The neural network memorization problem is to study the expressive power of neural networks to interpolate a finite dataset. Although memorization is widely believed to have a close relationship with the strong generalizability of deep learning when using overparameterized models, to the best of our knowledge, there exists no theoretical study on the generalizability of memorization neural networks. In this paper, we give the first theoretical analysis of this topic.

Molecular docking, a technique for predicting ligand binding poses, is crucial in structure-based drug design for understanding protein-ligand interactions. Recent advancements in docking methods, particularly those leveraging geometric deep learning (GDL), have demonstrated significant efficiency and accuracy advantages over traditional sampling methods. Despite these advancements, current methods are often tailored for specific docking settings, and limitations such as the neglect of protein side-chain structures, difficulties in handling large binding pockets, and challenges in predicting physically valid structures exist. To accommodate various docking settings and achieve accurate, efficient, and physically reliable docking, we propose a novel two-stage docking framework, DeltaDock, consisting of pocket prediction and site-specific docking.

Due to statistical lower bounds on the learnability of many function classes under privacy constraints, there has been recent interest in leveraging public data to improve the performance of private learning algorithms. In this model, algorithms must always guarantee differential privacy with respect to the private samples while also ensuring learning guarantees when the private data distribution is sufficiently close to that of the public data. Previous work has demonstrated that when sufficient public, unlabelled data is available, private learning can be made statistically tractable, but the resulting algorithms have all been computationally inefficient. In this work, we present the first computationally efficient, algorithms to provably leverage public data to learn privately whenever a function class is learnable non-privately, where our notion of computational efficiency is with respect to the number of calls to an optimization oracle for the function class. In addition to this general result, we provide specialized algorithms with improved sample complexities in the special cases when the function class is convex or when the task is binary classification.

Ongoing efforts that span over decades show a rise of AI methods for accelerating scientific discovery, yet accelerating discovery in mathematics remains a persistent challenge for AI.Specifically, AI methods were not effective in creation of formulas for mathematical constants because each such formula must be correct for infinite digits of precision, with'near-true' formulas providing no insight toward the correct ones. Consequently, formula discovery lacks a clear distance metric needed to guide automated discovery in this realm.In this work, we propose a systematic methodology for categorization, characterization, and pattern identification of such formulas. The key to our methodology is introducing metrics based on the convergence dynamics of the formulas, rather than on the numerical value of the formula. These metrics enable the first automated clustering of mathematical formulas.We demonstrate this methodology on Polynomial Continued Fraction formulas, which are ubiquitous in their intrinsic connections to mathematical constants, and generalize many mathematical functions and structures.We test our methodology on a set of 1,768,900 such formulas, identifying many known formulas for mathematical constants, and discover previously unknown formulas for $\pi$, $\ln(2)$, Gauss', and Lemniscate's constants. The uncovered patterns enable a direct generalization of individual formulas to infinite families, unveiling rich mathematical structures. This success paves the way towards a generative model that creates formulas fulfilling specified mathematical properties, accelerating the rate of discovery of useful formulas.

Large Language Models (LLMs) are widely used in today's tasks of natural language processing. To support applications like multi-turn chats, document understanding, and content generation, models with long context lengths are growing in importance.However, managing long contexts brings substantial challenges due to the expansion of key-value cache (KV cache). Longer KV cache requires larger memory, limiting the batch-size thus decreasing throughput. Also, computing attention over long KV cache incurs more memory access, hurting the end-to-end latency.Prior works find that it is sufficient to use only the recent and high-impact tokens for attention computation, allowing the eviction of less vital tokens to shrink cache size.Nonetheless, we observe a dynamic shift in token importance across different decoding steps. Tokens initially evicted might regain importance after certain decoding steps.To address this, we propose ArkVale, a page-based KV cache manager that can recognize and recall currently important tokens evicted before. We asynchronously copy the filled page into external memory (e.g., CPU memory) as backup and summarize it into a much smaller digest by constructing the bounding-volume of its keys. Before attention computation, we measure all pages' importance based on their digests, recall the important ones, evict the unimportant ones, and select the top-ranked pages for attention computation. Experiment results show that ArkVale performs well on various long context tasks with negligible accuracy loss under 2k$\sim$4k cache budget and can improve decoding latency to $2.2\times$ and batching throughput to $4.6\times$ because it applies attention on only a small subset of pages and reduce per-sample memory usage of KV cache.

