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Deep Learning · Large Language Models

Aleksandar Petrov, Phil Torr, Adel Bibi

Despite the widespread adoption of prompting, prompt tuning and prefix-tuning of transformer models, our theoretical understanding of these fine-tuning methods remains limited. A key question is whether one can arbitrarily modify the behavior of a pretrained model by prompting or prefix-tuning it. Formally, whether prompting and prefix-tuning a pretrained model can universally approximate sequence-to-sequence functions. This paper answers in the affirmative and demonstrates that much smaller pretrained models than previously thought can be universal approximators when prefixed. In fact, prefix-tuning a single attention head is sufficient to approximate any continuous function making the attention mechanism uniquely suited for universal approximation. Moreover, any sequence-to-sequence function can be approximated by prefixing a transformer with depth linear in the sequence length. Beyond these density-type results, we also offer Jackson-type bounds on the length of the prefix needed to approximate a function to a desired precision.

Reinforcement Learning · Batch/Offline

Marek Petrik, Guy Tennenholtz, Mohammad Ghavamzadeh

We study how to make decisions that minimize Bayesian regret in offline linear bandits. Prior work suggests that one must take actions with maximum lower confidence bound (LCB) on their reward. We argue that reliance on LCB is inherently flawed in this setting and propose a new algorithm that directly minimizes upper-bounds on the Bayesian regret using efficient conic optimization solvers. Our bounds build heavily on new connections to monetary risk measures. Proving a matching lower-bound, we show that our upper-bounds are tight, and by minimizing them we are guaranteed to outperform the LCB approach. Our numerical results on synthetic domains confirm that our approach is superior to maximizing LCB.

Deep Learning · Everything Else

Adeel Pervez, Francesco Locatello, Efstratios Gavves

This paper presents *Mechanistic Neural Networks*, a neural network design for machine learning applications in the sciences. It incorporates a new *Mechanistic Block* in standard architectures to explicitly learn governing differential equations as representations, revealing the underlying dynamics of data and enhancing interpretability and efficiency in data modeling. Central to our approach is a novel *Relaxed Linear Programming Solver* (NeuRLP) inspired by a technique that reduces solving linear ODEs to solving linear programs. This integrates well with neural networks and surpasses the limitations of traditional ODE solvers enabling scalable GPU parallel processing. Overall, Mechanistic Neural Networks demonstrate their versatility for scientific machine learning applications, adeptly managing tasks from equation discovery to dynamic systems modeling. We prove their comprehensive capabilities in analyzing and interpreting complex scientific data across various applications, showing significant performance against specialized state-of-the-art methods. Source code is available at https://github.com/alpz/mech-nn.

Deep Learning · Generative Models and Autoencoders

Frank Permenter, Chenyang Yuan

Denoising is intuitively related to projection. Indeed, under the manifold hypothesis, adding random noise is approximately equivalent to orthogonal perturbation. Hence, learning to denoise is approximately learning to project. In this paper, we use this observation to interpret denoising diffusion models as approximate gradient descent applied to the Euclidean distance function. We then provide straight-forward convergence analysis of the DDIM sampler under simple assumptions on the projection error of the denoiser. Finally, we propose a new gradient-estimation sampler, generalizing DDIM using insights from our theoretical results. In as few as 5-10 function evaluations, our sampler achieves state-of-the-art FID scores on pretrained CIFAR-10 and CelebA models and can generate high quality samples on latent diffusion models.

Social Aspects · Everything Else

Juan Perdomo

Algorithmic predictions are increasingly used to inform the allocations of goods and interventions in the public sphere. In these domains, predictions serve as a means to an end. They provide stakeholders with insights into likelihood of future events as a means to improve decision making quality, and enhance social welfare. However, if maximizing welfare is the ultimate goal, prediction is only a small piece of the puzzle. There are various other policy levers a social planner might pursue in order to improve bottom-line outcomes, such as expanding access to available goods, or increasing the effect sizes of interventions. Given this broad range of design decisions, a basic question to ask is: What is the relative value of prediction in algorithmic decision making? How do the improvements in welfare arising from better predictions compare to those of other policy levers? The goal of our work is to initiate the formal study of these questions. Our main results are theoretical in nature. We identify simple, sharp conditions determining the relative value of prediction vis-à-vis expanding access, within several statistical models that are popular amongst quantitative social scientists. Furthermore, we illustrate how these theoretical insights can guide the design of algorithmic decision making systems in practice.

