63 accepted papers
Vericoding refers to the generation of formally verified code from rigorous specifications. Recent AI models show promise in vericoding, but a unified methodology for cross-paradigm evaluation is lacking. Existing benchmarks test only an individual language/tool (e.g., Dafny, Verus, and Lean) and ea…
Automated theorem proving (ATP) --- the task of generating a proof that passes automated proof verification given a math question in formal language --- is a critical challenge at the intersection of mathematics and Artificial Intelligence (AI). We introduce Goedel-Prover-V2, a family of two languag…
Reasoning training incentivizes LLMs to produce long chains of thought (long CoT), which among other things, allows them to explore solution strategies with self-checking. This results in higher accuracy, but inflates context length, token/compute cost, and answer latency. We ask: Can current models…
Language models often show little to no improvement (i.e., “saturation”) when trained via vanilla supervised fine-tuning (SFT) on data similar to what they saw in their training set (e.g., MATH). We introduce a new fine-tuning strategy, STAT, to train such a student model by using the metacognition…
Reward models are key to language model post-training and inference pipelines. Conveniently, recent work showed that every language model defines an implicit reward model (IM-RM), without requiring any architectural changes. However, such IM-RMs tend to generalize worse, especially out-of-distributi…
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 syste…
LLM-based formal proof assistants (e.g., in Lean) hold great promise for automating mathematical discovery. But beyond syntactic correctness, do these systems truly understand mathematical structure as humans do? We investigate this question in context of mathematical inequalities---specifically the…
We introduce INSTRUCT-SKILLMIX, an automated approach for creating diverse, high quality SFT data for instruction-following. The pipeline involves two stages, each leveraging an existing powerful LLM: (1) Skill extraction: uses the LLM to extract core “skills” for instruction-following by directly p…
Recent reports claim that large language models (LLMs) now outperform elite humans in competitive programming. Drawing on knowledge from a group of medalists in international algorithmic contests, we revisit this claim, examining how LLMs differ from human experts and where limitations still remain.…
We formalize a new concept for LLMs, **context-enhanced learning**. It involves standard gradient-based learning on text except that the context is enhanced with additional data on which no auto-regressive gradients are computed. This setting is a gradient-based analog of usual in-context learning (…
Machine unlearning algorithms are increasingly important as legal concerns arise around the provenance of training data, but verifying the success of unlearning is often difficult. Provable guarantees for unlearning are often limited to supervised learning settings. In this paper, we provide the fir…
Direct Preference Optimization (DPO) and its variants are increasingly used for aligning language models with human preferences. Although these methods are designed to teach a model to generate preferred responses more frequently relative to dispreferred responses, prior work has observed that the…
Weak-to-Strong Generalization (Burns et al.,2024) is the phenomenon whereby a strong student, say GPT-4, learns a task from a weak teacher, say GPT-2, and ends up significantly outperforming the teacher. We show that this phenomenon does not require a complex and pretrained learner like GPT-4, can a…
The success of Reinforcement Learning from Human Feedback (RLHF) critically depends on the quality of the reward model. However, while this quality is primarily evaluated through accuracy, it remains unclear whether accuracy fully captures what makes a reward model an effective teacher. We address t…
In distributed deep learning with data parallelism, synchronizing gradients at each training step can cause a huge communication overhead, especially when many nodes work together to train large models. Local gradient methods, such as Local SGD, address this issue by allowing workers to compute lo…
As large language models (LLMs) become increasingly advanced, their ability to exhibit compositional generalization---the capacity to combine learned skills in novel ways not encountered during training---has garnered significant attention. This type of generalization, particularly in scenarios beyo…
Chart understanding plays a pivotal role when applying Multimodal Large Language Models (MLLMs) to real-world tasks such as analyzing scientific papers or financial reports. However, existing datasets often focus on oversimplified and homogeneous charts with template-based questions, leading to an o…
Compositionality is a critical capability in Text-to-Image (T2I) models, as it reflects their ability to understand and combine multiple concepts from text descriptions. Existing evaluations of compositional capability rely heavily on human-designed text prompts or fixed templates, limiting their di…
Public LLMs such as the Llama 2-Chat underwent alignment training and were considered safe. Recently Qi et al. (2024) reported that even benign fine-tuning on seemingly safe datasets can give rise to unsafe behaviors in the models. The current paper is about methods and best practices to mitigate su…
Instruction tuning has unlocked powerful capabilities in large language models (LLMs), using combined datasets to develop general-purpose chatbots. However, real-world applications often require a specialized suite of skills (e.g., reasoning). The challenge lies in identifying the most relevant data…
