Learning useful representations is a key ingredient to the success of modern machine learning. Currently, representation learning mostly relies on embedding data into Euclidean space. However, recent work has shown that data in some domains is better modeled by non-euclidean metric spaces, and inappropriate geometry can result in inferior performance. In this paper, we aim to eliminate the inductive bias imposed by the embedding space geometry. Namely, we propose to map data into more general non-vector metric spaces: a weighted graph with a shortest path distance. By design, such graphs can model arbitrary geometry with a proper configuration of edges and weights. Our main contribution is PRODIGE: a method that learns a weighted graph representation of data end-to-end by gradient descent. Greater generality and fewer model assumptions make PRODIGE more powerful than existing embedding-based approaches. We confirm the superiority of our method via extensive experiments on a wide range of tasks, including classification, compression, and collaborative filtering.

Pre-trained language models have been successful on text classification tasks, but are prone to learning spurious correlations from biased datasets, and are thus vulnerable when making inferences in a new domain. Prior work reveals such spurious patterns via post-hoc explanation algorithms which compute the importance of input features. Further, the model is regularized to align the importance scores with human knowledge, so that the unintended model behaviors are eliminated. However, such a regularization technique lacks flexibility and coverage, since only importance scores towards a pre-defined list of features are adjusted, while more complex human knowledge such as feature interaction and pattern generalization can hardly be incorporated. In this work, we propose to refine a learned language model for a target domain by collecting human-provided compositional explanations regarding observed biases. By parsing these explanations into executable logic rules, the human-specified refinement advice from a small set of explanations can be generalized to more training examples. We additionally introduce a regularization term allowing adjustments for both importance and interaction of features to better rectify model behavior. We demonstrate the effectiveness of the proposed approach on two text classification tasks by showing improved performance in target domain as well as improved model fairness after refinement.

We establish closed-form enumeration formulas for chromatic feature vectors of 2-trees under the bichromatic triangle constraint. These efficiently computable structural features derive from constrained graph colorings where each triangle uses exactly two colors, forbidding monochromatic and rainbow triangles, a constraint arising in distributed systems where components avoid complete concentration or isolation. For theta graphs Theta_n, we prove r_k(Theta_n) = S(n-2, k-1) for k >= 3 (Stirling numbers of the second kind) and r_2(Theta_n) = 2^(n-2) + 1, computable in O(n) time. For fan graphs Phi_n, we establish r_2(Phi_n) = F_{n+1} (Fibonacci numbers) and derive explicit formulas r_k(Phi_n) = sum_{t=k-1}^{n-1} a_{n-1,t} * S(t, k-1) with efficiently computable binomial coefficients, achieving O(n^2) computation per component. Unlike classical chromatic polynomials, which assign identical features to all n-vertex 2-trees, bichromatic constraints provide informative structural features. While not complete graph invariants, these features capture meaningful structural properties through connections to Fibonacci polynomials, Bell numbers, and independent set enumeration. Applications include Byzantine fault tolerance in hierarchical networks, VM allocation in cloud computing, and secret-sharing protocols in distributed cryptography.

Human-annotated datasets with explicit difficulty ratings are essential in intelligent educational systems. Although embedding vector spaces are widely used to represent semantic closeness and are promising for analyzing text difficulty, the abundance of embedding methods creates a challenge in selecting the most suitable method. This study proposes the Educational Cone Model, which is a geometric framework based on the assumption that easier texts are less diverse (focusing on fundamental concepts), whereas harder texts are more diverse. This assumption leads to a cone-shaped distribution in the embedding space regardless of the embedding method used. The model frames the evaluation of embeddings as an optimization problem with the aim of detecting structured difficulty-based patterns. By designing specific loss functions, efficient closed-form solutions are derived that avoid costly computation. Empirical tests on real-world datasets validated the model's effectiveness and speed in identifying the embedding spaces that are best aligned with difficulty-annotated educational texts.

We study the multi-objective linear contextual bandit problem, where multiple possible conflicting objectives must be optimized simultaneously. We propose \texttt{MOL-TS}, the \textit{first} Thompson Sampling algorithm with Pareto regret guarantees for this problem. Unlike standard approaches that compute an empirical Pareto front each round, \texttt{MOL-TS} samples parameters across objectives and efficiently selects an arm from a novel \emph{effective Pareto front}, which accounts for repeated selections over time. Our analysis shows that \texttt{MOL-TS} achieves a worst-case Pareto regret bound of $\widetilde{O}(d^{3/2}\sqrt{T})$, where $d$ is the dimension of the feature vectors, $T$ is the total number of rounds, matching the best known order for randomized linear bandit algorithms for single objective. Empirical results confirm the benefits of our proposed approach, demonstrating improved regret minimization and strong multi-objective performance.

Sheaf Neural Networks equip graph structures with a cellular sheaf: a geometric structure which assigns local vector spaces (stalks) and a linear learnable restriction/transport maps to nodes and edges, yielding an edge-aware inductive bias that handles heterophily and limits oversmoothing. However, common Neural Sheaf Diffusion implementations rely on SVD-based sheaf normalization and dense per-edge restriction maps, which scale with stalk dimension, require frequent Laplacian rebuilds, and yield brittle gradients. To address these limitations, we introduce Polynomial Neural Sheaf Diffusion (PolyNSD), a new sheaf diffusion approach whose propagation operator is a degree-K polynomial in a normalised sheaf Laplacian, evaluated via a stable three-term recurrence on a spectrally rescaled operator. This provides an explicit K-hop receptive field in a single layer (independently of the stalk dimension), with a trainable spectral response obtained as a convex mixture of K+1 orthogonal polynomial basis responses. PolyNSD enforces stability via convex mixtures, spectral rescaling, and residual/gated paths, reaching new state-of-the-art results on both homophilic and heterophilic benchmarks, inverting the Neural Sheaf Diffusion trend by obtaining these results with just diagonal restriction maps, decoupling performance from large stalk dimension, while reducing runtime and memory requirements.

Neural Information Processing Systems http://nips.cc/

We investigate an unsupervised generative approach for network embedding.

Neural Information Processing Systems http://nips.cc/

Because cardinality is a simple property of any set, we argue that such bounds do not fully capture the rich structure endowed by the metric.