Reinforcement Learning · Multi-agent

Johan Peralez, Aurélien Delage, Olivier Buffet, Jilles Dibangoye

A recent theory shows that a multi-player decentralized partially observable Markov decision process can be transformed into an equivalent single-player game, enabling the application of Bellman's principle of optimality to solve the single-player game by breaking it down into single-stage subgames. However, this approach entangles the decision variables of all players at each single-stage subgame, resulting in backups with a double-exponential complexity. This paper demonstrates how to disentangle these decision variables while maintaining optimality under hierarchical information sharing, a prominent management style in our society. To achieve this, we apply the principle of optimality to solve any single-stage subgame by breaking it down further into smaller subgames, enabling us to make single-player decisions at a time. Our approach reveals that extensive-form games always exist with solutions to a single-stage subgame, significantly reducing time complexity. Our experimental results show that the algorithms leveraging these findings can scale up to much larger multi-player games without compromising optimality.

Ankit Pensia

We study the algorithmic problem of sparse mean estimation in the presence of adversarial outliers. Specifically, the algorithm observes a *corrupted* set of samples from $\mathcal{N}(\mu,\mathbf{I}_d)$, where the unknown mean $\mu \in \mathbb{R}^d$ is constrained to be $k$-sparse. A series of prior works has developed efficient algorithms for robust sparse mean estimation with sample complexity $\mathrm{poly}(k,\log d, 1/\epsilon)$ and runtime $d^2 \mathrm{poly}(k,\log d,1/\epsilon)$, where $\epsilon$ is the fraction of contamination. In particular, the fastest runtime of existing algorithms is quadratic in the dimension, which can be prohibitive in high dimensions. This quadratic barrier in the runtime stems from the reliance of these algorithms on the sample covariance matrix, which is of size $d^2$. Our main contribution is an algorithm for robust sparse mean estimation which runs in _subquadratic_ time using $\mathrm{poly}(k,\log d,1/\epsilon)$ samples. Our results build on algorithmic advances in detecting weak correlations, a generalized version of the light-bulb problem by Valiant (2015).

Probabilistic Methods · Monte Carlo and Sampling Methods

Xinyu Peng, Ziyang Zheng, Wenrui Dai, Nuoqian Xiao, Chenglin Li, Junni Zou, Hongkai Xiong

Recent diffusion models provide a promising zero-shot solution to noisy linear inverse problems without retraining for specific inverse problems. In this paper, we reveal that recent methods can be uniformly interpreted as employing a Gaussian approximation with hand-crafted isotropic covariance for the intractable denoising posterior to approximate the conditional posterior mean. Inspired by this finding, we propose to improve recent methods by using more principled covariance determined by maximum likelihood estimation. To achieve posterior covariance optimization without retraining, we provide general plug-and-play solutions based on two approaches specifically designed for leveraging pre-trained models with and without reverse covariance. We further propose a scalable method for learning posterior covariance prediction based on representation with orthonormal basis. Experimental results demonstrate that the proposed methods significantly enhance reconstruction performance without requiring hyperparameter tuning.

