How Divergence Becomes Decision Flips in Compressed Language Models

High-dimensional language-model embeddings increase storage and search costs, while supervised compressors can overfit when relevance labels are scarce. We present DIVE (Dimensionality reduction with Implicit View Ensembles), a residual compression adapter codesigned with a self-limiting hinge loss, geometry distillation, and head-wise NT-Xent over implicit coordinate views. The hinge stops updating satisfied ranking constraints, while the dense objectives stabilize the compressed representation; only the first head is retained at inference. Under query-disjoint evaluation with two LLM2Vec backbones, five BEIR benchmarks, 128d and 256d outputs, and six baselines, DIVE is the strongest adapter on all five primary benchmarks. It also outperforms PCA and an autoencoder in comparisons against unsupervised compressors.

Diffusion language models (DLMs) have recently emerged as competitive alternatives to autoregressive (AR) language models, yet differences in their activation dynamics remain poorly understood. We characterize these dynamics in LLaDA-8B and identify a striking layer-collapse property: a few early layers exhibit highly similar, collapsed activation patterns dominated by a single large super-outlier persisting over a long token range. Despite its apparent redundancy, this outlier is critical: pruning it causes outputs to degrade into repetitive random token loops. Paradoxically, layers in LLaDA contain more redundant representations overall, with redundancy most pronounced in earlier layers -- the reverse of AR models, where deeper layers grow redundant due to undertraining. Our analysis indicates that layer collapse in DLMs is not driven by undertraining but by overtraining: a dominant outlier becomes an indispensable information carrier while remaining representations collapse into redundant structure. These findings have strong practical implications, verified through controlled pre-training experiments. DLMs are surprisingly robust to compression: LLaDA under 3-bit GPTQ quantization drops only -1.8% on GSM8K, whereas Llama-3.1-8B drops -64.7%. Optimal sparsity allocation also reverses between families: at 50% average sparsity, allocating more to early layers in LLaDA yields +8.4% over the reverse strategy, while the same allocation costs Llama -8.4%. Our findings reveal that the DLM training objective fundamentally reshapes layer dynamics relative to AR models, with direct consequences for compression and deployment. Code: github.com/Conzel/super-outlier-dlm.

Modern LLM deployments use a number of implementation choices and inference optimizations (e.g., batching, custom kernels, and quantization) on top of fixed weights, so two engines serving "the same model" can produce meaningfully different distributions. We study the problem of estimating the total variation (TV) distance between two length-$n$ autoregressive distributions to additive error $\varepsilon$, under three access models. (1) Under sample access, we use $\widetilde{O}(n^2 K/\varepsilon^2)$ queries, where $K$ is the maximum support of the next-token distribution. This improves upon the $\widetilde{O}(n^3 m/\varepsilon^5)$-query estimator of Meel et al. (2025), where $m \geq K$ is the total size of the token alphabet. (2) Under logit access, we use $O(n/\varepsilon^2)$ queries, and this is tight. (3) Under noisy logit access, we smoothly interpolate between the above two guarantees: if probability values are given to relative error $σ$, we use $\widetilde{O}((n+n^2σ^2)/\varepsilon^2)$ queries. We complement our theoretical results with an empirical evaluation of our algorithms, for example measuring the distance between SGLang and vLLM serving identical weights. Our experiments highlight the robustness and practicality of estimating the total variation distance, which remains estimable where the KL divergence is infinite. Our code is available at https://github.com/XunZhiyang/llm-tv-estimation.