CascadeFormer: Depth-Tapered Transformers Motivated by Gradient Fan-in Asymmetry

Deep Transformers are composed of uniformly stacked residual blocks, yet their deepest layers often add little value. We present two efficiency methods that exploit this asymmetry. CascadeFormer tapers width with depth to match the uneven information flow across layers, achieving comparable perplexity to a uniform baseline at the same training budget while reducing latency by 8.6% and increasing throughput by 9.4%. CascadeFlow Pruning removes layers using accumulated training gradients, with no post hoc analysis. It outperforms standard heuristics on perplexity and rank-stability and stays competitive on downstream accuracy. To motivate these methods, we propose Gradient Fan-in Asymmetry (GFA) as a structural account of why deeper layers contribute less. In Pre-LayerNorm residual stacks, the gradient at a layer is the sum of an identity path and all downstream functional paths, producing a gradient fan-in that decays linearly with depth (and quadratically under deep supervision), yielding richer gradients for early layers and sparser ones for later layers. We provide correlational and interventional evidence for GFA on models trained from scratch up to 1.2B parameters. Across Transformers and ResNets, accumulated training gradients follow the theoretical fan-in and are associated with post hoc layer importance. Two interventions point to structure rather than magnitude as the bottleneck: equalizing per-layer gradient norms does not restore late-layer value, while increasing downstream path counts via parameter-shared repetition restores and elevates it. Whether gradient magnitude proxies fan-in beyond high-rank regimes, and how these dynamics behave at the 100B+ scale, remain open questions.

SpotAttention: Plug-In Block-Sparse Routing for Pretrained Long-Context Transformers

Long contexts have become standard in pretrained LLMs, yet they remain expensive to run: prefill compute grows quadratically with sequence length, and every decode step re-reads a key-value cache that grows linearly with it. Sparse attention cuts these costs by attending only to a relevant subset of past tokens, but selecting that subset is itself expensive. We present SpotAttention, a lightweight selector that attaches to a frozen pretrained transformer and learns by KL distillation to estimate its attention distribution. The selector picks the top-K keys each query attends to, and because its estimate is a calibrated distribution, a dual top-p rule reads the per-query, per-layer budget directly from it. Across Qwen3 (dense, 4B-32B) and Qwen3.5 (hybrid linear/full attention, 4B-9B), SpotAttention matches dense accuracy at contexts up to 128K tokens, eight times the training length. Decode at L=128K runs 3.9x faster than FlashAttention and 1.8x faster than Twilight, the strongest training-free baseline. Quantizing the selector's K-cache to INT4 or FP4 microscale shrinks it 3.5x at no accuracy cost.

Process-Verified Reinforcement Learning for Theorem Proving via Lean

While reinforcement learning from verifiable rewards (RLVR) typically has relied on a single binary verification signal, symbolic proof assistants in formal reasoning offer rich, fine-grained structured feedback. This gap between structured processes and unstructured rewards highlights the importance of feedback that is both dense and sound. In this work, we demonstrate that the Lean proof assistant itself can serve as a symbolic process oracle, supplying both outcome-level and fine-grained tactic-level verified feedback during training. Proof attempts are parsed into tactic sequences, and Lean's elaboration marks both locally sound steps and the earliest failing step, yielding dense, verifier-grounded credit signals rooted in type theory. We incorporate these structured rewards into a GRPO-style reinforcement learning objective with first-error propagation and first-token credit methods that balances outcome- and process-level advantages. Experiments with STP-Lean and DeepSeek-Prover-V1.5 show that tactic-level supervision outperforms outcome-only baselines in most settings, delivering improvements on benchmarks such as MiniF2F and ProofNet. Beyond empirical gains, our study highlights a broader perspective: symbolic proof assistants are not only verifiers at evaluation time, but can also act as process-level reward oracles during training. This opens a path toward reinforcement learning frameworks that combine the scalability of language models with the reliability of symbolic verification for formal reasoning.

