arXiv subjects

Bingbin Liu

Publications and source records attributed to Bingbin Liu.

16 recordsLinked to original sources

arXiv2026

When Does Online Imitation Learning Help in LLM Post-Training? The Role of (Non-)Realizability Beyond Horizon

Online imitation learning (IL), particularly on-policy distillation, has emerged as a strong LLM post-training approach, often outperforming offline supervised fine-tuning (SFT). Yet a principled understanding of when and why online interaction helps remains unclear. In this work, we challenge the view that error accumulation is the main source of online IL's advantage, and instead show that the benefits of online interaction depend critically on whether the setting is realizable, i.e., whether the student policy class can represent the expert policy. Under realizability, we empirically find that offline IL already matches expert performance. In contrast, in non-realizable (misspecified) settings, we prove that offline IL encounters an information-theoretic bottleneck even when horizon $H=1$, and propose a structural characterization of misspecification relative to the reward, under which online IL provably achieves high performance despite a large distributional mismatch between the expert and student policies.

cs.LG↗

arXiv2026

Less Data, Faster Training: repeating smaller datasets speeds up learning via sampling biases

This work investigates the ``small-vs-large gap'', where repeating on fewer samples can lead to compute saving during training compared to using a larger dataset. This is observed across algorithmic tasks, architectures and optimizers and cannot be explained using prior theory. We argue that the speedup comes from appropriate layer-wise growth enabled by sampling biases, which is more pronounced when the dataset size is smaller. We provide both theoretical analysis and empirical evidence from various interventions. Our results suggest that using a smaller dataset with more repetitions is not just a fallback strategy under data scarcity, but can be proactively leveraged as a favorable inductive biases for optimization, particularly in reasoning tasks.

cs.LG↗

arXiv2026

The two clocks and the innovation window: When and how generative models learn rules

Generative models trained on finite data face a fundamental tension: their score-matching or next-token objective converges to the empirical training distribution rather than the population distribution we seek to learn. Using rule-valid synthetic tasks, we trace this tension across two training timescales: $\tau_{\mathrm{rule}}$, the step at which generations first become rule-valid, and $\tau_{\mathrm{mem}}$, the step at which models begin reproducing training samples. Focusing on parity and extending to other binary rules and combinatorial puzzles, we characterize how these two clocks, $\tau_{\mathrm{rule}}$ and $\tau_{\mathrm{mem}}$, depend on key aspects of the learning setup. Specifically, we show that $\tau_{\mathrm{rule}}$ increases with rule complexity and decreases with model capacity, while $\tau_{\mathrm{mem}}$ is approximately invariant to the rule and scales nearly linearly with dataset size $N$. We define the \emph{innovation window} as the interval $[\tau_{\mathrm{rule}}, \tau_{\mathrm{mem}}]$. This window widens with increasing $N$ and narrows with rule complexity, and may vanish entirely when $\tau_{\mathrm{rule}} \geq \tau_{\mathrm{mem}}$. The same two-clock structure arises in both diffusion (DiT) and autoregressive (GPT) models, with architecture-dependent offsets. Dissecting the learned score of DiT models reveals a corresponding evolution of the optimization landscapes, where rule-valid samples' basins expand substantially around $\tau_{\mathrm{rule}}$, while training samples' basins begin to dominate around $\tau_{\mathrm{mem}}$. Together, these results yield a unified and predictive account of when and how generative models exhibit genuine innovation.

cs.LG↗

arXiv2025

In Good GRACEs: Principled Teacher Selection for Knowledge Distillation

Knowledge distillation is an efficient strategy to use data generated by large "teacher" language models to train smaller capable "student" models, but selecting the optimal teacher for a specific student-task combination requires expensive trial-and-error. We propose a lightweight score called GRACE to quantify how effective a teacher will be for post-training a student model. GRACE measures distributional properties of the student's gradients without access to a verifier, teacher logits, teacher internals, or test data. From an information-theoretic perspective, GRACE connects to leave-one-out stability of gradient-based algorithms, which controls the generalization performance of the distilled students. On GSM8K and MATH, GRACE correlates strongly (up to 86% Spearman correlation) with the performance of the distilled LLaMA and OLMo students. In particular, training a student using the GRACE-selected teacher can improve the performance by up to 7.4% over naively using the best-performing teacher. Further, GRACE can provide guidance on crucial design choices in distillation, including (1) the best temperature to use when generating from the teacher, (2) the best teacher to use given a size constraint, and (3) the best teacher to use within a specific model family. Altogether, our findings demonstrate that GRACE can efficiently and effectively identify a strongly compatible teacher for a given student and provide fine-grained guidance on how to perform distillation.