Social Aspects · Trustworthy Machine Learning

Hongyi Peng, Han Yu, Xiaoli Tang, Xiaoxiao Li

Federated learning (FL) enables collaborative machine learning across distributed data owners, but data heterogeneity poses a challenge for model calibration. While prior work focused on improving accuracy for non-iid data, calibration remains under-explored. This study reveals existing FL aggregation approaches lead to sub-optimal calibration, and theoretical analysis shows despite constraining variance in clients’ label distributions, global calibration error is still asymptotically lower bounded. To address this, we propose a novel Federated Calibration (FedCal) approach, emphasizing both local and global calibration. It leverages client-specific scalers for local calibration to effectively correct output misalignment without sacrificing prediction accuracy. These scalers are then aggregated via weight averaging to generate a global scaler, minimizing the global calibration error. Extensive experiments demonstrate that FedCal significantly outperforms the best-performing baseline, reducing global calibration error by 47.66% on average.

Dezhi Peng, Zhenhua Yang, Jiaxin Zhang, Chongyu Liu, Yongxin Shi, Kai Ding, Fengjun Guo, Lianwen Jin

Existing optical character recognition (OCR) methods rely on task-specific designs with divergent paradigms, architectures, and training strategies, which significantly increases the complexity of research and maintenance and hinders the fast deployment in applications. To this end, we propose UPOCR, a simple-yet-effective generalist model for Unified Pixel-level OCR interface. Specifically, the UPOCR unifies the paradigm of diverse OCR tasks as image-to-image transformation and the architecture as a vision Transformer (ViT)-based encoder-decoder with learnable task prompts. The prompts push the general feature representations extracted by the encoder towards task-specific spaces, endowing the decoder with task awareness. Moreover, the model training is uniformly aimed at minimizing the discrepancy between the predicted and ground-truth images regardless of the inhomogeneity among tasks. Experiments are conducted on three pixel-level OCR tasks including text removal, text segmentation, and tampered text detection. Without bells and whistles, the experimental results showcase that the proposed method can simultaneously achieve state-of-the-art performance on three tasks with a unified single model, which provides valuable strategies and insights for future research on generalist OCR models. Code is available at https://github.com/shannanyinxiang/UPOCR.

Reinforcement Learning

Andi Peng, Yuying Sun, Tianmin Shu, David Abel

Humans use context to specify preferences over behaviors, i.e. their reward functions. Yet, algorithms for inferring reward models from preference data do not take this social learning view into account. Inspired by pragmatic human communication, we study how to extract fine-grained data regarding why an example is preferred that is useful for learning an accurate reward model. We propose to enrich preference queries to ask both (1) which features of a given example are preferable in addition to (2) comparisons between objects. We derive an approach for learning from these feature-level preferences, both for cases where users specify which features are reward-relevant, and when users do not. We evaluate our approach on linear bandit settings in both visual and language-based domains. Results support the efficiency of our approach in quickly converging to accurate rewards with less comparisons vs. example-only labels. Finally, we validate the real-world applicability with a behavioral experiment on a mushroom foraging task. Our findings suggest that incorporating pragmatic feature preferences is a promising approach for more efficient user-aligned reward learning.

Social Aspects · Fairness, Equity, Justice and Safety

Duo Peng, Qiuhong Ke, Jun Liu

Text-to-Image (T2I) models have raised security concerns due to their potential to generate inappropriate or harmful images. In this paper, we propose UPAM, a novel framework that investigates the robustness of T2I models from the attack perspective. Unlike most existing attack methods that focus on deceiving textual defenses, UPAM aims to deceive both textual and visual defenses in T2I models. UPAM enables gradient-based optimization, offering greater effectiveness and efficiency than previous methods. Given that T2I models might not return results due to defense mechanisms, we introduce a Sphere-Probing Learning (SPL) scheme to support gradient optimization even when no results are returned. Additionally, we devise a Semantic-Enhancing Learning (SEL) scheme to finetune UPAM for generating target-aligned images. Our framework also ensures attack stealthiness. Extensive experiments demonstrate UPAM's effectiveness and efficiency.

