Aditya Nagarsekar

Karan Bania, Soham Kalburgi, Manit Tanwar et al.

Linear recurrent neural networks (LRNNs) provide a structured approach to sequence modeling that bridges classical linear dynamical systems and modern deep learning, offering both expressive power and theoretical guarantees on stability and trainability. In recent years, multiple LRNN-based architectures have been proposed, each introducing distinct parameterizations, discretization schemes, and implementation constraints. However, existing implementations are fragmented across different software frameworks, often rely on framework-specific optimizations, and in some cases require custom CUDA kernels or lack publicly available code altogether. As a result, using, comparing, or extending LRNNs requires substantial implementation effort. To address this, we introduce $\texttt{lrnnx}$, a unified software library that implements several modern LRNN architectures under a common interface. The library exposes multiple levels of control, allowing users to work directly with core components or higher-level model abstractions. $\texttt{lrnnx}$ aims to improve accessibility, reproducibility, and extensibility of LRNN research and applications. We make our code available under a permissive MIT license.

Neeraj Mohan Sushma, Aditya Nagarsekar, Cabrel Teguemne Fokam et al.

Modern deep neural network architectures are trained via backpropagation, which requires errors to be sequentially propagated through all layers before parameters can be updated. This introduces two limitations: locking, where layer-wise updates are strictly interdependent and cannot proceed in parallel, and the weight transport problem, which requires symmetric forward and backward pathways for exact gradient computation. These constraints restrict parallelism, increase memory and communication overhead, and pose challenges for scalable learning. In this work, we propose Hierarchical Block-Local Learning (HBLL), a framework that decomposes deep neural networks into hierarchically linked blocks trained using local learning objectives derived from variational principles, eliminating the need for full end-to-end backpropagation while maintaining effective information propagation across the network. HBLL is the first algorithm that is able to train deep neural networks in $\mathcal{O}(\log N)$ parallel time complexity, where $N$ is the number of network layers. We show that HBLL implicitly defines a family of subnetworks corresponding to different hierarchical paths, enabling flexible inference with different effective numbers of layers. We evaluate HBLL on a set of challenging vision and language modeling tasks, achieving competitive performance. We also extend HBLL to recurrent sequence architectures, applying to settings that otherwise rely on backpropagation through time.

Anish Sathyanarayanan, Aditya Nagarsekar, Aarush Rathore

Chain-of-thought (CoT) prompting is widely assumed to expose a model's reasoning process and improve transparency. We attempted to enforce this assumption by penalizing unfaithful reasoning, but found that surface-level compliance does not guarantee causal reliance. Our central finding is negative: even when CoT is verbose, strategic, and flagged by surface-level manipulation detectors, model answers are often causally independent of the CoT content. We present a diagnostic framework for auditing this failure mode: it combines (i) an interpretable behavioral module that scores manipulation-relevant signals in CoT text and (ii) a causal probe that measures CoT-mediated influence (CMI) via hidden-state patching and reports a bypass score ($1-\mathrm{CMI}$), quantifying the degree to which the answer is produced by a bypass circuit independent of the rationale. In pilot evaluations, audit-aware prompting increases detectable manipulation signals (mean risk-score delta: $+5.10$), yet causal probes reveal task-dependent mediation: many QA items exhibit near-total bypass (CMI $\approx 0$), while some logic problems show stronger mediation (CMI up to $0.56$). Layer-wise analysis reveals narrow and task-dependent ``reasoning windows'' even when mean CMI is low.

Dhruv Gupta, Aditya Nagarsekar, Vraj Shah et al.

Modern datasets often contain high-dimensional features exhibiting complex dependencies. To effectively analyze such data, dimensionality reduction methods rely on estimating the dataset's intrinsic dimension (id) as a measure of its underlying complexity. However, estimating id is challenging due to its dependence on scale: at very fine scales, noise inflates id estimates, while at coarser scales, estimates stabilize to lower, scale-invariant values. This paper introduces a novel, scalable, and parallelizable method called eDCF, which is based on Connectivity Factor (CF), a local connectivity-based metric, to robustly estimate intrinsic dimension across varying scales. Our method consistently matches leading estimators, achieving comparable values of mean absolute error (MAE) on synthetic benchmarks with noisy samples. Moreover, our approach also attains higher exact intrinsic dimension match rates, reaching up to 25.0% compared to 16.7% for MLE and 12.5% for TWO-NN, particularly excelling under medium to high noise levels and large datasets. Further, we showcase our method's ability to accurately detect fractal geometries in decision boundaries, confirming its utility for analyzing realistic, structured data.