cs.LG↗

arXiv2025

Adam or Gauss-Newton? A Comparative Study In Terms of Basis Alignment and SGD Noise

Diagonal preconditioners are computationally feasible approximate to second-order optimizers, which have shown significant promise in accelerating training of deep learning models. Two predominant approaches are based on Adam and Gauss-Newton (GN) methods: the former leverages statistics of current gradients and is the de-factor optimizers for neural networks, and the latter uses the diagonal elements of the Gauss-Newton matrix and underpins some of the recent diagonal optimizers such as Sophia. In this work, we compare these two diagonal preconditioning methods through the lens of two key factors: the choice of basis in the preconditioner, and the impact of gradient noise from mini-batching. To gain insights, we analyze these optimizers on quadratic objectives and logistic regression under all four quadrants. We show that regardless of the basis, there exist instances where Adam outperforms both GN$^{-1}$ and GN$^{-1/2}$ in full-batch settings. Conversely, in the stochastic regime, Adam behaves similarly to GN$^{-1/2}$ for linear regression under a Gaussian data assumption. These theoretical results are supported by empirical studies on both convex and non-convex objectives.

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arXiv2024

Progressive distillation induces an implicit curriculum

Knowledge distillation leverages a teacher model to improve the training of a student model. A persistent challenge is that a better teacher does not always yield a better student, to which a common mitigation is to use additional supervision from several ``intermediate'' teachers. One empirically validated variant of this principle is progressive distillation, where the student learns from successive intermediate checkpoints of the teacher. Using sparse parity as a sandbox, we identify an implicit curriculum as one mechanism through which progressive distillation accelerates the student's learning. This curriculum is available only through the intermediate checkpoints but not the final converged one, and imparts both empirical acceleration and a provable sample complexity benefit to the student. We then extend our investigation to Transformers trained on probabilistic context-free grammars (PCFGs) and real-world pre-training datasets (Wikipedia and Books). Through probing the teacher model, we identify an analogous implicit curriculum where the model progressively learns features that capture longer context. Our theoretical and empirical findings on sparse parity, complemented by empirical observations on more complex tasks, highlight the benefit of progressive distillation via implicit curriculum across setups.

cs.LG↗

arXiv2023

TinyGSM: achieving >80% on GSM8k with small language models

Small-scale models offer various computational advantages, and yet to which extent size is critical for problem-solving abilities remains an open question. Specifically for solving grade school math, the smallest model size so far required to break the 80\% barrier on the GSM8K benchmark remains to be 34B. Our work studies how high-quality datasets may be the key for small language models to acquire mathematical reasoning. We introduce \texttt{TinyGSM}, a synthetic dataset of 12.3M grade school math problems paired with Python solutions, generated fully by GPT-3.5. After finetuning on \texttt{TinyGSM}, we find that a duo of a 1.3B generation model and a 1.3B verifier model can achieve 81.5\% accuracy, outperforming existing models that are orders of magnitude larger. This also rivals the performance of the GPT-3.5 ``teacher'' model (77.4\%), from which our model's training data is generated. Our approach is simple and has two key components: 1) the high-quality dataset \texttt{TinyGSM}, 2) the use of a verifier, which selects the final outputs from multiple candidate generations.

cs.LG↗

arXiv2023

Transformers are uninterpretable with myopic methods: a case study with bounded Dyck grammars

Interpretability methods aim to understand the algorithm implemented by a trained model (e.g., a Transofmer) by examining various aspects of the model, such as the weight matrices or the attention patterns. In this work, through a combination of theoretical results and carefully controlled experiments on synthetic data, we take a critical view of methods that exclusively focus on individual parts of the model, rather than consider the network as a whole. We consider a simple synthetic setup of learning a (bounded) Dyck language. Theoretically, we show that the set of models that (exactly or approximately) solve this task satisfy a structural characterization derived from ideas in formal languages (the pumping lemma). We use this characterization to show that the set of optima is qualitatively rich; in particular, the attention pattern of a single layer can be ``nearly randomized'', while preserving the functionality of the network. We also show via extensive experiments that these constructions are not merely a theoretical artifact: even after severely constraining the architecture of the model, vastly different solutions can be reached via standard training. Thus, interpretability claims based on inspecting individual heads or weight matrices in the Transformer can be misleading.