Large language models are often ranked according to their level of alignment with human preferences---a model is better than other models if its outputs are more frequently preferred by humans. One of the popular ways to elicit human preferences utilizes pairwise comparisons between the outputs provided by different models to the same inputs. However, since gathering pairwise comparisons by humans is costly and time-consuming, it has become a common practice to gather pairwise comparisons by a strong large language model---a model strongly aligned with human preferences. Surprisingly, practitioners cannot currently measure the uncertainty that any mismatch between human and model preferences may introduce in the constructed rankings. In this work, we develop a statistical framework to bridge this gap. Given a (small) set of pairwise comparisons by humans and a large set of pairwise comparisons by a model, our framework provides a rank-set---a set of possible ranking positions---for each of the models under comparison. Moreover, it guarantees that, with a probability greater than or equal to a user-specified value, the rank-sets cover the true ranking consistent with the distribution of human pairwise preferences asymptotically. Using pairwise comparisons made by humans in the LMSYS Chatbot Arena platform and pairwise comparisons made by three strong large language models, we empirically demonstrate the effectivity of our framework and show that the rank-sets constructed using only pairwise comparisons by the strong large language models are often inconsistent with (the distribution of) human pairwise preferences.

Sequential recommendation systems predict the next interaction item based on users' past interactions, aligning recommendations with individual preferences. Leveraging the strengths of Large Language Models (LLMs) in knowledge comprehension and reasoning, recent approaches are eager to apply LLMs to sequential recommendation. A common paradigm is converting user behavior sequences into instruction data, and fine-tuning the LLM with parameter-efficient fine-tuning (PEFT) methods like Low-Rank Adaption (LoRA). However, the uniform application of LoRA across diverse user behaviors is insufficient to capture individual variability, resulting in negative transfer between disparate sequences.To address these challenges, we propose Instance-wise LoRA (iLoRA). We innovatively treat the sequential recommendation task as a form of multi-task learning, integrating LoRA with the Mixture of Experts (MoE) framework. This approach encourages different experts to capture various aspects of user behavior. Additionally, we introduce a sequence representation guided gate function that generates customized expert participation weights for each user sequence, which allows dynamic parameter adjustment for instance-wise recommendations.

Sample efficiency in Reinforcement Learning (RL) has traditionally been driven by algorithmic enhancements. In this work, we demonstrate that scaling can also lead to substantial improvements. We conduct a thorough investigation into the interplay of scaling model capacity and domain-specific RL enhancements. These empirical findings inform the design choices underlying our proposed BRO (Bigger, Regularized, Optimistic) algorithm. The key innovation behind BRO is that strong regularization allows for effective scaling of the critic networks, which, paired with optimistic exploration, leads to superior performance. BRO achieves state-of-the-art results, significantly outperforming the leading model-based and model-free algorithms across 40 complex tasks from the DeepMind Control, MetaWorld, and MyoSuite benchmarks. BRO is the first model-free algorithm to achieve near-optimal policies in the notoriously challenging Dog and Humanoid tasks.

The $k$-sparse parity problem is a classical problem in computational complexity and algorithmic theory, serving as a key benchmark for understanding computational classes. In this paper, we solve the $k$-sparse parity problem with sign stochastic gradient descent, a variant of stochastic gradient descent (SGD) on two-layer fully-connected neural networks. We demonstrate that this approach can efficiently solve the $k$-sparse parity problem on a $d$-dimensional hypercube ($k\le O(\sqrt{d})$) with a sample complexity of $\tilde{O}(d^{k-1})$ using $2^{\Theta(k)}$ neurons, matching the established $\Omega(d^{k})$ lower bounds of Statistical Query (SQ) models. Our theoretical analysis begins by constructing a good neural network capable of correctly solving the $k$-parity problem. We then demonstrate how a trained neural network with sign SGD can effectively approximate this good network, solving the $k$-parity problem with small statistical errors. To the best of our knowledge, this is the first result that matches the SQ lower bound for solving $k$-sparse parity problem using gradient-based methods.

We study the evaluation of a policy under best-and worst-case perturbations to a Markov decision process (MDP), using transition observations from the original MDP, whether they are generated under the same or a different policy. This is an important problem when there is the possibility of a shift between historical and future environments, \emph{e.g.} due to unmeasured confounding, distributional shift, or an adversarial environment. We propose a perturbation model that allows changes in the transition kernel densities up to a given multiplicative factor or its reciprocal, extending the classic marginal sensitivity model (MSM) for single time-step decision-making to infinite-horizon RL. We characterize the sharp bounds on policy value under this model -- \emph{i.e.}, the tightest possible bounds based on transition observations from the original MDP -- and we study the estimation of these bounds from such transition observations. We develop an estimator with several important guarantees: it is semiparametrically efficient, and remains so even when certain necessary nuisance functions, such as worst-case Q-functions, are estimated at slow, nonparametric rates. Our estimator is also asymptotically normal, enabling straightforward statistical inference using Wald confidence intervals. Moreover, when certain nuisances are estimated inconsistently, the estimator still provides valid, albeit possibly not sharp, bounds on the policy value.