PRISM: Demystifying Retention and Interaction in Mid-Training

We present PRISM, a comprehensive empirical study of mid-training design choices for large language models. Through controlled experiments across seven base models spanning four families (Granite, LLaMA, Mistral, Nemotron-H), two architecture types (dense Transformer and attention-Mamba hybrid), and scales from 3B to 24B parameters, we show that mid-training on approximately 27B high-quality tokens yields consistent gains of +15 to +40 points on math, +5 to +12 points on code, and +6 to +13 points on science benchmarks while preserving general performance. The full PRISM to RL pipeline improves macro-average across six reasoning benchmarks from under 12 to 29-42 (a 3-4x improvement), whereas RL applied directly to most of the base models remains substantially less effective, with AIME scores near zero. Data composition matters most at mid-training, not RL: including science data during mid-training unlocks +17 to +28 point GPQA-Diamond gains during RL, while changing the RL mix produces less than 2 point differences. Mechanistically, mid-training densely restructures over 90% of model weights, while RL makes sparse, front-loaded refinements to approximately 5% of parameters. Representation analysis (CKA) confirms that RL consistently preserves mid-training's representational geometry (over 0.998 CKA) across architectures. Crucially, RL applies identical weight changes regardless of starting point, yet only succeeds on mid-trained models, consistent with mid-training placing the model in a configuration from which RL can effectively improve performance. Our results demonstrate that retention-aware mid-training is highly effective for reliable reasoning enhancement and provide practical guidance for designing robust mid-training pipelines.

Distilling to Hybrid Attention Models via KL-Guided Layer Selection

Distilling pretrained softmax attention Transformers into more efficient hybrid architectures that interleave softmax and linear attention layers is a promising approach for improving the inference efficiency of LLMs without requiring expensive pretraining from scratch. A critical factor in the conversion process is layer selection, i.e., deciding on which layers to convert to linear attention variants. This paper describes a simple and efficient recipe for layer selection that uses layer importance scores derived from a small amount of training on generic text data. Once the layers have been selected we use a recent pipeline for the distillation process itself \citep[RADLADS;][]{goldstein2025radlads}, which consists of attention weight transfer, hidden state alignment, KL-based distribution matching, followed by a small amount of finetuning. We find that this approach is more effective than existing approaches for layer selection, including heuristics that uniformly interleave linear attentions based on a fixed ratio, as well as more involved approaches that rely on specialized diagnostic datasets.

FlashFormer: Whole-Model Kernels for Efficient Low-Batch Inference

The size and compute characteristics of modern large language models have led to an increased interest in developing specialized kernels tailored for training and inference. Existing kernels primarily optimize for compute utilization, targeting the large-batch training and inference settings. However, low-batch inference, where memory bandwidth and kernel launch overheads contribute are significant factors, remains important for many applications of interest such as in edge deployment and latency-sensitive applications. This paper describes FlashFormer, a proof-of-concept kernel for accelerating single-batch inference for transformer-based large language models. Across various model sizes and quantizations settings, we observe nontrivial speedups compared to existing state-of-the-art inference kernels.

PaTH Attention: Position Encoding via Accumulating Householder Transformations

The attention mechanism is a core primitive in modern large language models (LLMs) and AI more broadly. Since attention by itself is permutation-invariant, position encoding is essential for modeling structured domains such as language. Rotary position encoding (RoPE) has emerged as the de facto standard approach for position encoding and is part of many modern LLMs. However, in RoPE the key/query transformation between two elements in a sequence is only a function of their relative position and otherwise independent of the actual input. This limits the expressivity of RoPE-based transformers. This paper describes PaTH, a flexible data-dependent position encoding scheme based on accumulated products of Householder(like) transformations, where each transformation is data-dependent, i.e., a function of the input. We derive an efficient parallel algorithm for training through exploiting a compact representation of products of Householder matrices, and implement a FlashAttention-style blockwise algorithm that minimizes I/O cost. Across both targeted synthetic benchmarks and moderate-scale real-world language modeling experiments, we find that PaTH demonstrates superior performance compared to RoPE and other recent baselines.

Do Larger Language Models Imply Better Reasoning? A Pretraining Scaling Law for Reasoning

Large Language Models (LLMs) have demonstrated remarkable capabilities across a wide range of tasks requiring complex reasoning. However, the effects of scaling on their reasoning abilities remain insufficiently understood. In this paper, we introduce a synthetic multihop reasoning environment designed to closely replicate the structure and distribution of real-world large-scale knowledge graphs. Our reasoning task involves completing missing edges in the graph, which requires advanced multi-hop reasoning and mimics real-world reasoning scenarios. To evaluate this, we pretrain language models (LMs) from scratch solely on triples from the incomplete graph and assess their ability to infer the missing edges. Interestingly, we observe that overparameterization can impair reasoning performance due to excessive memorization. We investigate different factors that affect this U-shaped loss curve, including graph structure, model size, and training steps. To predict the optimal model size for a specific knowledge graph, we find an empirical scaling that linearly maps the knowledge graph search entropy to the optimal model size. This work provides new insights into the relationship between scaling and reasoning in LLMs, shedding light on possible ways to optimize their performance for reasoning tasks.