cs.LG↗

arXiv2023

Understanding Augmentation-based Self-Supervised Representation Learning via RKHS Approximation and Regression

Data augmentation is critical to the empirical success of modern self-supervised representation learning, such as contrastive learning and masked language modeling. However, a theoretical understanding of the exact role of augmentation remains limited. Recent work has built the connection between self-supervised learning and the approximation of the top eigenspace of a graph Laplacian operator, suggesting that learning a linear probe atop such representation can be connected to RKHS regression. Building on this insight, this work delves into a statistical analysis of augmentation-based pretraining. Starting from the isometry property, a geometric characterization of the target function given by the augmentation, we disentangle the effects of the model and the augmentation, and prove two generalization bounds that are free of model complexity. Our first bound works for an arbitrary encoder, where the prediction error is decomposed as the sum of an estimation error incurred by fitting a linear probe with RKHS regression, and an approximation error entailed by RKHS approximation. Our second bound specifically addresses the case where the encoder is near-optimal, that is it approximates the top-d eigenspace of the RKHS induced by the augmentation. A key ingredient in our analysis is the augmentation complexity, which we use to quantitatively compare different augmentations and analyze their impact on downstream performance.

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arXiv2023

Exposing Attention Glitches with Flip-Flop Language Modeling

Why do large language models sometimes output factual inaccuracies and exhibit erroneous reasoning? The brittleness of these models, particularly when executing long chains of reasoning, currently seems to be an inevitable price to pay for their advanced capabilities of coherently synthesizing knowledge, pragmatics, and abstract thought. Towards making sense of this fundamentally unsolved problem, this work identifies and analyzes the phenomenon of attention glitches, in which the Transformer architecture's inductive biases intermittently fail to capture robust reasoning. To isolate the issue, we introduce flip-flop language modeling (FFLM), a parametric family of synthetic benchmarks designed to probe the extrapolative behavior of neural language models. This simple generative task requires a model to copy binary symbols over long-range dependencies, ignoring the tokens in between. We find that Transformer FFLMs suffer from a long tail of sporadic reasoning errors, some of which we can eliminate using various regularization techniques. Our preliminary mechanistic analyses show why the remaining errors may be very difficult to diagnose and resolve. We hypothesize that attention glitches account for (some of) the closed-domain hallucinations in natural LLMs.

cs.LG↗

arXiv2022

Transformers Learn Shortcuts to Automata

Algorithmic reasoning requires capabilities which are most naturally understood through recurrent models of computation, like the Turing machine. However, Transformer models, while lacking recurrence, are able to perform such reasoning using far fewer layers than the number of reasoning steps. This raises the question: what solutions are learned by these shallow and non-recurrent models? We find that a low-depth Transformer can represent the computations of any finite-state automaton (thus, any bounded-memory algorithm), by hierarchically reparameterizing its recurrent dynamics. Our theoretical results characterize shortcut solutions, whereby a Transformer with $o(T)$ layers can exactly replicate the computation of an automaton on an input sequence of length $T$. We find that polynomial-sized $O(\log T)$-depth solutions always exist; furthermore, $O(1)$-depth simulators are surprisingly common, and can be understood using tools from Krohn-Rhodes theory and circuit complexity. Empirically, we perform synthetic experiments by training Transformers to simulate a wide variety of automata, and show that shortcut solutions can be learned via standard training. We further investigate the brittleness of these solutions and propose potential mitigations.

cs.LG↗

arXiv2022

Masked prediction tasks: a parameter identifiability view

The vast majority of work in self-supervised learning, both theoretical and empirical (though mostly the latter), have largely focused on recovering good features for downstream tasks, with the definition of "good" often being intricately tied to the downstream task itself. This lens is undoubtedly very interesting, but suffers from the problem that there isn't a "canonical" set of downstream tasks to focus on -- in practice, this problem is usually resolved by competing on the benchmark dataset du jour. In this paper, we present an alternative lens: one of parameter identifiability. More precisely, we consider data coming from a parametric probabilistic model, and train a self-supervised learning predictor with a suitably chosen parametric form. Then, we ask whether we can read off the ground truth parameters of the probabilistic model from the optimal predictor. We focus on the widely used self-supervised learning method of predicting masked tokens, which is popular for both natural languages and visual data. While incarnations of this approach have already been successfully used for simpler probabilistic models (e.g. learning fully-observed undirected graphical models), we focus instead on latent-variable models capturing sequential structures -- namely Hidden Markov Models with both discrete and conditionally Gaussian observations. We show that there is a rich landscape of possibilities, out of which some prediction tasks yield identifiability, while others do not. Our results, borne of a theoretical grounding of self-supervised learning, could thus potentially beneficially inform practice. Moreover, we uncover close connections with uniqueness of tensor rank decompositions -- a widely used tool in studying identifiability through the lens of the method of moments.