Deep Learning

Bo Peng, zhen fang, Guangquan Zhang, Jie Lu

Knowledge distillation (KD) provides an efficient framework for transferring knowledge from a teacher model to a student model by aligning their predictive distributions. The existing KD methods adopt the same strategy as the teacher to formulate the student's predictive distribution. However, employing the same distribution-modeling strategy typically causes sub-optimal knowledge transfer due to the discrepancy in model capacity between teacher and student models. Designing student-friendly teachers contributes to alleviating the capacity discrepancy, while it requires either complicated or student-specific training schemes. To cast off this dilemma, we propose to introduce an auxiliary variable to promote the ability of the student to model predictive distribution. The auxiliary variable is defined to be related to target variables, which will boost the model prediction. Specifically, we reformulate the predictive distribution with the auxiliary variable, deriving a novel objective function of KD. Theoretically, we provide insights to explain why the proposed objective function can outperform the existing KD methods. Experimentally, we demonstrate that the proposed objective function can considerably and consistently outperform existing KD methods.

Deep Learning

Amit Peleg, Matthias Hein

Neural networks typically generalize well when fitting the data perfectly, even though they are heavily overparameterized. Many factors have been pointed out as the reason for this phenomenon, including an implicit bias of stochastic gradient descent (SGD) and a possible simplicity bias arising from the neural network architecture. The goal of this paper is to disentangle the factors that influence generalization stemming from optimization and architectural choices by studying *random* and *SGD-optimized* networks that achieve zero training error. We experimentally show, in the low sample regime, that overparameterization in terms of increasing width is beneficial for generalization, and this benefit is due to the bias of SGD and not due to an architectural bias. In contrast, for increasing depth, overparameterization is detrimental for generalization, but random and SGD-optimized networks behave similarly, so this can be attributed to an architectural bias.

Deep Learning · Large Language Models

Zehua Pei, Huiling Zhen, Mingxuan Yuan, Yu Huang, Bei Yu

Due to the growing complexity of modern Integrated Circuits (ICs), there is a need for automated circuit design methods. Recent years have seen increasing research in hardware design language generation to facilitate the design process. In this work, we propose a Verilog generation framework, BetterV, which fine-tunes large language models (LLMs) on processed domain-specific datasets and incorporates generative discriminators for guidance on particular design demands. Verilog modules are collected, filtered, and processed from the internet to form a clean and abundant dataset. Instruct-tuning methods are specially designed to fine-tune the LLMs to understand knowledge about Verilog. Furthermore, data are augmented to enrich the training set and are also used to train a generative discriminator on particular downstream tasks, providing guidance for the LLMs to optimize Verilog implementation. BetterV has the ability to generate syntactically and functionally correct Verilog, outperforming GPT-4 on the VerilogEval benchmark. With the help of task-specific generative discriminators, BetterV achieves remarkable improvements on various electronic design automation (EDA) downstream tasks, including netlist node reduction for synthesis and verification runtime reduction with Boolean Satisfiability (SAT) solving.

Deep Learning · Theory

Edward Pearce-Crump, William J. Knottenbelt

Permutation equivariant neural networks are typically used to learn from data that lives on a graph. However, for any graph $G$ that has $n$ vertices, using the symmetric group $S_n$ as its group of symmetries does not take into account the relations that exist between the vertices. Given that the actual group of symmetries is the automorphism group Aut$(G)$, we show how to construct neural networks that are equivariant to Aut$(G)$ by obtaining a full characterisation of the learnable, linear, Aut$(G)$-equivariant functions between layers that are some tensor power of $\mathbb{R}^{n}$. In particular, we find a spanning set of matrices for these layer functions in the standard basis of $\mathbb{R}^{n}$. This result has important consequences for learning from data whose group of symmetries is a finite group because a theorem by Frucht (1938) showed that any finite group is isomorphic to the automorphism group of a graph.

