Karthik Viswanathan

Kirill Vishniakov, Boulbaba Ben Amor, Engin Tekin et al.

We introduce Gene42, a novel family of Genomic Foundation Models (GFMs) designed to manage context lengths of up to 192,000 base pairs (bp) at a single-nucleotide resolution. Gene42 models utilize a decoder-only (LLaMA-style) architecture with a dense self-attention mechanism. Initially trained on fixed-length sequences of 4,096 bp, our models underwent continuous pretraining to extend the context length to 192,000 bp. This iterative extension allowed for the comprehensive processing of large-scale genomic data and the capture of intricate patterns and dependencies within the human genome. Gene42 is the first dense attention model capable of handling such extensive long context lengths in genomics, challenging state-space models that often rely on convolutional operators among other mechanisms. Our pretrained models exhibit notably low perplexity values and high reconstruction accuracy, highlighting their strong ability to model genomic data. Extensive experiments on various genomic benchmarks have demonstrated state-of-the-art performance across multiple tasks, including biotype classification, regulatory region identification, chromatin profiling prediction, variant pathogenicity prediction, and species classification. The models are publicly available at huggingface.co/inceptionai.

Karthik Viswanathan, Yuri Gardinazzi, Giada Panerai et al.

We investigate the relationship between the geometry of token embeddings and their role in the next token prediction within transformer models. An important aspect of this connection uses the notion of empirical measure, which encodes the distribution of token point clouds across transformer layers and drives the evolution of token representations in the mean-field interacting picture. We use metrics such as intrinsic dimension, neighborhood overlap, and cosine similarity to observationally probe these empirical measures across layers. To validate our approach, we compare these metrics to a dataset where the tokens are shuffled, which disrupts the syntactic and semantic structure. Our findings reveal a correlation between the geometric properties of token embeddings and the cross-entropy loss of next token predictions, implying that prompts with higher loss values have tokens represented in higher-dimensional spaces.

Yuri Gardinazzi, Karthik Viswanathan, Giada Panerai et al.

Understanding the decision-making processes of large language models is critical given their widespread applications. To achieve this, we aim to connect a formal mathematical framework - zigzag persistence from topological data analysis - with practical and easily applicable algorithms. Zigzag persistence is particularly effective for characterizing data as it dynamically transforms across model layers. Within this framework, we introduce topological descriptors that measure how topological features, $p$-dimensional holes, persist and evolve throughout the layers. Unlike methods that assess each layer individually and then aggregate the results, our approach directly tracks the full evolutionary path of these features. This offers a statistical perspective on how prompts are rearranged and their relative positions changed in the representation space, providing insights into the system's operation as an integrated whole. To demonstrate the expressivity and applicability of our framework, we highlight how sensitive these descriptors are to different models and a variety of datasets. As a showcase application to a downstream task, we use zigzag persistence to establish a criterion for layer pruning, achieving results comparable to state-of-the-art methods while preserving the system-level perspective.

Karthik Viswanathan, Sang Eon Park

We introduce a cumulant-expansion framework for quantifying how large language models (LLMs) internalize higher-order statistical structure during next-token prediction. By treating the softmax entropy of each layer's logit distribution as a perturbation around its "center" distribution, we derive closed-form cumulant observables that isolate successively higher-order correlations. Empirically, we track these cumulants in GPT-2 and Pythia models on Pile-10K prompts. (i) Structured prompts exhibit a characteristic rise-and-plateau profile across layers, whereas token-shuffled prompts remain flat, revealing the dependence of the cumulant profile on meaningful context. (ii) During training, all cumulants increase monotonically before saturating, directly visualizing the model's progression from capturing variance to learning skew, kurtosis, and higher-order statistical structures. (iii) Mathematical prompts show distinct cumulant signatures compared to general text, quantifying how models employ fundamentally different processing mechanisms for mathematical versus linguistic content. Together, these results establish cumulant analysis as a lightweight, mathematically grounded probe of feature-learning dynamics in high-dimensional neural networks.

Anahita Fathi Kazerooni, Nastaran Khalili, Xinyang Liu et al.

Pediatric tumors of the central nervous system are the most common cause of cancer-related death in children. The five-year survival rate for high-grade gliomas in children is less than 20\%. Due to their rarity, the diagnosis of these entities is often delayed, their treatment is mainly based on historic treatment concepts, and clinical trials require multi-institutional collaborations. The MICCAI Brain Tumor Segmentation (BraTS) Challenge is a landmark community benchmark event with a successful history of 12 years of resource creation for the segmentation and analysis of adult glioma. Here we present the CBTN-CONNECT-DIPGR-ASNR-MICCAI BraTS-PEDs 2023 challenge, which represents the first BraTS challenge focused on pediatric brain tumors with data acquired across multiple international consortia dedicated to pediatric neuro-oncology and clinical trials. The BraTS-PEDs 2023 challenge focuses on benchmarking the development of volumentric segmentation algorithms for pediatric brain glioma through standardized quantitative performance evaluation metrics utilized across the BraTS 2023 cluster of challenges. Models gaining knowledge from the BraTS-PEDs multi-parametric structural MRI (mpMRI) training data will be evaluated on separate validation and unseen test mpMRI dataof high-grade pediatric glioma. The CBTN-CONNECT-DIPGR-ASNR-MICCAI BraTS-PEDs 2023 challenge brings together clinicians and AI/imaging scientists to lead to faster development of automated segmentation techniques that could benefit clinical trials, and ultimately the care of children with brain tumors.