Stick-breaking Attention

The self-attention mechanism traditionally relies on the softmax operator, necessitating positional embeddings like RoPE, or position biases to account for token order. But current methods using still face length generalisation challenges. We propose an alternative attention mechanism based on the stick-breaking process: For each token before the current, we determine a break point $\beta_{i,j}$, which represents the proportion of the remaining stick to allocate to the current token. We repeat the process until the stick is fully allocated, resulting in a sequence of attention weights. This process naturally incorporates recency bias, which has linguistic motivations for grammar parsing (Shen et. al., 2017). We study the implications of replacing the conventional softmax-based attention mechanism with stick-breaking attention. We then discuss implementation of numerically stable stick-breaking attention and adapt Flash Attention to accommodate this mechanism. When used as a drop-in replacement for current softmax+RoPE attention systems, we find that stick-breaking attention performs competitively with current methods on length generalisation and downstream tasks. Stick-breaking also performs well at length generalisation, allowing a model trained with $2^{11}$ context window to perform well at $2^{14}$ with perplexity improvements.

Calibrating Expressions of Certainty

We present a novel approach to calibrating linguistic expressions of certainty, e.g., "Maybe" and "Likely". Unlike prior work that assigns a single score to each certainty phrase, we model uncertainty as distributions over the simplex to capture their semantics more accurately. To accommodate this new representation of certainty, we generalize existing measures of miscalibration and introduce a novel post-hoc calibration method. Leveraging these tools, we analyze the calibration of both humans (e.g., radiologists) and computational models (e.g., language models) and provide interpretable suggestions to improve their calibration.

SITAR: Semi-supervised Image Transformer for Action Recognition

Recognizing actions from a limited set of labeled videos remains a challenge as annotating visual data is not only tedious but also can be expensive due to classified nature. Moreover, handling spatio-temporal data using deep $3$D transformers for this can introduce significant computational complexity. In this paper, our objective is to address video action recognition in a semi-supervised setting by leveraging only a handful of labeled videos along with a collection of unlabeled videos in a compute efficient manner. Specifically, we rearrange multiple frames from the input videos in row-column form to construct super images. Subsequently, we capitalize on the vast pool of unlabeled samples and employ contrastive learning on the encoded super images. Our proposed approach employs two pathways to generate representations for temporally augmented super images originating from the same video. Specifically, we utilize a 2D image-transformer to generate representations and apply a contrastive loss function to minimize the similarity between representations from different videos while maximizing the representations of identical videos. Our method demonstrates superior performance compared to existing state-of-the-art approaches for semi-supervised action recognition across various benchmark datasets, all while significantly reducing computational costs.

Power Scheduler: A Batch Size and Token Number Agnostic Learning Rate Scheduler

Finding the optimal learning rate for language model pretraining is a challenging task. This is not only because there is a complicated correlation between learning rate, batch size, number of training tokens, model size, and other hyperparameters but also because it is prohibitively expensive to perform a hyperparameter search for large language models with Billions or Trillions of parameters. Recent studies propose using small proxy models and small corpus to perform hyperparameter searches and transposing the optimal parameters to large models and large corpus. While the zero-shot transferability is theoretically and empirically proven for model size related hyperparameters, like depth and width, the zero-shot transfer from small corpus to large corpus is underexplored. In this paper, we study the correlation between optimal learning rate, batch size, and number of training tokens for the recently proposed WSD scheduler. After thousands of small experiments, we found a power-law relationship between variables and demonstrated its transferability across model sizes. Based on the observation, we propose a new learning rate scheduler, Power scheduler, that is agnostic about the number of training tokens and batch size. The experiment shows that combining the Power scheduler with Maximum Update Parameterization (muP) can consistently achieve impressive performance with one set of hyperparameters regardless of the number of training tokens, batch size, model size, and even model architecture. Our 3B dense and MoE models trained with the Power scheduler achieve comparable performance as state-of-the-art small language models. We open-source these pretrained models at https://ibm.biz/BdKhLa.

Scaling Granite Code Models to 128K Context

This paper introduces long-context Granite code models that support effective context windows of up to 128K tokens. Our solution for scaling context length of Granite 3B/8B code models from 2K/4K to 128K consists of a light-weight continual pretraining by gradually increasing its RoPE base frequency with repository-level file packing and length-upsampled long-context data. Additionally, we also release instruction-tuned models with long-context support which are derived by further finetuning the long context base models on a mix of permissively licensed short and long-context instruction-response pairs. While comparing to the original short-context Granite code models, our long-context models achieve significant improvements on long-context tasks without any noticeable performance degradation on regular code completion benchmarks (e.g., HumanEval). We release all our long-context Granite code models under an Apache 2.0 license for both research and commercial use.