Reinforcement Learning · Deep RL

Brahma Pavse, Matthew Zurek, Yudong Chen, Qiaomin Xie, Josiah Hanna

In many reinforcement learning (RL) applications, we want policies that reach desired states and then keep the controlled system within an acceptable region around the desired states over an indefinite period of time. This latter objective is called *stability* and is especially important when the state space is unbounded, such that the states can be arbitrarily far from each other and the agent can drift far away from the desired states. For example, in stochastic queuing networks, where queues of waiting jobs can grow without bound, the desired state is all-zero queue lengths. Here, a stable policy ensures queue lengths are finite while an optimal policy minimizes queue lengths. Since an optimal policy is also stable, one would expect that RL algorithms would implicitly give us stable policies. However, in this work, we find that deep RL algorithms that directly minimize the distance to the desired state during online training often result in unstable policies, i.e., policies that drift far away from the desired state. We attribute this instability to poor credit-assignment for destabilizing actions. We then introduce an approach based on two ideas: 1) a Lyapunov-based cost-shaping technique and 2) state transformations to the unbounded state space. We conduct an empirical study on various queueing networks and traffic signal control problems and find that our approach performs competitively against strong baselines with knowledge of the transition dynamics. Our code is available here: https://github.com/Badger-RL/STOP

Optimization · Bilevel optimization

Anselm Paulus, Georg Martius, Vit Musil

Embedding parameterized optimization problems as layers into machine learning architectures serves as a powerful inductive bias. Training such architectures with stochastic gradient descent requires care, as degenerate derivatives of the embedded optimization problem often render the gradients uninformative. We propose Lagrangian Proximal Gradient Descent (LPGD), a flexible framework for training architectures with embedded optimization layers that seamlessly integrates into automatic differentiation libraries. LPGD efficiently computes meaningful replacements of the degenerate optimization layer derivatives by re-running the forward solver oracle on a perturbed input. LPGD captures various previously proposed methods as special cases, while fostering deep links to traditional optimization methods. We theoretically analyze our method and demonstrate on historical and synthetic data that LPGD converges faster than gradient descent even in a differentiable setup.

Theory · Learning Theory

Pratik Patil, Jin-Hong Du, Ryan Tibshirani

We study the behavior of optimal ridge regularization and optimal ridge risk for out-of-distribution prediction, where the test distribution deviates arbitrarily from the train distribution. We establish general conditions that determine the sign of the optimal regularization level under covariate and regression shifts. These conditions capture the alignment between the covariance and signal structures in the train and test data and reveal stark differences compared to the in-distribution setting. For example, a negative regularization level can be optimal under covariate shift or regression shift, even when the training features are isotropic or the design is underparameterized. Furthermore, we prove that the optimally tuned risk is monotonic in the data aspect ratio, even in the out-of-distribution setting and when optimizing over negative regularization levels. In general, our results do not make any modeling assumptions for the train or the test distributions, except for moment bounds, and allow for arbitrary shifts and the widest possible range of (negative) regularization levels.

Probabilistic Methods · Variational Inference

Yash Patel, Declan McNamara, Jackson Loper, Jeffrey Regier, Ambuj Tewari

Amortized variational inference is an often employed framework in simulation-based inference that produces a posterior approximation that can be rapidly computed given any new observation. Unfortunately, there are few guarantees about the quality of these approximate posteriors. We propose Conformalized Amortized Neural Variational Inference (CANVI), a procedure that is scalable, easily implemented, and provides guaranteed marginal coverage. Given a collection of candidate amortized posterior approximators, CANVI constructs conformalized predictors based on each candidate, compares the predictors using a metric known as predictive efficiency, and returns the most efficient predictor. CANVI ensures that the resulting predictor constructs regions that contain the truth with a user-specified level of probability. CANVI is agnostic to design decisions in formulating the candidate approximators and only requires access to samples from the forward model, permitting its use in likelihood-free settings. We prove lower bounds on the predictive efficiency of the regions produced by CANVI and explore how the quality of a posterior approximation relates to the predictive efficiency of prediction regions based on that approximation. Finally, we demonstrate the accurate calibration and high predictive efficiency of CANVI on a suite of simulation-based inference benchmark tasks and an important scientific task: analyzing galaxy emission spectra.