Abhishek Panigrahi

Sanjeev Arora, Zhiyuan Li, Abhishek Panigrahi

Deep learning experiments by Cohen et al. [2021] using deterministic Gradient Descent (GD) revealed an Edge of Stability (EoS) phase when learning rate (LR) and sharpness (i.e., the largest eigenvalue of Hessian) no longer behave as in traditional optimization. Sharpness stabilizes around $2/$LR and loss goes up and down across iterations, yet still with an overall downward trend. The current paper mathematically analyzes a new mechanism of implicit regularization in the EoS phase, whereby GD updates due to non-smooth loss landscape turn out to evolve along some deterministic flow on the manifold of minimum loss. This is in contrast to many previous results about implicit bias either relying on infinitesimal updates or noise in gradient. Formally, for any smooth function $L$ with certain regularity condition, this effect is demonstrated for (1) Normalized GD, i.e., GD with a varying LR $η_t =\fracη{\| \nabla L(x(t)) \|}$ and loss $L$; (2) GD with constant LR and loss $\sqrt{L- \min_x L(x)}$. Both provably enter the Edge of Stability, with the associated flow on the manifold minimizing $λ_{1}(\nabla^2 L)$. The above theoretical results have been corroborated by an experimental study.

Abhishek Panigrahi, Nikunj Saunshi, Haoyu Zhao et al.

Pre-trained language models can be fine-tuned to solve diverse NLP tasks, including in few-shot settings. Thus fine-tuning allows the model to quickly pick up task-specific ``skills,'' but there has been limited study of where these newly-learnt skills reside inside the massive model. This paper introduces the term skill localization for this problem and proposes a solution. Given the downstream task and a model fine-tuned on that task, a simple optimization is used to identify a very small subset of parameters ($\sim0.01$% of model parameters) responsible for ($>95$%) of the model's performance, in the sense that grafting the fine-tuned values for just this tiny subset onto the pre-trained model gives performance almost as well as the fine-tuned model. While reminiscent of recent works on parameter-efficient fine-tuning, the novel aspects here are that: (i) No further re-training is needed on the subset (unlike, say, with lottery tickets). (ii) Notable improvements are seen over vanilla fine-tuning with respect to calibration of predictions in-distribution ($40$-$90$% error reduction) as well as the quality of predictions out-of-distribution (OOD). In models trained on multiple tasks, a stronger notion of skill localization is observed, where the sparse regions corresponding to different tasks are almost disjoint, and their overlap (when it happens) is a proxy for task similarity. Experiments suggest that localization via grafting can assist certain forms of continual learning.

Sadhika Malladi, Kaifeng Lyu, Abhishek Panigrahi et al. · tsinghua

Approximating Stochastic Gradient Descent (SGD) as a Stochastic Differential Equation (SDE) has allowed researchers to enjoy the benefits of studying a continuous optimization trajectory while carefully preserving the stochasticity of SGD. Analogous study of adaptive gradient methods, such as RMSprop and Adam, has been challenging because there were no rigorously proven SDE approximations for these methods. This paper derives the SDE approximations for RMSprop and Adam, giving theoretical guarantees of their correctness as well as experimental validation of their applicability to common large-scaling vision and language settings. A key practical result is the derivation of a $\textit{square root scaling rule}$ to adjust the optimization hyperparameters of RMSprop and Adam when changing batch size, and its empirical validation in deep learning settings.

Haoyu Zhao, Abhishek Panigrahi, Rong Ge et al.

Pre-trained language models have been shown to encode linguistic structures, e.g. dependency and constituency parse trees, in their embeddings while being trained on unsupervised loss functions like masked language modeling. Some doubts have been raised whether the models actually are doing parsing or only some computation weakly correlated with it. We study questions: (a) Is it possible to explicitly describe transformers with realistic embedding dimension, number of heads, etc. that are capable of doing parsing -- or even approximate parsing? (b) Why do pre-trained models capture parsing structure? This paper takes a step toward answering these questions in the context of generative modeling with PCFGs. We show that masked language models like BERT or RoBERTa of moderate sizes can approximately execute the Inside-Outside algorithm for the English PCFG [Marcus et al, 1993]. We also show that the Inside-Outside algorithm is optimal for masked language modeling loss on the PCFG-generated data. We also give a construction of transformers with $50$ layers, $15$ attention heads, and $1275$ dimensional embeddings in average such that using its embeddings it is possible to do constituency parsing with $>70\%$ F1 score on PTB dataset. We conduct probing experiments on models pre-trained on PCFG-generated data to show that this not only allows recovery of approximate parse tree, but also recovers marginal span probabilities computed by the Inside-Outside algorithm, which suggests an implicit bias of masked language modeling towards this algorithm.

Abhishek Panigrahi, Sadhika Malladi, Mengzhou Xia et al.

Recent works attribute the capability of in-context learning (ICL) in large pre-trained language models to implicitly simulating and fine-tuning an internal model (e.g., linear or 2-layer MLP) during inference. However, such constructions require large memory overhead, which makes simulation of more sophisticated internal models intractable. In this work, we propose an efficient construction, Transformer in Transformer (in short, TinT), that allows a transformer to simulate and fine-tune complex models internally during inference (e.g., pre-trained language models). In particular, we introduce innovative approximation techniques that allow a TinT model with less than 2 billion parameters to simulate and fine-tune a 125 million parameter transformer model within a single forward pass. TinT accommodates many common transformer variants and its design ideas also improve the efficiency of past instantiations of simple models inside transformers. We conduct end-to-end experiments to validate the internal fine-tuning procedure of TinT on various language modeling and downstream tasks. For example, even with a limited one-step budget, we observe TinT for a OPT-125M model improves performance by 4-16% absolute on average compared to OPT-125M. These findings suggest that large pre-trained language models are capable of performing intricate subroutines. To facilitate further work, a modular and extensible codebase for TinT is included.

