Spherical Soft-Masking (S-SM), a drop-in replacement that aggregates the top-(k) predictions with a Fr'echet mean on the hypersphere and blends this mean with the mask direction using spherical linear interpolation (SLERP), then restores the native mask norm.
Abstract
Soft-masking accelerates the convergence of Masked Diffusion Language Models (MDLMs). Existing formulations build this blend with linear interpolation (LERP) in the raw embedding space, which implicitly treats that space as Euclidean. We analyze the embedding space of MDLMs and find that the mask and predicted-token embeddings maintain a near-constant angle of (\approx 73^\circ) throughout training, while embedding norms remain essentially flat across vocabulary-frequency rank. These indicate a hyperspherical geometry, for which LERP is the wrong interpolation primitive. We introduce Spherical Soft-Masking (S-SM), a drop-in replacement that aggregates the top-(k) predictions with a Fr'echet mean on the hypersphere and blends this mean with the mask direction using spherical linear interpolation (SLERP), then restores the native mask norm. We evaluate S-SM on continued pre-training of a released 169M-parameter MDLM checkpoint across a wide range of inference-time step budgets, SLERP feedback avoids the training degradation that LERP feedback induces and delivers MAUVE gains of up to 2x over the vanilla MDLM baseline and 27.5-56.1% over TopK/LERP at various sampling budgets, alongside consistently lower generative perplexity (16.9-19.6% over the baseline), while leaving output entropy and convergence essentially unchanged.
Masked diffusion language models (MDLMs) enable parallel generation and bidirectional context modeling, but their positional context differs fundamentally from that of autoregressive (AR) models. Whereas AR decoding exposes a contiguous prefix, MDLM denoising produces dynamic, non-contiguous configurations of revealed and masked tokens. Conventional positional encodings such as RoPE capture sequence order and pairwise displacement but remain insensitive to this evolving token-availability structure. To address this limitation, we propose MDLMPE, a positional encoding designed specifically for masked diffusion. To the best of our knowledge, MDLMPE is the first method to make positional representations explicitly aware of the changing revealed/masked configuration. It represents token availability as a binary sequence, applies distance-aware Gaussian weighting, and projects the resulting pattern through a cosine basis to obtain distribution-aware positional features. These features are added to token embeddings and mapped by a lightweight MLP to angular offsets that modulate the standard RoPE phases. Extensive experiments on LLaDA and DREAM demonstrate that MDLMPE generally outperforms conventional positional encoding methods across supervised fine-tuning, pretraining, zero-shot evaluation, and block-diffusion settings. Further ablations show that the complete combination of availability state, Gaussian locality, spectral basis, and embedding injection yields the strongest result. These results establish the evolving token-availability distribution as a useful positional signal for masked diffusion language models.
Tong-Tong Ling, Hang Lei, Feng Xiao et al.· 0 citations
This work proposes a simple continual pre-training approach for directly adapting pretrained GPT2 checkpoints to uniform-noise diffusion, and establishes connections among SEDD, MDLM/GIDD, M2S, and Neural CTMC by expressing their conditional losses as a single generalized Kullback--Leibler objective over model reverse rates.
Xiaoyi Jiang, Jingyuan Li, Yixuan Jiang et al.· 0 citations
Diffusion language models (DLMs) update many tokens in parallel, yet practical decoders often use a fixed denoising horizon. Many predictions stabilize early, but blockwise decoding continues until all positions are resolved, causing repeated dense forward passes. Existing accelerators often rely on learned filters, modified scores, dependency models, or cache-specific mechanisms. We ask whether native trajectory signals can identify residual positions likely to match the deterministic dense endpoint. We propose CORA-Diff, a training-free method that preserves the original transfer rule and applies confidence-and-persistence gating only to positions that rule leaves unresolved. Accepted tokens remain visible as context, and the block terminates once all positions are resolved. This requires no backbone change, learned acceptance model, or logit modification. Our theory explains why high-confidence, persistent predictions are more likely to match the fixed-horizon dense endpoint, and paired post-intervention trajectories provide direct empirical support. We select one operating point on a separate GSM8K calibration subset and freeze it for all evaluations. Under a matched Learn2PD-style LLaDA protocol, CORA-Diff has the lowest measured runtime in all eight task-length settings. Task scores match or exceed dense decoding in five settings, and the largest observed drop is 1.22 points. Its incremental speedups over EOS-aware dense decoding are 2.70x and 3.32x on GSM8K and HumanEval. It also reaches 13.14x under the fixed-horizon 1024/1024 mechanism-isolation protocol and transfers to Dream without retuning at 3.18x-3.53x. These results show that native confidence and persistence enable reliable residual acceptance, reducing repeated denoising computation while preserving task quality.
Seer is proposed, a training-free framework that detects their valid semantic boundary using a Signal-to-Noise Ratio (SNR)-based criterion and performs one-shot truncation of the redundant suffix for all subsequent computations, offering a highly efficient, plug-and-play solution for DMLLM acceleration.
Joint-Embedding Predictive Architectures (JEPAs) are effective for images, video, and audio, yet deterministic JEPA-style latent prediction has not become a standard objective for text encoders. We argue that this gap reflects a mismatch between squared-error latent prediction and the conditional structure of language. The key requirement is conditional concentration: given a context and target location, the target representation should lie near a single meaningful point. Local image prediction often satisfies this through spatial continuity, whereas masked text can admit multiple valid token or span completions whose representations need not share a coherent center. We formalize this mismatch through three conditions---predictability, non-collapse, and low conditional variance---and show how their failure creates centroid degeneracy and collapse pressure in text. Matched I-JEPA and T-JEPA experiments reveal the predicted sequence: mutual-information saturation and elevated target variance precede train--validation instability, effective-rank degeneration, cosine collapse, and poor downstream transfer. The same pattern appears across five independent data seeds, indicating that it is not a sampling artifact. These results do not rule out predictive learning for language; they show that text-compatible JEPA objectives must preserve multiple plausible completions rather than compress them into a single latent point.
Kolmogorov--Arnold Networks (KANs) replace fixed node activations with learned one-dimensional edge functions, offering an explicit interface for interpretation and a possible alternative to transformer feed-forward networks. We test these claims separately. In a six-layer, 10M-parameter B-spline KAN, we reconstruct all 884,736 feed-forward edges: 87.8\% exceed (NLS>0.1) and 0.4\% are inactive. Pruning the lowest-activity 20--25\% causes negligible loss increase, although structured MLP neuron pruning tolerates comparable sparsity. The audit replicates on BabyLM, but grid-size sweeps show that near-total fPCA compression and high closed-form-fit coverage are properties of the low-capacity grid-2 basis, not universal KAN behavior. For replacement, we evaluate MLP, SwiGLU, grouped Chebyshev, and rational GR-KAN networks on BabyLM. The KAN-family and gated variants improve validation loss over the GELU MLP, but this ordering does not transfer to standardized benchmarks: across ten seeds and 59,875 BLiMP pairs, accuracies span 62.4--63.1\%, EWoK remains at chance, and a (+0.7)-point GR-KAN effect on BLiMP reverses on the supplement. Larger tests are also cautionary: parameter-matched MLPEdge underperforms the MLP on Wikitext-103, and 286M-parameter GR-KAN remains below a SwiGLU ClimbMix baseline after stabilization. Thus, small-basis KANs provide a practical, corpus-transferable interface for auditing learned scalar transformations, but the tested replacements show no consistent benchmark, quality, or latency advantage over strong MLP baselines.