Recurrent Neural Network (RNN) is a fundamental structure in deep learning. Recently, some works study the training process of over-parameterized neural networks, and show that over-parameterized networks can learn functions in some notable concept classes with a provable generalization error bound. In this paper, we analyze the training and generalization for RNNs with random initialization, and provide the following improvements over recent works:(1) For a RNN with input sequence $x=(X_1,X_2,...,X_L)$, previous works study to learn functions that are summation of $f(\beta^T_lX_l)$ and require normalized conditions that $||X_l||\leq\epsilon$ with some very small $\epsilon$ depending on the complexity of $f$. In this paper, using detailed analysis about the neural tangent kernel matrix, we prove a generalization error bound to learn such functions without normalized conditions and show that some notable concept classes are learnable with the numbers of iterations and samples scaling almost-polynomially in the input length $L$.(2) Moreover, we prove a novel result to learn N-variables functions of input sequence with the form $f(\beta^T[X_{l_1},...,X_{l_N}])$, which do not belong to the ``additive'' concept class, i,e., the summation of function $f(X_l)$. And we show that when either $N$ or $l_0=\max(l_1,..,l_N)-\min(l_1,..,l_N)$ is small, $f(\beta^T[X_{l_1},...,X_{l_N}])$ will be learnable with the number iterations and samples scaling almost-polynomially in the input length $L$.

Despite remarkable success in a variety of applications, it is well-known that deep learning can fail catastrophically when presented with out-of-distribution data. Toward addressing this challenge, we consider the \emph{domain generalization} problem, wherein predictors are trained using data drawn from a family of related training domains and then evaluated on a distinct and unseen test domain. We show that under a natural model of data generation and a concomitant invariance condition, the domain generalization problem is equivalent to an infinite-dimensional constrained statistical learning problem; this problem forms the basis of our approach, which we call Model-Based Domain Generalization. Due to the inherent challenges in solving constrained optimization problems in deep learning, we exploit nonconvex duality theory to develop unconstrained relaxations of this statistical problem with tight bounds on the duality gap. Based on this theoretical motivation, we propose a novel domain generalization algorithm with convergence guarantees. In our experiments, we report improvements of up to 30% over state-of-the-art domain generalization baselines on several benchmarks including ColoredMNIST, Camelyon17-WILDS, FMoW-WILDS, and PACS.

Large scale field-phenotyping approaches have the potential to solve important questions about the relationship of plant genotype to plant phenotype. Computational approaches to measuring the phenotype (the observable plant features) are required to address the problem at a large scale, but machine learning approaches to extract phenotypes from sensor data have been hampered by limited access to (a) sufficiently large, organized multi-sensor datasets, (b) field trials that have a large scale and significant number of genotypes, (c) full genetic sequencing of those phenotypes, and (d) datasets sufficiently organized so that algorithm centered researchers can directly address the real biological problems. To address this, we present SGxP, a novel benchmark dataset from a large-scale field trial consisting of the complete genotype of over 300 sorghum varieties, and time sequences of imagery from several field plots growing each variety, taken with RGB and laser 3D scanner imaging. To lower the barrier to entry and facilitate further developments, we provide a set of well organized, multi-sensor imagery and corresponding genomic data. We implement baseline deep learning based phenotyping approaches to create baseline results for individual sensors and multi-sensor fusion for detecting genetic mutations with known impacts. We also provide and support an open-ended challenge by identifying thousands of genetic mutations whose phenotypic impacts are currently unknown. A web interface for machine learning researchers and practitioners to share approaches, visualizations and hypotheses supports engagement with plant biologists to further the understanding of the sorghum genotype x phenotype relationship. The full dataset, leaderboard (including baseline results) and discussion forums can be found at http://sorghumsnpbenchmark.com.

Deep Learning methods are known to suffer from calibration issues: they typically produce over-confident estimates. These problems are exacerbated in the low data regime. Although the calibration of probabilistic models is well studied, calibrating extremely over-parametrized models in the low-data regime presents unique challenges. We show that deep-ensembles do not necessarily lead to improved calibration properties. In fact, we show that standard ensembling methods, when used in conjunction with modern techniques such as mixup regularization, can lead to less calibrated models. This text examines the interplay between three of the most simple and commonly used approaches to leverage deep learning when data is scarce: data-augmentation, ensembling, and post-processing calibration methods. We demonstrate that, although standard ensembling techniques certainly help to boost accuracy, the calibration of deep ensembles relies on subtle trade-offs. We also find that calibration methods such as temperature scaling need to be slightly tweaked when used with deep-ensembles and, crucially, need to be executed after the averaging process. Our simulations indicate that, in the low data regime, this simple strategy can halve the Expected Calibration Error (ECE) on a range of benchmark classification problems when compared to standard deep-ensembles.