NLP has recently made exciting progress toward training language models (LMs) with strong scientific problem-solving skills. However, model development has not focused on real-life use-cases of LMs for science, including applications in education that require processing long scientific documents. To…
With LLMs shifting their role from statistical modeling of language to serving as general-purpose AI agents, how should LLM evaluations change? Arguably, a key ability of an AI agent is to flexibly combine, as needed, the basic skills it has learned. The capability to combine skills plays an importa…
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…
It has become standard to solve NLP tasks by fine-tuning pre-trained language models (LMs), especially in low-data settings. There is minimal theoretical understanding of empirical success, e.g., why fine-tuning a model with $10^8$ or more parameters on a couple dozen training points does not result…
Fine-tuning language models (LMs) has yielded success on diverse downstream tasks, but as LMs grow in size, backpropagation requires a prohibitively large amount of memory. Zeroth-order (ZO) methods can in principle estimate gradients using only two forward passes but are theorized to be catastrophi…
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 int…
Influence functions estimate effect of individual data points on predictions of the model on test data and were adapted to deep learning in \cite{koh2017understanding}. They have been used for detecting data poisoning, detecting helpful and harmful examples, influence of groups of datapoints, etc. R…
Local SGD is a communication-efficient variant of SGD for large-scale training, where multiple GPUs perform SGD independently and average the model parameters periodically. It has been recently observed that Local SGD can not only achieve the design goal of reducing the communication overhead but al…
As part of the effort to understand implicit bias of gradient descent in overparametrized models, several results have shown how the training trajectory on the overparametrized model can be understood as mirror descent on a different objective. The main result here is a complete characterization of…
Saliency methods compute heat maps that highlight portions of an input that were most important for the label assigned to it by a deep net. Evaluations of saliency methods convert this heat map into a new masked input by retaining the $k$ highest-ranked pixels of the original input and replacing the…
Research on generalization bounds for deep networks seeks to give ways to predict test error using just the training dataset and the network parameters. While generalization bounds can give many insights about architecture design, training algorithms etc., what they do not currently do is yield good…
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 RMSpro…
Contrastive learning is a popular form of self-supervised learning that encourages augmentations (views) of the same input to have more similar representations compared to augmentations of different inputs. Recent attempts to theoretically explain the success of contrastive learning on downstream cl…
Deep learning experiments by \citet{cohen2021gradient} using deterministic Gradient Descent (GD) revealed an
Normalization layers (e.g., Batch Normalization, Layer Normalization) were introduced to help with optimization difficulties in very deep nets, but they clearly also help generalization, even in not-so-deep nets. Motivated by the long-held belief that flatter minima lead to better generalization, th…
Understanding the implicit bias of Stochastic Gradient Descent (SGD) is one of the key challenges in deep learning, especially for overparametrized models, where the local minimizers of the loss function $L$ can form a manifold. Intuitively, with a sufficiently small learning rate $\eta$, SGD tracks…
Autoregressive language models, pretrained using large text corpora to do well on next word prediction, have been successful at solving many downstream tasks, even with zero-shot usage. However, there is little theoretical understanding of this success. This paper initiates a mathematical study of t…
Gradient inversion attack (or input recovery from gradient) is an emerging threat to the security and privacy preservation of Federated learning, whereby malicious eavesdroppers or participants in the protocol can recover (partially) the clients' private data. This paper evaluates existing attacks a…
The generalization mystery of overparametrized deep nets has motivated efforts to understand how gradient descent (GD) converges to low-loss solutions that generalize well. Real-life neural networks are initialized from small random values and trained with cross-entropy loss for classification (unli…
It is generally recognized that finite learning rate (LR), in contrast to infinitesimal LR, is important for good generalization in real-life deep nets. Most attempted explanations propose approximating finite-LR SGD with Itô Stochastic Differential Equations (SDEs), but formal justification for thi…
Convolutional neural networks often dominate fully-connected counterparts in generalization performance, especially on image classification tasks. This is often explained in terms of \textquotedblleft better inductive bias.\textquotedblright\ However, this has not been made mathematically rigorous,…
One popular trend in meta-learning is to learn from many training tasks a common initialization that a gradient-based method can use to solve a new task with few samples. The theory of meta-learning is still in its early stages, with several recent learning-theoretic analyses of methods such as Rept…
Intriguing empirical evidence exists that deep learning can work well with exotic schedules for varying the learning rate. This paper suggests that the phenomenon may be due to Batch Normalization or BN(Ioffe & Szegedy, 2015), which is ubiq- uitous and provides benefits in optimization and generaliz…