Bastion: Budget-Aware Speculative Decoding with Tree-structured Block Diffusion Drafting

Block-diffusion drafters have recently emerged as a powerful alternative for speculative decoding by predicting multiple future-token distributions in a single parallel step. However, since these parallel predictions are sampled from position-wise marginals rather than fully conditioned sequences, committing to a single greedy path often fails to capture the target model's preferred trajectory. To address this, we propose BASTION, a budget-aware speculative decoding framework with tree-based diffusion drafting. Unlike existing methods that rely on static tree topologies, BASTION dynamically constructs query-dependent trees by balancing draft quality against hardware constraints. Our framework integrates three synergistic components: (1) an acceptance surrogate that estimates expected accepted length via path confidence, (2) an online latency estimator that calibrates a hardware-aware roofline model, and (3) an adaptive best-first expansion that grows the tree until marginal gains no longer justify incremental verification costs. BASTION is training-free, preserves the target model's distribution, and requires no per-setting tuning. Across diverse benchmarks and GPU architectures, BASTION achieves up to a 6.61x speedup over standard autoregressive decoding, outperforming state-of-the-art block-diffusion baselines by 39%.

Instance-Optimal Estimation with Multiple LLM Judges on a Budget

Evaluating large language models increasingly relies on LLM-as-a-judge protocols, but such evaluations remain costly: different judges have different prices and reliabilities, and the difficulty of each prompt-response pair can vary substantially. This raises a basic allocation question: under a fixed budget, how should one distribute evaluation queries across heterogeneous judges and instances to obtain the most accurate score estimates? We formalize this question as *budgeted heteroskedastic multi-judge estimation*. Given $K$ prompt-response pairs, $J$ judges with known costs, and unknown query-judge variances, the goal is to estimate a bounded score vector while minimizing an $\ell_p$-error. Our first contribution is to analyze the inverse-variance weighted estimator (IVWE) and to derive the oracle allocation that minimizes its error rate. Since this allocation depends on the unknown variances, we then address the practical unknown-variance setting by proposing EST-IVWE, an adaptive algorithm that constructs and leverages *optimistically biased* variance estimates to stabilize the empirical allocation. We prove that EST-IVWE matches the oracle IVWE rate up to lower-order terms in the budget. Our second and central theoretical contribution is a matching *local* minimax lower bound, which establishes the instance-optimality of the proposed algorithms. A key technical insight is that Fano-type high-probability arguments are too coarse for this problem: their packing construction loses the local variance structure that governs the optimal allocation. We instead use an Assouad-type in-expectation argument, based on local perturbations, which preserves this structure and yields the sharp allocation-dependent lower bound. Finally, we numerically validate the superiority of our approach over naïve uniform allocation on synthetic and HelpSteer2 datasets.

PerMix-RLVR: Preserving Persona Expressivity under Verifiable-Reward Alignment

Persona prompting has been widely adopted to steer large language models (LLMs) behavior and improve their instruction performance by assigning specific characters. However, identifying an optimal persona is time-consuming, and its impact on output quality remains poorly understood. Prior work has mainly addressed this issue at the prompt level via inference-time strategies, incurring additional computation. In this work, we avoid inference-time prompt search by tackling persona sensitivity during training, aiming to train models that adapt their behavior to diverse personas while preserving task performance. In particular, we find that reinforcement learning with verifiable rewards (RLVR) systematically reduces sensitivity to persona prompts, but also reveals an inherent trade-off of outcome-based optimization: while RLVR improves robustness on tasks with verifiable goals, it can also degrade persona expressivity when needed, e.g., in-character role-playing. To address this limitation, we propose PerMix-RLVR, a persona-mixed RLVR strategy that mitigates the persona robustness-fidelity trade-off, preserving strong robustness to harmful persona variation while enabling faithful persona adoption when required. Concretely, PerMix-RLVR improves persona stability score (PSS) over RLVR by +21.2% on MATH500, while also enhancing persona fidelity by +11.4% on PersonaGym.

