Trading Utility for Dynamic Fairness in Multiple Resource Division with Sequential Demand

Dynamic multi-resource allocation is a central problem in shared computing environments, where users' demands arrive sequentially and resources must be distributed fairly without knowledge of future demands. Existing methods emphasize fairness guarantees such as Sharing Incentive, Envy Freeness, and Dynamic Pareto Optimality, but often overlook system utility. Moreover, these fairness criteria are mutually incompatible, preventing strict enforcement of them at the same time. We propose a neural allocation mechanism that reconciles fairness with utility through multi-objective optimization during sequential rollout. We first formalize fairness in the dynamic setting via stepwise loss functions for Sharing Incentive, Envy Freeness, and Dynamic Pareto Optimality, enabling differentiable training. Leveraging non-wastefulness, we parameterized the solutions by constraining allocations to the subspace of demand while allowing elastic over-allocation when resources remain available. Empirical results demonstrate that our learned allocator achieves substantially higher utility at comparable levels of fairness, uncovering clear Pareto-frontier-like tradeoffs across metrics.

The Structural Origin of Attention Sink: Variance Discrepancy, Super Neurons, and Dimension Disparity

Despite the prevalence of the attention sink phenomenon in Large Language Models (LLMs), where initial tokens disproportionately monopolize attention scores, its structural origins remain elusive. This work provides a \textit{mechanistic explanation} for this phenomenon. First, we trace its root to the value aggregation process inherent in self-attention, which induces a systematic variance discrepancy. We further demonstrate that this discrepancy is drastically amplified by the activation of super neurons within Feed-Forward Network (FFN) layers. Specifically, the channel-sparse down-projections trigger a dimension disparity of the first-token representation, necessitating the formation of attention sinks as a structural anchor. Then, we validate this causal chain through two controlled interventions: (i) isolating the aggregation effect via attention mask modifications and (ii) amplifying the variance of targeted token representations. Both interventions can replicate attention sinks at arbitrary positions. Our mechanistic understanding offers a foundation for the systematic control of sink formation. Finally, as a proof of concept, we propose \textit{head-wise RMSNorm}, an architectural modification that stabilizes value aggregation outputs during pre-training. Our experiments demonstrate that restoring statistical parity across positions significantly accelerates convergence.

Fairness Risks for Group-conditionally Missing Demographics

Fairness-aware classification models have gained increasing attention in recent years as concerns grow on discrimination against some demographic groups. Most existing models require full knowledge of the sensitive features, which can be impractical due to privacy, legal issues, and an individual's fear of discrimination. The key challenge we will address is the group dependency of the unavailability, e.g., people of some age range may be more reluctant to reveal their age. Our solution augments general fairness risks with probabilistic imputations of the sensitive features, while jointly learning the group-conditionally missing probabilities in a variational auto-encoder. Our model is demonstrated effective on both image and tabular datasets, achieving an improved balance between accuracy and fairness.

How Does Adaptive Optimization Impact Local Neural Network Geometry?

Adaptive optimization methods are well known to achieve superior convergence relative to vanilla gradient methods. The traditional viewpoint in optimization, particularly in convex optimization, explains this improved performance by arguing that, unlike vanilla gradient schemes, adaptive algorithms mimic the behavior of a second-order method by adapting to the global geometry of the loss function. We argue that in the context of neural network optimization, this traditional viewpoint is insufficient. Instead, we advocate for a local trajectory analysis. For iterate trajectories produced by running a generic optimization algorithm OPT, we introduce $R^{\text{OPT}}_{\text{med}}$, a statistic that is analogous to the condition number of the loss Hessian evaluated at the iterates. Through extensive experiments, we show that adaptive methods such as Adam bias the trajectories towards regions where $R^{\text{Adam}}_{\text{med}}$ is small, where one might expect faster convergence. By contrast, vanilla gradient methods like SGD bias the trajectories towards regions where $R^{\text{SGD}}_{\text{med}}$ is comparatively large. We complement these empirical observations with a theoretical result that provably demonstrates this phenomenon in the simplified setting of a two-layer linear network. We view our findings as evidence for the need of a new explanation of the success of adaptive methods, one that is different than the conventional wisdom.