Laziz U. Abdullaev

Laziz U. Abdullaev, Noelle Y. L. Wong, Ryan T. Z. Lee et al.

Representation steering offers a lightweight mechanism for controlling the behavior of large language models (LLMs) by intervening on internal activations at inference time. Most existing methods rely on a single global steering direction, typically obtained via difference-in-means over contrastive datasets. This approach implicitly assumes that the target concept is homogeneously represented across the embedding space. In practice, however, LLM representations can be highly non-homogeneous, exhibiting clustered, context-dependent structure, which renders global steering directions brittle. In this work, we view representation steering through the lens of optimal transport (OT), noting that standard difference-in-means steering implicitly corresponds to the OT map between two unimodal Gaussian distributions with identical covariance, yielding a global translation. To relax this restrictive assumption, we theoretically model source and target representations as Gaussian mixture models and formulate steering as a discrete OT problem between semantic latent clusters. From the resulting transport plan, we derive an explicit, input-dependent steering map via barycentric projection, producing a smooth, kernel-weighted combination of cluster-level shifts. We term this method Concept Heterogeneity-aware Representation Steering (CHaRS). Through numerous experimental settings, we show that CHaRS yields more effective behavioral control than global steering.

Stefan K. Nielsen, Rachel S. Y. Teo, Laziz U. Abdullaev et al.

Sparse Mixture-of-Experts (MoE) architectures have emerged as a promising approach to decoupling model capacity from computational cost. At the core of the MoE model is the router, which learns the underlying clustering structure of the input distribution in order to send input tokens to appropriate experts. However, latent clusters may be unidentifiable in high dimension, which causes slow convergence, susceptibility to data contamination, and overall degraded representations as the router is unable to perform appropriate token-expert matching. We examine the router through the lens of clustering optimization and derive optimal feature weights that maximally identify the latent clusters. We use these weights to compute the token-expert routing assignments in an adaptively transformed space that promotes well-separated clusters, which helps identify the best-matched expert for each token. In particular, for each expert cluster, we compute a set of weights that scales features according to whether that expert clusters tightly along that feature. We term this novel router the Adaptive Clustering (AC) router. Our AC router enables the MoE model to obtain three connected benefits: 1) faster convergence, 2) better robustness to data corruption, and 3) overall performance improvement, as experts are specialized in semantically distinct regions of the input space. We empirically demonstrate the advantages of our AC router over baseline routing methods when applied on a variety of MoE backbones for language modeling and image recognition tasks in both clean and corrupted settings.

Minh-Khoi Nguyen-Nhat, Rachel S. Y. Teo, Laziz Abdullaev et al.

Sparse Mixture of Experts (SMoE) has emerged as a promising solution to achieving unparalleled scalability in deep learning by decoupling model parameter count from computational cost. By activating only a small subset of parameters per sample, SMoE enables significant growth in model capacity while maintaining efficiency. However, SMoE struggles to adapt to distributional shifts, leading to reduced robustness under data contamination. In this work, we introduce SymphonySMoE, a novel family of SMoE that introduces a social graph to model interactions among experts. This graph-based structure enhances the token routing process, addressing the robustness challenges that are inherent in conventional SMoE designs. SymphonySMoE is lightweight, modular, and integrates seamlessly with existing SMoE-based models such as the XMoE and the Generalist Language Model. We provide both theoretical analysis and empirical evidence demonstrating SymphonySMoE's advantages over baseline SMoE. Extensive experiments on language modeling and visual instruction tuning validate our method's effectiveness. We further highlight the scalability of SymphonySMoE to models with 4.2 and 7.4 billion parameters, showcasing its applicability in fine-tuning tasks for large-scale systems.

Laziz U. Abdullaev, Maksim Tkachenko, Tan M. Nguyen

The self-attention mechanism, a cornerstone of Transformer-based state-of-the-art deep learning architectures, is largely heuristic-driven and fundamentally challenging to interpret. Establishing a robust theoretical foundation to explain its remarkable success and limitations has therefore become an increasingly prominent focus in recent research. Some notable directions have explored understanding self-attention through the lens of image denoising and nonparametric regression. While promising, existing frameworks still lack a deeper mechanistic interpretation of various architectural components that enhance self-attention, both in its original formulation and subsequent variants. In this work, we aim to advance this understanding by developing a unifying image processing framework, capable of explaining not only the self-attention computation itself but also the role of components such as positional encoding and residual connections, including numerous later variants. We also pinpoint potential distinctions between the two concepts building upon our framework, and make effort to close this gap. We introduce two independent architectural modifications within transformers. While our primary objective is interpretability, we empirically observe that image processing-inspired modifications can also lead to notably improved accuracy and robustness against data contamination and adversaries across language and vision tasks as well as better long sequence understanding.

Stefan K. Nielsen, Laziz U. Abdullaev, Rachel S. Y. Teo et al.

Pairwise dot-product self-attention is key to the success of transformers that achieve state-of-the-art performance across a variety of applications in language and vision. This dot-product self-attention computes attention weights among the input tokens using Euclidean distance, which makes the model prone to representation collapse and vulnerable to contaminated samples. In this paper, we propose using a Mahalanobis distance metric for computing the attention weights to stretch the underlying feature space in directions of high contextual relevance. In particular, we define a hyper-ellipsoidal neighborhood around each query to increase the attention weights of the tokens lying in the contextually important directions. We term this novel class of attention Elliptical Attention. Our Elliptical Attention provides two benefits: 1) reducing representation collapse and 2) enhancing the model's robustness as Elliptical Attention pays more attention to contextually relevant information rather than focusing on some small subset of informative features. We empirically demonstrate the advantages of Elliptical Attention over the baseline dot-product attention and state-of-the-art attention methods on various practical tasks, including object classification, image segmentation, and language modeling across different data modalities.