AlphaGrad: Non-Linear Gradient Normalization Optimizer

We introduce AlphaGrad, a memory-efficient, conditionally stateless optimizer addressing the memory overhead and hyperparameter complexity of adaptive methods like Adam. AlphaGrad enforces scale invariance via tensor-wise L2 gradient normalization followed by a smooth hyperbolic tangent transformation, $g' = \tanh(\alpha \cdot \tilde{g})$, controlled by a single steepness parameter $\alpha$. Our contributions include: (1) the AlphaGrad algorithm formulation; (2) a formal non-convex convergence analysis guaranteeing stationarity; (3) extensive empirical evaluation on diverse RL benchmarks (DQN, TD3, PPO). Compared to Adam, AlphaGrad demonstrates a highly context-dependent performance profile. While exhibiting instability in off-policy DQN, it provides enhanced training stability with competitive results in TD3 (requiring careful $\alpha$ tuning) and achieves substantially superior performance in on-policy PPO. These results underscore the critical importance of empirical $\alpha$ selection, revealing strong interactions between the optimizer's dynamics and the underlying RL algorithm. AlphaGrad presents a compelling alternative optimizer for memory-constrained scenarios and shows significant promise for on-policy learning regimes where its stability and efficiency advantages can be particularly impactful.

Optimal Scaling Laws for Efficiency Gains in a Theoretical Transformer-Augmented Sectional MoE Framework

This paper introduces a theoretical framework for a Transformer-augmented, sectional Mixture-of-Experts (MoE) architecture that aims to enhance computational efficiency while preserving model scalability. Unlike conventional MoE models, which route entire token embeddings to selected experts, our approach portions the embedding dimension itself -- assigning segments of each token's representation to dedicated experts. To combat losses in token representation, we utilize a pre-expert transformer layer to recompute attention across tokens and reduce the sequence length dimensionality. We extend our theory by deriving optimal scaling laws that a non-linear relationship between the number of experts and factors such as model dimensionality, sequence length, and system overhead. These formulations yield closed-form and numerically-solvable expressions for identifying the optimal expert count under given architectural and hardware constraints. As a result, our framework not only provides theoretical bounds for computing efficiency with varying frameworks but also guides practical design choices for scaling large models effectively. While empirical validation is pending, we present a comprehensive experimental road map to evaluate the framework's efficiency, scalability, and practicality in future work.

A NotSo Simple Way to Beat Simple Bench

This paper presents a novel framework for enhancing reasoning capabilities in large language models (LLMs) by leveraging iterative reasoning and feedback-driven methodologies. Building on the limitations identified in the SimpleBench benchmark, a dataset designed to evaluate logical coherence and real-world reasoning, we propose a multi-step prompting strategy coupled with global consistency checks to improve model accuracy and robustness. Through comparative analysis of state-of-the-art models, including Claude 3 Opus, Claude 3.5, GPT- 4o, and o1-preview, we demonstrate that iterative reasoning significantly enhances model performance, with improvements observed in both standard accuracy metrics (AVG@5) and a newly introduced metric, Extreme Averaging (EAG@5). Our results reveal model-specific strengths: Claude excels in maintaining logical consistency, while GPT-4o exhibits exploratory creativity but struggles with ambiguous prompts. By analyzing case studies and identifying gaps in spatial and temporal reasoning, we highlight areas for further refinement. The findings underscore the potential of structured reasoning frameworks to address inherent model limitations, irrespective of pretraining methodologies. This study lays the groundwork for integrating dynamic feedback mechanisms, adaptive restart strategies, and diverse evaluation metrics to advance LLM reasoning capabilities across complex and multi-domain problem spaces.