Recent research shows that the following two models are equivalent: (a) infinitely wide neural networks (NNs) trained under l2 loss by gradient descent with infinitesimally small learning rate (b) kernel regression with respect to so-called Neural Tangent Kernels (NTKs) (Jacot et al., 2018). An effi…
How can multiple distributed entities train a shared deep net on their private data while protecting data privacy? This paper introduces InstaHide, a simple encryption of training images. Encrypted images can be used in standard deep learning pipelines (PyTorch, Federated Learning etc.) with no addi…
Adversarial training is a popular method to give neural nets robustness against adversarial perturbations. In practice adversarial training leads to low robust training loss. However, a rigorous explanation for why this happens under natural conditions is still missing. Recently a convergence theory…
A common strategy in modern learning systems is to learn a representation that is useful for many tasks, a.k.a. representation learning. We study this strategy in the imitation learning setting for Markov decision processes (MDPs) where multiple experts’ trajectories are available. We formulate repr…
Recent works (e.g., (Li \& Arora, 2020)) suggest that the use of popular normalization schemes (including Batch Normalization) in today's deep learning can move it far from a traditional optimization viewpoint, e.g., use of exponentially increasing learning rates. The current paper highlights other…
We analyze speed of convergence to global optimum for gradient descent training a deep linear neural network by minimizing the L2 loss over whitened data. Convergence at a linear rate is guaranteed when the following hold: (i) dimensions of hidden layers are at least the minimum of the input and ou…
Recent empirical works have successfully used unlabeled data to learn feature representations that are broadly useful in downstream classification tasks. Several of these methods are reminiscent of the well-known word2vec embedding algorithm: leveraging availability of pairs of semantically “similar…
Mode connectivity is a surprising phenomenon in the loss landscape of deep nets. Optima---at least those discovered by gradient-based optimization---turn out to be connected by simple paths on which the loss function is almost constant. Often, these paths can be chosen to be piece-wise linear, with…
Recent works have cast some light on the mystery of why deep nets fit any data and generalize despite being very overparametrized. This paper analyzes training and generalization for a simple 2-layer ReLU net with random initialization, and provides the following improvements over recent works: (i)…
Efforts to understand the generalization mystery in deep learning have led to the belief that gradient-based optimization induces a form of implicit regularization, a bias towards models of low "complexity." We study the implicit regularization of gradient descent over deep linear neural networks f…
How well does a classic deep net architecture like AlexNet or VGG19 classify on a standard dataset such as CIFAR-10 when its “width”— namely, number of channels in convolutional layers, and number of nodes in fully-connected internal layers — is allowed to increase to infinity? Such questions have c…
Batch Normalization (BN) has become a cornerstone of deep learning across diverse architectures, appearing to help optimization as well as generalization. While the idea makes intuitive sense, theoretical analysis of its effectiveness has been lacking. Here theoretical support is provided for one of…
Low-dimensional vector embeddings, computed using LSTMs or simpler techniques, are a popular approach for capturing the “meaning” of text and a form of unsupervised learning useful for downstream tasks. However, their power is not theoretically understood. The current paper derives formal understand…
Do GANS (Generative Adversarial Nets) actually learn the target distribution? The foundational paper of Goodfellow et al. (2014) suggested they do, if they were given sufficiently large deep nets, sample size, and computation time. A recent theoretical analysis in Arora et al. (2017) raised doubts w…
Conventional wisdom in deep learning states that increasing depth improves expressiveness but complicates optimization. This paper suggests that, sometimes, increasing depth can speed up optimization. The effect of depth on optimization is decoupled from expressiveness by focusing on settings where…
Deep nets generalize well despite having more parameters than the number of training samples. Recent works try to give an explanation using PAC-Bayes and Margin-based analyses, but do not as yet result in sample complexity bounds better than naive parameter counting. The current paper shows generali…
We study the control of symmetric linear dynamical systems with unknown dynamics and a hidden state. Using a recent spectral filtering technique for concisely representing such systems in a linear basis, we formulate optimal control in this setting as a convex program. This approach eliminates the n…
The success of neural network methods for computing word embeddings has motivated methods for generating semantic embeddings of longer pieces of text, such as sentences and paragraphs. Surprisingly, Wieting et al (ICLR'16) showed that such complicated methods are outperformed, especially in out-of-d…
It is shown that training of generative adversarial network (GAN) may not have good generalization properties; e.g., training may appear successful but the trained distribution may be far from target distribution in standard metrics. However, generalization does occur for a weaker metric called neur…
Recently, there has been considerable progress on designing algorithms with provable guarantees —typically using linear algebraic methods—for parameter learning in latent variable models. Designing provable algorithms for inference has proved more difficult. Here we take a first step towards provabl…