N. Nayak

Oam Patel, Jason Wang, Nikhil Shivakumar Nayak et al. · harvard

Soft prompts have been popularized as a cheap and easy way to improve task-specific LLM performance beyond few-shot prompts. Despite their origin as an automated prompting method, however, soft prompts and other trainable prompts remain a black-box method with no immediately interpretable connections to prompting. We create a novel theoretical framework for evaluating the interpretability of trainable prompts based on two desiderata: faithfulness and scrutability. We find that existing methods do not naturally satisfy our proposed interpretability criterion. Instead, our framework inspires a new direction of trainable prompting methods that explicitly optimizes for interpretability. To this end, we formulate and test new interpretability-oriented objective functions for two state-of-the-art prompt tuners: Hard Prompts Made Easy (PEZ) and RLPrompt. Our experiments with GPT-2 demonstrate a fundamental trade-off between interpretability and the task-performance of the trainable prompt, explicating the hardness of the soft prompt interpretability problem and revealing odd behavior that arises when one optimizes for an interpretability proxy.

Mustafa Eyceoz, Nikhil Shivakumar Nayak, Hao Wang et al.

Modern causal language models stack many attention blocks to improve performance, but not all blocks are necessary for every task. We propose Hopscotch, a simple yet effective method that identifies and skips attention blocks with least contributions to a task and adapts to preserve output quality. Hopscotch jointly optimizes which blocks to skip and how to scale the outputs of the remaining layers. By introducing lightweight, trainable scaling parameters to attention and MLP blocks, it mitigates distribution shifts in hidden states caused by removing attention blocks. Hopscotch does not modify model weights or require access to pretraining or instruction-tuning data, and is compatible with existing model compression techniques. When applied to $\texttt{Llama-3.1-8B}$ and $\texttt{Qwen2.5-7B}$, Hopscotch achieves less than a 2% drop in performance even after skipping four attention blocks.

Nikhil Shivakumar Nayak, Krishnateja Killamsetty, Ligong Han et al.

Continual learning in large language models (LLMs) is prone to catastrophic forgetting, where adapting to new tasks significantly degrades performance on previously learned ones. Existing methods typically rely on low-rank, parameter-efficient updates that limit the model's expressivity and introduce additional parameters per task, leading to scalability issues. To address these limitations, we propose a novel continual full fine-tuning approach leveraging adaptive singular value decomposition (SVD). Our method dynamically identifies task-specific low-rank parameter subspaces and constrains updates to be orthogonal to critical directions associated with prior tasks, thus effectively minimizing interference without additional parameter overhead or storing previous task gradients. We evaluate our approach extensively on standard continual learning benchmarks using both encoder-decoder (T5-Large) and decoder-only (LLaMA-2 7B) models, spanning diverse tasks including classification, generation, and reasoning. Empirically, our method achieves state-of-the-art results, up to 7% higher average accuracy than recent baselines like O-LoRA, and notably maintains the model's general linguistic capabilities, instruction-following accuracy, and safety throughout the continual learning process by reducing forgetting to near-negligible levels. Our adaptive SVD framework effectively balances model plasticity and knowledge retention, providing a practical, theoretically grounded, and computationally scalable solution for continual learning scenarios in large language models.

Nikhil Shivakumar Nayak

This study investigates enhancing option pricing by extending the Black-Scholes model to include stochastic volatility and interest rate variability within the Partial Differential Equation (PDE). The PDE is solved using the finite difference method. The extended Black-Scholes model and a machine learning-based LSTM model are developed and evaluated for pricing Google stock options. Both models were backtested using historical market data. While the LSTM model exhibited higher predictive accuracy, the finite difference method demonstrated superior computational efficiency. This work provides insights into model performance under varying market conditions and emphasizes the potential of hybrid approaches for robust financial modeling.

Lingge Li, Nitish Nayak, Jianming Bian et al.

The unified approach of Feldman and Cousins allows for exact statistical inference of small signals that commonly arise in high energy physics. It has gained widespread use, for instance, in measurements of neutrino oscillation parameters in long-baseline experiments. However, the approach relies on the Neyman construction of the classical confidence interval and is computationally intensive as it is typically done in a grid-based fashion over the entire parameter space. In this letter, we propose an efficient algorithm for the Feldman-Cousins approach using Gaussian processes to construct confidence intervals iteratively. We show that in the neutrino oscillation context, one can obtain confidence intervals 5 times faster in one dimension and 10 times faster in two dimensions, while maintaining an accuracy above 99.5%.