Dan Friedman, Abhishek Panigrahi, Danqi Chen · princeton

What kind of internal mechanisms might Transformers use to conduct fluid, natural-sounding conversations? Prior work has illustrated by construction how Transformers can solve various synthetic tasks, such as sorting a list or recognizing formal languages, but it remains unclear how to extend this approach to a conversational setting. In this work, we propose using ELIZA, a classic rule-based chatbot, as a setting for formal, mechanistic analysis of Transformer-based chatbots. ELIZA allows us to formally model key aspects of conversation, including local pattern matching and long-term dialogue state tracking. We first present a theoretical construction of a Transformer that implements the ELIZA chatbot. Building on prior constructions, particularly those for simulating finite-state automata, we show how simpler mechanisms can be composed and extended to produce more sophisticated behavior. Next, we conduct a set of empirical analyses of Transformers trained on synthetically generated ELIZA conversations. Our analysis illustrates the kinds of mechanisms these models tend to prefer--for example, models favor an induction head mechanism over a more precise, position-based copying mechanism; and using intermediate generations to simulate recurrent data structures, akin to an implicit scratchpad or Chain-of-Thought. Overall, by drawing an explicit connection between neural chatbots and interpretable, symbolic mechanisms, our results provide a new framework for the mechanistic analysis of conversational agents.

Abhishek Panigrahi, Nikunj Saunshi, Kaifeng Lyu et al. · tsinghua

Recent developments in large language models have sparked interest in efficient pretraining methods. Stagewise training approaches to improve efficiency, like gradual stacking and layer dropping (Reddi et al, 2023; Zhang & He, 2020), have recently garnered attention. The prevailing view suggests that stagewise dropping strategies, such as layer dropping, are ineffective, especially when compared to stacking-based approaches. This paper challenges this notion by demonstrating that, with proper design, dropping strategies can be competitive, if not better, than stacking methods. Specifically, we develop a principled stagewise training framework, progressive subnetwork training, which only trains subnetworks within the model and progressively increases the size of subnetworks during training, until it trains the full network. We propose an instantiation of this framework - Random Part Training (RAPTR) - that selects and trains only a random subnetwork (e.g. depth-wise, width-wise) of the network at each step, progressively increasing the size in stages. We show that this approach not only generalizes prior works like layer dropping but also fixes their key issues. Furthermore, we establish a theoretical basis for such approaches and provide justification for (a) increasing complexity of subnetworks in stages, conceptually diverging from prior works on layer dropping, and (b) stability in loss across stage transitions in presence of key modern architecture components like residual connections and layer norms. Through comprehensive experiments, we demonstrate that RAPTR can significantly speed up training of standard benchmarks like BERT and UL2, up to 33% compared to standard training and, surprisingly, also shows better downstream performance on UL2, improving QA tasks and SuperGLUE by 1.5%; thereby, providing evidence of better inductive bias.

Simon Park, Abhishek Panigrahi, Yun Cheng et al. · princeton

Vision Language Models (VLMs) are impressive at visual question answering and image captioning. But they underperform on multi-step visual reasoning -- even compared to LLMs on the same tasks presented in text form -- giving rise to perceptions of modality imbalance or brittleness. Towards a systematic study of such issues, we introduce a synthetic framework for assessing the ability of VLMs to perform algorithmic visual reasoning, comprising three tasks: Table Readout, Grid Navigation, and Visual Analogy. Each has two levels of difficulty, SIMPLE and HARD, and even the SIMPLE versions are difficult for frontier VLMs. We propose strategies for training on the SIMPLE version of tasks that improve performance on the corresponding HARD task, i.e., simple-to-hard (S2H) generalization. This controlled setup, where each task also has an equivalent text-only version, allows a quantification of the modality imbalance and how it is impacted by training strategy. We show that 1) explicit image-to-text conversion is important in promoting S2H generalization on images, by transferring reasoning from text; 2) conversion can be internalized at test time. We also report results of mechanistic study of this phenomenon. We identify measures of gradient alignment that can identify training strategies that promote better S2H generalization. Ablations highlight the importance of chain-of-thought.

Suman Kalyan Maity, Abhishek Panigrahi, Sayan Ghosh et al.

In this paper, we develop a content-cum-user based deep learning framework DeepTagRec to recommend appropriate question tags on Stack Overflow. The proposed system learns the content representation from question title and body. Subsequently, the learnt representation from heterogeneous relationship between user and tags is fused with the content representation for the final tag prediction. On a very large-scale dataset comprising half a million question posts, DeepTagRec beats all the baselines; in particular, it significantly outperforms the best performing baseline T agCombine achieving an overall gain of 60.8% and 36.8% in precision@3 and recall@10 respectively. DeepTagRec also achieves 63% and 33.14% maximum improvement in exact-k accuracy and top-k accuracy respectively over TagCombine