data-driven methods for estimating the real cohomology groups $H^k (X ; \mathbb{R})$ of a compact metric-measure space $(X, d_X, \mu_X)$ embedded in a metric-measure space $(Y,d_Y,\mu_Y)$, given a finite set of points $S$ sampled from a uniform distrbution $\mu_X$ on $X$, possibly corrupted with noise from $Y$. We present the results of several computational experiments in the case that $X$ is embedded in $\mathbb{R}^n$, where two of the three algorithms performed well.

Gaussian splatting enables fast novel view synthesis in static 3D environments. However, reconstructing real-world environments remains challenging as distractors or occluders break the multi-view consistency assumption required for accurate 3D reconstruction. Most existing methods rely on external semantic information from pre-trained models, introducing additional computational overhead as pre-processing steps or during optimization. In this work, we propose a novel method, DeSplat, that directly separates distractors and static scene elements purely based on volume rendering of Gaussian primitives. We initialize Gaussians within each camera view for reconstructing the view-specific distractors to separately model the static 3D scene and distractors in the alpha compositing stages. DeSplat yields an explicit scene separation of static elements and distractors, achieving comparable results to prior distractor-free approaches without sacrificing rendering speed. We demonstrate DeSplat's effectiveness on three benchmark data sets for distractor-free novel view synthesis. See the project website at https://aaltoml.github.io/desplat/.

Injecting semantics into 3D Gaussian Splatting (3DGS) has recently garnered significant attention. While current approaches typically distill 3D semantic features from 2D foundational models (e.g., CLIP and SAM) to facilitate novel view segmentation and semantic understanding, their heavy reliance on 2D supervision can undermine cross-view semantic consistency and necessitate complex data preparation processes, therefore hindering view-consistent scene understanding. In this work, we present FreeGS, an unsupervised semantic-embedded 3DGS framework that achieves view-consistent 3D scene understanding without the need for 2D labels. Instead of directly learning semantic features, we introduce the IDentity-coupled Semantic Field (IDSF) into 3DGS, which captures both semantic representations and view-consistent instance indices for each Gaussian. We optimize IDSF with a two-step alternating strategy: semantics help to extract coherent instances in 3D space, while the resulting instances regularize the injection of stable semantics from 2D space. Additionally, we adopt a 2D-3D joint contrastive loss to enhance the complementarity between view-consistent 3D geometry and rich semantics during the bootstrapping process, enabling FreeGS to uniformly perform tasks such as novel-view semantic segmentation, object selection, and 3D object detection. Extensive experiments on LERF-Mask, 3D-OVS, and ScanNet datasets demonstrate that FreeGS performs comparably to state-of-the-art methods while avoiding the complex data preprocessing workload.

Due to network operation and maintenance relying heavily on network traffic monitoring, traffic matrix analysis has been one of the most crucial issues for network management related tasks. However, it is challenging to reliably obtain the precise measurement in computer networks because of the high measurement cost, and the unavoidable transmission loss. Although some methods proposed in recent years allowed estimating network traffic from partial flow-level or link-level measurements, they often perform poorly for traffic matrix estimation nowadays. Despite strong assumptions like low-rank structure and the prior distribution, existing techniques are usually task-specific and tend to be significantly worse as modern network communication is extremely complicated and dynamic. To address the dilemma, this paper proposed a diffusion-based traffic matrix analysis framework named Diffusion-TM, which leverages problem-agnostic diffusion to notably elevate the estimation performance in both traffic distribution and accuracy. The novel framework not only takes advantage of the powerful generative ability of diffusion models to produce realistic network traffic, but also leverages the denoising process to unbiasedly estimate all end-to-end traffic in a plug-and-play manner under theoretical guarantee. Moreover, taking into account that compiling an intact traffic dataset is usually infeasible, we also propose a two-stage training scheme to make our framework be insensitive to missing values in the dataset. With extensive experiments with real-world datasets, we illustrate the effectiveness of Diffusion-TM on several tasks. Moreover, the results also demonstrate that our method can obtain promising results even with $5\%$ known values left in the datasets.

We propose a pair of completely data-driven algorithms for unsupervised classification and dimension reduction, and we empirically study their performance on a number of data sets, both simulated data in three-dimensions and images from the COIL-20 data set. The algorithms take as input a set of points sampled from a uniform distribution supported on a metric space, the latter embedded in an ambient metric space, and they output a clustering or reduction of dimension of the data. They work by constructing a natural family of graphs from the data and selecting the graph which maximizes the relative von Neumann entropy of certain normalized heat operators constructed from the graphs. Once the appropriate graph is selected, the eigenvectors of the graph Laplacian may be used to reduce the dimension of the data, and clusters in the data may be identified with the kernel of the associated graph Laplacian. Notably, these algorithms do not require information about the size of a neighborhood or the desired number of clusters as input, in contrast to popular algorithms such as $k$-means, and even more modern spectral methods such as Laplacian eigenmaps, among others. In our computational experiments, our clustering algorithm outperforms $k$-means clustering on data sets with non-trivial geometry and topology, in particular data whose clusters are not concentrated around a specific point, and our dimension reduction algorithm is shown to work well in several simple examples.

Over the past few years, the federated learning ($\texttt{FL}$) community has witnessed a proliferation of new $\texttt{FL}$ algorithms. However, our understating of the theory of $\texttt{FL}$ is still fragmented, and a thorough, formal comparison of these algorithms remains elusive. Motivated by this gap, we show that many of the existing $\texttt{FL}$ algorithms can be understood from an operator splitting point of view. This unification allows us to compare different algorithms with ease, to refine previous convergence results and to uncover new algorithmic variants. In particular, our analysis reveals the vital role played by the step size in $\texttt{FL}$ algorithms. The unification also leads to a streamlined and economic way to accelerate $\texttt{FL}$ algorithms, without incurring any communication overhead. We perform numerical experiments on both convex and nonconvex models to validate our findings.