cs.LG↗

arXiv2021

Analyzing and Improving the Optimization Landscape of Noise-Contrastive Estimation

Noise-contrastive estimation (NCE) is a statistically consistent method for learning unnormalized probabilistic models. It has been empirically observed that the choice of the noise distribution is crucial for NCE's performance. However, such observations have never been made formal or quantitative. In fact, it is not even clear whether the difficulties arising from a poorly chosen noise distribution are statistical or algorithmic in nature. In this work, we formally pinpoint reasons for NCE's poor performance when an inappropriate noise distribution is used. Namely, we prove these challenges arise due to an ill-behaved (more precisely, flat) loss landscape. To address this, we introduce a variant of NCE called "eNCE" which uses an exponential loss and for which normalized gradient descent addresses the landscape issues provably when the target and noise distributions are in a given exponential family.

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arXiv2021

Contrastive learning of strong-mixing continuous-time stochastic processes

Contrastive learning is a family of self-supervised methods where a model is trained to solve a classification task constructed from unlabeled data. It has recently emerged as one of the leading learning paradigms in the absence of labels across many different domains (e.g. brain imaging, text, images). However, theoretical understanding of many aspects of training, both statistical and algorithmic, remain fairly elusive. In this work, we study the setting of time series -- more precisely, when we get data from a strong-mixing continuous-time stochastic process. We show that a properly constructed contrastive learning task can be used to estimate the transition kernel for small-to-mid-range intervals in the diffusion case. Moreover, we give sample complexity bounds for solving this task and quantitatively characterize what the value of the contrastive loss implies for distributional closeness of the learned kernel. As a byproduct, we illuminate the appropriate settings for the contrastive distribution, as well as other hyperparameters in this setup.

stat.ML↗

arXiv2020

Spatiotemporal Relationship Reasoning for Pedestrian Intent Prediction

Reasoning over visual data is a desirable capability for robotics and vision-based applications. Such reasoning enables forecasting of the next events or actions in videos. In recent years, various models have been developed based on convolution operations for prediction or forecasting, but they lack the ability to reason over spatiotemporal data and infer the relationships of different objects in the scene. In this paper, we present a framework based on graph convolution to uncover the spatiotemporal relationships in the scene for reasoning about pedestrian intent. A scene graph is built on top of segmented object instances within and across video frames. Pedestrian intent, defined as the future action of crossing or not-crossing the street, is a very crucial piece of information for autonomous vehicles to navigate safely and more smoothly. We approach the problem of intent prediction from two different perspectives and anticipate the intention-to-cross within both pedestrian-centric and location-centric scenarios. In addition, we introduce a new dataset designed specifically for autonomous-driving scenarios in areas with dense pedestrian populations: the Stanford-TRI Intent Prediction (STIP) dataset. Our experiments on STIP and another benchmark dataset show that our graph modeling framework is able to predict the intention-to-cross of the pedestrians with an accuracy of 79.10% on STIP and 79.28% on \rev{Joint Attention for Autonomous Driving (JAAD) dataset up to one second earlier than when the actual crossing happens. These results outperform the baseline and previous work. Please refer to http://stip.stanford.edu/ for the dataset and code.

cs.CV↗

arXiv2018

Learning to Decompose and Disentangle Representations for Video Prediction

Our goal is to predict future video frames given a sequence of input frames. Despite large amounts of video data, this remains a challenging task because of the high-dimensionality of video frames. We address this challenge by proposing the Decompositional Disentangled Predictive Auto-Encoder (DDPAE), a framework that combines structured probabilistic models and deep networks to automatically (i) decompose the high-dimensional video that we aim to predict into components, and (ii) disentangle each component to have low-dimensional temporal dynamics that are easier to predict. Crucially, with an appropriately specified generative model of video frames, our DDPAE is able to learn both the latent decomposition and disentanglement without explicit supervision. For the Moving MNIST dataset, we show that DDPAE is able to recover the underlying components (individual digits) and disentanglement (appearance and location) as we would intuitively do. We further demonstrate that DDPAE can be applied to the Bouncing Balls dataset involving complex interactions between multiple objects to predict the video frame directly from the pixels and recover physical states without explicit supervision.

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