Deep neural networks often inherit social and demographic biases from annotated data during model training, leading to unfair predictions, especially in the presence of sensitive attributes like race, age, gender etc. Existing methods fall prey to the inherent data imbalance between attribute groups and inadvertently emphasize on sensitive attributes, worsening unfairness and performance. To surmount these challenges, we propose SHaSaM (Submodular Hard Sample Mining), a novel combinatorial approach that models fairness-driven representation learning as a submodular hard-sample mining problem. Our two-stage approach comprises of SHaSaM-MINE, which introduces a submodular subset selection strategy to mine hard positives and negatives — effectively mitigating data imbalance, and SHaSaM-LEARN, which introduces a family of combinatorial loss functions based on Submodular Conditional Mutual Information to maximize the decision boundary between target classes while minimizing the influence of sensitive attributes. This unified formulation restricts the model from learning features tied to sensitive attributes, significantly enhancing fairness without sacrificing performance. Experiments on CelebA and UTKFace demonstrate that SHaSaM achieves state-of-the-art results, with up to 2.7 points improvement in model fairness (Equalized Odds) and a 3.5% gain in Accuracy, within fewer epochs as compared to existing methods.

Handling heterogeneous data in tabular datasets poses a significant challenge for deep learning models. While attention-based architectures and self-supervised learning have achieved notable success, their application to tabular data remains less effective over linear and tree based models. Although several breakthroughs have been achieved by models which transform tables into uni-modal transformations like image, language and graph, these models often underperform in the presence of feature heterogeneity. To address this gap, we introduce TabGLM (Tabular Graph Language Model), a novel multi-modal architecture designed to model both structural and semantic information from a table. TabGLM transforms each row of a table into a fully connected graph and serialized text, which are then encoded using a graph neural network (GNN) and a text encoder, respectively. By aligning these representations through a joint, multi-modal, self-supervised learning objective, TabGLM leverages complementary information from both modalities, thereby enhancing feature learning. TabGLM's flexible graph-text pipeline efficiently processes heterogeneous datasets with significantly fewer parameters over existing Deep Learning approaches. Evaluations across 25 benchmark datasets demonstrate substantial performance gains, with TabGLM achieving an average AUC-ROC improvement of up to 5.56% over State-of-the-Art (SoTA) tabular learning methods.

In this paper, we introduce, InSQuaD, designed to enhance the performance of In-Context Learning (ICL) models through Submodular Mutual Information (SMI) enforcing Quality and Diversity among in-context exemplars. InSQuaD achieves this through two principal strategies: First, we model the ICL task as a targeted selection problem and introduce a unified selection strategy based on SMIs which mines relevant yet diverse in-context examples encapsulating the notions of quality and diversity. Secondly, we address a common pitfall in existing retrieval models which model query relevance, often overlooking diversity, critical for ICL. InSQuaD introduces a combinatorial training paradigm which learns the parameters of an SMI function to enforce both quality and diversity in the retrieval model through a novel likelihood-based loss. To further aid the learning process we augment an existing multi-hop question answering dataset with synthetically generated paraphrases. Adopting the retrieval model trained using this strategy alongside the novel targeted selection formulation for ICL on nine benchmark datasets shows significant improvements validating the efficacy of our approach.

Open-World Object Detection (OWOD) enriches traditional object detectors by enabling continual discovery and integration of unknown objects via human guidance. However, existing OWOD approaches frequently suffer from semantic confusion between known and unknown classes, alongside catastrophic forgetting, leading to diminished unknown recall and degraded known-class accuracy. To overcome these challenges, we propose **C**ombinato**r**ial **O**pen-**W**orld **D**etection (**CROWD**), a unified framework reformulating unknown object discovery and adaptation as an interwoven combinatorial (set-based) data-discovery (CROWD-Discover) and representation learning (CROWD-Learn) task. CROWD-Discover strategically mines unknown instances by maximizing Submodular Conditional Gain (SCG) functions, selecting representative examples distinctly dissimilar from known objects. Subsequently, CROWD-Learn employs novel combinatorial objectives that jointly disentangle known and unknown representations while maintaining discriminative coherence among known classes, thus mitigating confusion and forgetting. Extensive evaluations on OWOD benchmarks illustrate that CROWD achieves improvements of 2.83% and 2.05% in known-class accuracy on M-OWODB and S-OWODB, respectively, and nearly 2.4$\times$ unknown recall compared to leading baselines.

In this paper we introduce the **SCoRe** (**S**ubmodular **Co**mbinatorial **Re**presentation Learning) framework, a novel approach in representation learning that addresses inter-class bias and intra-class variance. SCoRe provides a new combinatorial viewpoint to representation learning, by introducing a family of loss functions based on set-based submodular information measures. We develop two novel combinatorial formulations for loss functions, using the *Total Information* and *Total Correlation*, that naturally minimize intra-class variance and inter-class bias. Several commonly used metric/contrastive learning loss functions like supervised contrastive loss, orthogonal projection loss, and N-pairs loss, are all instances of SCoRe, thereby underlining the versatility and applicability of SCoRe in a broad spectrum of learning scenarios. Novel objectives in SCoRe naturally model class-imbalance with up to 7.6% improvement in classification on CIFAR-10-LT, CIFAR-100-LT, MedMNIST, 2.1% on ImageNet-LT, and 19.4% in object detection on IDD and LVIS (v1.0), demonstrating its effectiveness over existing approaches.