Multi-Drafter Speculative Decoding with Alignment Feedback

Speculative decoding (SD) accelerates large language model (LLM) inference by using a smaller model to draft future tokens, which are then verified by the target LLM. This preserves generation quality by accepting only aligned tokens. However, individual drafters, often trained for specific tasks or domains, exhibit limited effectiveness across diverse applications. To address this, we introduce \textsc{MetaSD}, a unified framework that integrates multiple drafters into the SD process. MetaSD dynamically allocates computational resources to heterogeneous drafters by leveraging alignment feedback and framing drafter selection as a multi-armed bandit problem. Extensive experiments show MetaSD consistently outperforms single-drafter approaches.

mSFT: Addressing Dataset Mixtures Overfitting Heterogeneously in Multi-task SFT

Current language model training commonly applies multi-task Supervised Fine-Tuning (SFT) using a homogeneous compute budget across all sub-datasets. This approach is fundamentally sub-optimal: heterogeneous learning dynamics cause faster-learning tasks to overfit early while slower ones remain under-fitted. To address this, we introduce mSFT, an iterative, overfitting-aware search algorithm for multi-task data mixtures. mSFT trains the model on an active mixture, identifies and excludes the earliest overfitting sub-dataset, and reverts to that specific optimal checkpoint before continuing. Extensive evaluations demonstrate that mSFT consistently outperforms 4 baselines across 10 benchmarks and 6 base models. Further analysis confirms mSFT maintains robust gains across diverse dataset sizes, task granularities, and is insensitive to its single new hyperparameter (compute budget). Notably, at low compute budget, mSFT can improve performance while lowering training FLOPs. Ultimately, mSFT establishes a practical overfitting-aware algorithm for multi-task SFT that maximizes the potential of models across diverse data mixtures.

mSFT: Addressing Dataset Mixtures Overfiting Heterogeneously in Multi-task SFT

Current language model training commonly applies multi-task Supervised Fine-Tuning (SFT) using a homogeneous compute budget across all sub-datasets. This approach is fundamentally sub-optimal: heterogeneous learning dynamics cause faster-learning tasks to overfit early while slower ones remain under-fitted. To address this, we introduce mSFT, an iterative, overfitting-aware search algorithm for multi-task data mixtures. mSFT trains the model on an active mixture, identifies and excludes the earliest overfitting sub-dataset, and reverts to that specific optimal checkpoint before continuing. Extensive evaluations demonstrate that mSFT consistently outperforms 4 baselines across 10 benchmarks and 6 base models. Further analysis confirms mSFT maintains robust gains across diverse dataset sizes, task granularities, and is insensitive to its single new hyperparameter (compute budget). Notably, at low compute budget, mSFT can improve performance while lowering training FLOPs. Ultimately, mSFT establishes a practical overfitting-aware algorithm for multi-task SFT that maximizes the potential of models across diverse data mixtures.

UniSAFE: A Comprehensive Benchmark for Safety Evaluation of Unified Multimodal Models

Unified Multimodal Models (UMMs) offer powerful cross-modality capabilities but introduce new safety risks not observed in single-task models. Despite their emergence, existing safety benchmarks remain fragmented across tasks and modalities, limiting the comprehensive evaluation of complex system-level vulnerabilities. To address this gap, we introduce UniSAFE, the first comprehensive benchmark for system-level safety evaluation of UMMs across 7 I/O modality combinations, spanning conventional tasks and novel multimodal-context image generation settings. UniSAFE is built with a shared-target design that projects common risk scenarios across task-specific I/O configurations, enabling controlled cross-task comparisons of safety failures. Comprising 6,802 curated instances, we use UniSAFE to evaluate 15 state-of-the-art UMMs, both proprietary and open-source. Our results reveal critical vulnerabilities across current UMMs, including elevated safety violations in multi-image composition and multi-turn settings, with image-output tasks consistently more vulnerable than text-output tasks. These findings highlight the need for stronger system-level safety alignment for UMMs. Our code and data are publicly available at https://github.com/segyulee/UniSAFE