Optimization of convex functions under stochastic zeroth-order feedback has been a major and challenging question in online learning. In this work, we consider the problem of optimizing second-order smooth and strongly convex functions where the algorithm is only accessible to noisy evaluations of the objective function it queries. We provide the first tight characterization for the rate of the minimax simple regret by developing matching upper and lower bounds. We propose an algorithm that features a combination of a bootstrapping stage and a mirror-descent stage. Our main technical innovation consists of a sharp characterization for the spherical-sampling gradient estimator under higher-order smoothness conditions, which allows the algorithm to optimally balance the bias-variance tradeoff, and a new iterative method for the bootstrapping stage, which maintains the performance for unbounded Hessian.

Multiplicative stochasticity such as Dropout improves the robustness and generalizability of deep neural networks. Here, we further demonstrate that always-on multiplicative stochasticity combined with simple threshold neurons are sufficient operations for deep neural networks. We call such models Neural Sampling Machines (NSM). We find that the probability of activation of the NSM exhibits a self-normalizing property that mirrors Weight Normalization, a previously studied mechanism that fulfills many of the features of Batch Normalization in an online fashion. The normalization of activities during training speeds up convergence by preventing internal covariate shift caused by changes in the input distribution. The always-on stochasticity of the NSM confers the following advantages: the network is identical in the inference and learning phases, making the NSM suitable for online learning, it can exploit stochasticity inherent to a physical substrate such as analog non-volatile memories for in-memory computing, and it is suitable for Monte Carlo sampling, while requiring almost exclusively addition and comparison operations. We demonstrate NSMs on standard classification benchmarks (MNIST and CIFAR) and event-based classification benchmarks (N-MNIST and DVS Gestures). Our results show that NSMs perform comparably or better than conventional artificial neural networks with the same architecture.

Local differential privacy is a strong notion of privacy in which the provider of the data guarantees privacy by perturbing the data with random noise. In the standard application of local differential privacy the distribution of the noise is constant and known by the learner. In this paper we generalize this approach by allowing the provider of the data to choose the distribution of the noise without disclosing any parameters of the distribution to the learner, under the constraint that the distribution is symmetrical. We consider this problem in the unconstrained Online Convex Optimization setting with noisy feedback. In this setting the learner receives the subgradient of a loss function, perturbed by noise, and aims to achieve sublinear regret with respect to some competitor, without constraints on the norm of the competitor. We derive the first algorithms that have adaptive regret bounds in this setting, i.e. our algorithms adapt to the unknown competitor norm, unknown noise, and unknown sum of the norms of the subgradients, matching state of the art bounds in all cases.

Transformers excel at in-context learning (ICL)--learning from demonstrations without parameter updates--but how they do so remains a mystery. Recent work suggests that Transformers may internally run Gradient Descent (GD), a first-order optimization method, to perform ICL. In this paper, we instead demonstrate that Transformers learn to approximate second-order optimization methods for ICL. For in-context linear regression, Transformers share a similar convergence rate as Iterative Newton's Method; both are exponentially faster than GD. Empirically, predictions from successive Transformer layers closely match different iterations of Newton's Method linearly, with each middle layer roughly computing 3 iterations; thus, Transformers and Newton's method converge at roughly the same rate.

Neural Information Processing Systems http://nips.cc/

Two-sided matching markets have long existed to pair agents in the absence of regulated exchanges. A common example is school choice, where a matching mechanism uses student and school preferences to assign students to schools. In such settings, forming preferences is both difficult and critical. Prior work has suggested various prediction mechanisms that help agents make decisions about their preferences. Although often deployed together, these matching and prediction mechanisms are almost always analyzed separately.

Recent advances in algorithmic design show how to utilize predictions obtained by machine learning models from past and present data. These approaches have demonstrated an enhancement in performance when the predictions are accurate, while also ensuring robustness by providing worst-case guarantees when predictions fail. In this paper we focus on online problems; prior research in this context was focused on a paradigm where the algorithms are oblivious of the predictors' design, treating them as a black box. In contrast, in this work, we unpack the predictor and integrate the learning problem it gives rise for within the algorithmic challenge. In particular we allow the predictor to learn as it receives larger parts of the input, with the ultimate goal of designing online learning algorithms specifically tailored for the algorithmic task at hand. Adopting this perspective, we focus on a number of fundamental problems, including caching and scheduling, which have been well-studied in the black-box setting. For each of the problems, we introduce new algorithms that take advantage of explicit and carefully designed learning rules.

We introduce OpenHuEval, the first benchmark for LLMs focusing on the Hungarian language and specifics. OpenHuEval is constructed from a vast collection of Hungarian-specific materials sourced from multiple origins. In the construction, we incorporated the latest design principles for evaluating LLMs, such as using real user queries from the internet, emphasizing the assessment of LLMs' generative capabilities, and employing LLM-as-judge to enhance the multidimensionality and accuracy of evaluations. Ultimately, OpenHuEval encompasses eight Hungarian-specific dimensions, featuring five tasks and 3953 questions. Consequently, OpenHuEval provides the comprehensive, in-depth, and scientifically accurate assessment of LLM performance in the context of the Hungarian language and its specifics. We evaluated current mainstream LLMs, including both traditional LLMs and recently developed Large Reasoning Models. The results demonstrate the significant necessity for evaluation and model optimization tailored to the Hungarian language and specifics. We also established the framework for analyzing the thinking processes of LRMs with OpenHuEval, revealing intrinsic patterns and mechanisms of these models in non-English languages, with Hungarian serving as a representative example. We will release OpenHuEval at https://github.com/opendatalab/OpenHuEval .

Although applying Mixture of Experts to large language models for learning new tasks is widely regarded as an effective strategy for continuous learning, there still remain two major challenges: (1) As the number of tasks grows, simple parameter expansion strategies can lead to excessively large models. (2) Modifying the parameters of the existing router results in the erosion of previously acquired knowledge. In this paper, we present an innovative framework named LLaVA-CMoE, which is a continuous Mixture of Experts (MoE) architecture without any replay data. Specifically, we have developed a method called Probe-Guided Knowledge Extension (PGKE), which employs probe experts to assess whether additional knowledge is required for a specific layer. This approach enables the model to adaptively expand its network parameters based on task distribution, thereby significantly improving the efficiency of parameter expansion. Additionally, we introduce a hierarchical routing algorithm called Probabilistic Task Locator (PTL), where high-level routing captures inter-task information and low-level routing focuses on intra-task details, ensuring that new task experts do not interfere with existing ones. Our experiments shows that our efficient architecture has substantially improved model performance on the Coin benchmark while maintaining a reasonable parameter count.