We study the grokking phenomenon through the lens of topology. Using persistent homology on point clouds derived from the embedding matrices of a range of models trained on modular arithmetic with varying primes, we identify a clear and consistent topological signature of grokking: a sharp increase in both the maximum and total persistence of first homology ($H_1$). Persistence diagrams reveal the emergence of a dominant long-lived topological feature together with increasingly structured secondary features, reflecting the underlying cyclic structure of the task. Compared to existing spectral and geometric diagnostics -- specifically, Fourier analysis and local intrinsic dimension -- persistent homology provides a unified geometric and topological characterization of representation learning, capturing both local and global multi-scale structure. Ablations across data regimes and control settings show that these topological transitions are tied to generalization rather than memorization. Our results suggest that persistent homology offers a principled and interpretable framework for analyzing how neural networks internalize latent structure during training.

Extreme multi-label text classification (XMC) seeks to find relevant labels from an extreme large label collection for a given text input. Many real-world applications can be formulated as XMC problems, such as recommendation systems, document tagging and semantic search. Recently, transformer based XMC methods, such as XTransformer and LightXML, have shown significant improvement over other XMC methods. Despite leveraging pre-trained transformer models for text representation, the fine-tuning procedure of transformer models on large label space still has lengthy computational time even with powerful GPUs. In this paper, we propose a novel recursive approach, XR-Transformer to accelerate the procedure through recursively fine-tuning transformer models on a series of multi-resolution objectives related to the original XMC objective function. Empirical results show that XRTransformer takes significantly less training time compared to other transformerbased XMC models while yielding better state-of-the-art results. In particular, on the public Amazon-3M dataset with 3 million labels, XR-Transformer is not only 20x faster than X-Transformer but also improves the Precision@1 from 51% to 54%. Our code is publicly available at https://github.com/amzn/pecos.

Linear RNN architectures, like Mamba, can be competitive with Transformer models in language modeling while having advantageous deployment characteristics. Given the focus on training large-scale Transformer models, we consider the challenge of converting these pretrained models for deployment. We demonstrate that it is feasible to distill large Transformers into linear RNNs by reusing the linear projection weights from attention layers with academic GPU resources. The resulting hybrid model, which incorporates a quarter of the attention layers, achieves performance comparable to the original Transformer in chat benchmarks and outperforms open-source hybrid Mamba models trained from scratch with trillions of tokens in both chat benchmarks and general benchmarks. Moreover, we introduce a hardware-aware speculative decoding algorithm that accelerates the inference speed of Mamba and hybrid models. Overall we show how, with limited computation resources, we can remove many of the original attention layers and generate from the resulting model more efficiently. Our top-performing model, distilled from Llama3-8B-Instruct, achieves a 29.61 length-controlled win rate on AlpacaEval 2 against GPT-4 and 7.35 on MT-Bench, surpassing the best 8B scale instruction-tuned linear RNN model. We also find that the distilled model has natural length extrapolation, showing almost perfect accuracy in the needle-in-a-haystack test at 20x the distillation length. Code and pre-trained checkpoints are open-sourced at MambaInLlama for distillation and SpeculativeMamba for speculative decoding.

The rapid proliferation of open-source language models significantly increases the risks of downstream backdoor attacks. These backdoors can introduce dangerous behaviours during model deployment and can evade detection by conventional cybersecurity monitoring systems. In this paper, we introduce a novel class of backdoors in transformer models, that, in contrast to prior art, are unelicitable in nature. Unelicitability prevents the defender from triggering the backdoor, making it impossible to properly evaluate ahead of deployment even if given full white-box access and using automated techniques, such as red-teaming or certain formal verification methods. We show that our novel construction is not only unelicitable thanks to using cryptographic techniques, but also has favourable robustness properties.We confirm these properties in empirical investigations, and provide evidence that our backdoors can withstand state-of-the-art mitigation strategies. Additionally, we expand on previous work by showing that our universal backdoors, while not completely undetectable in white-box settings, can be harder to detect than some existing designs. By demonstrating the feasibility of seamlessly integrating backdoors into transformer models, this paper fundamentally questions the efficacy of pre-deployment detection strategies.