Fixed-Point Reasoners: Stable and Adaptive Deep Looped Transformers

Looped architectures provide an inductive bias toward learning step-by-step procedures for tasks that require compositional reasoning. The number of effective layers reached by looping determines the quality of the solution these models find. Like deep architectures, looped architectures are prone to a signal propagation problem induced by depth as the halting decision is postponed. In this paper, we address this signal propagation issue using pre-norm layers and residual scaling. Building on these architectural modifications, we propose FPRM, a Transformer-based Fixed-Point Reasoning Model that uses fixed-point convergence as an end-to-end halting mechanism in a looped architecture. We show that fixed-point halting allows FPRM to adapt its compute to task difficulty. FPRM is effective on common reasoning benchmarks, namely Sudoku, Maze, state-tracking, and ARC-AGI.

How does the optimizer implicitly bias the model merging loss landscape?

Model merging methods combine models with different capabilities into a single one while maintaining the same inference cost. Two popular approaches are linear interpolation, which linearly interpolates between model weights, and task arithmetic, which combines task vectors obtained by the difference between finetuned and base models. While useful in practice, what properties make merging effective are poorly understood. This paper explores how the optimization process affects the loss landscape geometry and its impact on merging success. We show that a single quantity -- the effective noise scale -- unifies the impact of optimizer and data choices on model merging. Across architectures and datasets, the effectiveness of merging success is a non-monotonic function of effective noise, with a distinct optimum. Decomposing this quantity, we find that larger learning rates, stronger weight decay, smaller batch sizes, and data augmentation all independently modulate the effective noise scale, exhibiting the same qualitative trend. Unlike prior work that connects optimizer noise to the flatness or generalization of individual minima, we show that it also affects the global loss landscape, predicting when independently trained solutions can be merged. Our findings broaden the understanding of how optimization shapes the loss landscape geometry and its downstream consequences for model merging, suggesting the possibility of further manipulating the training dynamics to improve merging effectiveness.

Towards Meta-Pruning via Optimal Transport

Structural pruning of neural networks conventionally relies on identifying and discarding less important neurons, a practice often resulting in significant accuracy loss that necessitates subsequent fine-tuning efforts. This paper introduces a novel approach named Intra-Fusion, challenging this prevailing pruning paradigm. Unlike existing methods that focus on designing meaningful neuron importance metrics, Intra-Fusion redefines the overlying pruning procedure. Through utilizing the concepts of model fusion and Optimal Transport, we leverage an agnostically given importance metric to arrive at a more effective sparse model representation. Notably, our approach achieves substantial accuracy recovery without the need for resource-intensive fine-tuning, making it an efficient and promising tool for neural network compression. Additionally, we explore how fusion can be added to the pruning process to significantly decrease the training time while maintaining competitive performance. We benchmark our results for various networks on commonly used datasets such as CIFAR-10, CIFAR-100, and ImageNet. More broadly, we hope that the proposed Intra-Fusion approach invigorates exploration into a fresh alternative to the predominant compression approaches. Our code is available here: https://github.com/alexandertheus/Intra-Fusion.