Score matching (SM) provides a compelling approach to learn energy-based models (EBMs) by avoiding the calculation of partition function. However, it remains largely open to learn energy-based latent variable models (EBLVMs), except some special cases. This paper presents a bi-level score matching (BiSM) method to learn EBLVMs with general structures by reformulating SM as a bi-level optimization problem. The higher level introduces a variational posterior of the latent variables and optimizes a modified SM objective, and the lower level optimizes the variational posterior to fit the true posterior. To solve BiSM efficiently, we develop a stochastic optimization algorithm with gradient unrolling. Theoretically, we analyze the consistency of BiSM and the convergence of the stochastic algorithm. Empirically, we show the promise of BiSM in Gaussian restricted Boltzmann machines and highly nonstructural EBLVMs parameterized by deep convolutional neural networks. BiSM is comparable to the widely adopted contrastive divergence and SM methods when they are applicable; and can learn complex EBLVMs with intractable posteriors to generate natural images.

This work presents BAdam, an optimization method that leverages the block coordinate descent (BCD) framework with Adam's update rule. BAdam offers a memory efficient approach to the full parameter finetuning of large language models. We conduct a theoretical convergence analysis for BAdam in the deterministic case. Experimentally, we apply BAdam to finetune the Llama 3-8B and Llama 3-70B models using a single RTX3090-24GB GPU and 4 A100-80GB GPUs, respectively. The results confirm BAdam's efficiency in terms of memory usage, running time, and optimization capability. Furthermore, the downstream performance evaluation based on MT-bench and math benchmarks shows that BAdam outperforms existing memory efficient baselines such as LoRA. It also demonstrates that BAdam can achieve comparable or even superior performance compared to Adam. Finally, the ablation study using SGD's update rule illustrates the suitability of BCD for finetuning LLMs. Our code can be easily integrated into any PyTorch-based codebase and is available at https://github.com/Ledzy/BAdam.

Transformer is a new kind of calculation paradigm for deep learning which has shown strong performance on a large variety of computer vision tasks. However, compared with conventional deep models (e.g., convolutional neural networks), vision transformers require more computational resources which cannot be easily deployed on mobile devices. To this end, we present to reduce the energy consumptions using adder neural network (AdderNet). We first theoretically analyze the mechanism of self-attention and the difficulty for applying adder operation into this module. Specifically, the feature diversity, i.e., the rank of attention map using only additions cannot be well preserved. Thus, we develop an adder attention layer that includes an additional identity mapping. With the new operation, vision transformers constructed using additions can also provide powerful feature representations. Experimental results on several benchmarks demonstrate that the proposed approach can achieve highly competitive performance to that of the baselines while achieving an about 2~3 reduction on the energy consumption.

Despite its role in exploring and learning, the function and neural basis of this variability is still not well understood. Given the coupling between neural activity and behavior, we ask what type of neural variability does not compromise behavioral performance. While previous studies typically curtail variability to allow for high task performance in neural networks, our approach takes the reversed perspective. We investigate how to generate maximal neural variability while at the same time having high network performance. To do so, we extend to neural activity the maximum occupancy principle (MOP) developed for behavior, and refer to this new neural principle as NeuroMOP. NeuroMOP posits that the goal of the nervous system is to maximize future action-state entropy, a reward-free, intrinsic motivation that entails creating all possible activity patterns while avoiding terminal or dangerous ones.We show that this goal can be achieved through a neural network controller that injects currents (actions) into a recurrent neural network of fixed random weights to maximize future cumulative action-state entropy. High activity variability can be induced while adhering to an energy constraint or while avoiding terminal states defined by specific neurons' activities, also in a context-dependent manner. The network solves these tasks by flexibly switching between stochastic and deterministic modes as needed and projecting noise onto a null space. Based on future maximum entropy production, NeuroMOP contributes to a novel theory of neural variability that reconciles stochastic and deterministic behaviors within a single framework.

The use of deep learning techniques has achieved significant progress for program synthesis from input-output examples. However, when the program semantics become more complex, it still remains a challenge to synthesize programs that are consistent with the specification. In this work, we propose SED, a neural program generation framework that incorporates synthesis, execution, and debugging stages. Instead of purely relying on the neural program synthesizer to generate the final program, SED first produces initial programs using the neural program synthesizer component, then utilizes a neural program debugger to iteratively repair the generated programs. The integration of the debugger component enables SED to modify the programs based on the execution results and specification, which resembles the coding process of human programmers. On Karel, a challenging input-output program synthesis benchmark, SED reduces the error rate of the neural program synthesizer itself by a considerable margin, and outperforms the standard beam search for decoding.

A key goal in mechanistic interpretability is circuit analysis: finding sparse subgraphs of models corresponding to specific behaviors or capabilities. However, MLP sublayers make fine-grained circuit analysis on transformer-based language models difficult. In particular, interpretable features--such as those found by sparse autoencoders (SAEs)--are typically linear combinations of extremely many neurons, each with its own nonlinearity to account for. Circuit analysis in this setting thus either yields intractably large circuits or fails to disentangle local and global behavior.