arXiv:2502.17017v1 Announce Type: cross Abstract: Large language models (LLMs) have demonstrated impressive performance in various natural language processing tasks, yet their ability to perform multi-step logical reasoning remains an open challenge. Although Chain-of-Thought prompting has improved logical reasoning by enabling models to generate intermediate steps, it lacks mechanisms to assess the coherence of these logical transitions. In this paper, we propose a novel, lightweight evaluation strategy for logical reasoning that uses query-key alignments inside transformer attention heads. By computing a single forward pass and extracting a "QK-score" from carefully chosen heads, our method reveals latent representations that reliably separate valid from invalid inferences, offering a scalable alternative to traditional ablation-based techniques. We also provide an empirical validation on multiple logical reasoning benchmarks, demonstrating improved robustness of our evaluation method against distractors and increased reasoning depth. The experiments were conducted on a diverse set of models, ranging from 1.5B to 70B parameters.

arXiv:2012.15834v3 Announce Type: replace-cross Abstract: Neural network training is commonly based on SGD. However, the understanding of SGD's ability to converge to good local minima, given the non-convex nature of loss functions and the intricate geometric characteristics of loss landscapes, remains limited. In this paper, we apply topological data analysis methods to loss landscapes to gain insights into the learning process and generalization properties of deep neural networks. We use the loss function topology to relate the local behavior of gradient descent trajectories with the global properties of the loss surface. For this purpose, we define the neural network's Topological Obstructions score ("TO-score") with the help of robust topological invariants, barcodes of the loss function, which quantify the escapability of local minima for gradient-based optimization. Our two principal observations are: 1) the loss barcode of the neural network decreases with increasing depth and width, therefore the topological obstructions to learning diminish; 2) in certain situations there is a connection between the length of minima segments in the loss barcode and the minima's generalization errors. Our statements are based on extensive experiments with fully connected, convolutional, and transformer architectures and several datasets including MNIST, FMNIST, CIFAR10, CIFAR100, SVHN, and multilingual OSCAR text dataset.

arXiv:2506.01502v3 Announce Type: replace-cross Abstract: Learning population dynamics involves recovering the underlying process that governs particle evolution, given evolutionary snapshots of samples at discrete time points. Recent methods frame this as an energy minimization problem in probability space and leverage the celebrated JKO scheme for efficient time discretization. In this work, we introduce $\texttt{iJKOnet}$, an approach that combines the JKO framework with inverse optimization techniques to learn population dynamics. Our method relies on a conventional $\textit{end-to-end}$ adversarial training procedure and does not require restrictive architectural choices, e.g., input-convex neural networks. We establish theoretical guarantees for our methodology and demonstrate improved performance over prior JKO-based methods. The code of $\texttt{iJKOnet}$ is available at https://github.com/MuXauJl11110/iJKOnet.

arXiv:2509.22166v2 Announce Type: replace-cross Abstract: The demand for efficient large language model (LLM) inference has intensified the focus on sparsification techniques. While semi-structured (N:M) pruning is well-established for weights, its application to activation pruning remains underexplored despite its potential for dynamic, input-adaptive compression and reductions in I/O overhead. This work presents a comprehensive analysis of methods for post-training N:M activation pruning in LLMs. Across multiple LLMs, we demonstrate that pruning activations enables superior preservation of generative capabilities compared to weight pruning at equivalent sparsity levels. We evaluate lightweight, plug-and-play error mitigation techniques and pruning criteria, establishing strong hardware-friendly baselines that require minimal calibration. Furthermore, we explore sparsity patterns beyond NVIDIA's standard 2:4, showing that the 16:32 pattern achieves performance nearly on par with unstructured sparsity. However, considering the trade-off between flexibility and hardware implementation complexity, we focus on the 8:16 pattern as a superior candidate. Our findings provide both effective practical methods for activation pruning and a motivation for future hardware to support more flexible sparsity patterns. Our code is available https://anonymous.4open.science/r/Structured-Sparse-Activations-Inference-EC3C/README.md .