Boosting is a highly successful ML-born optimization setting in which one is required to computationally efficiently learn arbitrarily good models based on the access to a weak learner oracle, providing classifiers performing at least slightly differently from random guessing. A key difference with gradient-based optimization is that boosting's original model does not requires access to first order information about a loss, yet the decades long history of boosting has quickly evolved it into a first order optimization setting -- sometimes even wrongfully *defining* it as such. Owing to recent progress extending gradient-based optimization to use only a loss' zeroth ($0^{th}$) order information to learn, this begs the question: what loss functions be efficiently optimized with boosting and what is the information really needed for boosting to meet the *original* boosting blueprint's requirements?We provide a constructive formal answer essentially showing that *any* loss function can be optimized with boosting and thus boosting can achieve a feat not yet known to be possible in the classical $0^{th}$ order setting, since loss functions are not required to be be convex, nor differentiable or Lipschitz -- and in fact not required to be continuous either. Some tools we use are rooted in quantum calculus, the mathematical field -- not to be confounded with quantum computation -- that studies calculus without passing to the limit, and thus without using first order information.

ABSTRACT An appropriate distance metric is crucial for categorical data clustering, as the distance between categorical data cannot be directly calculated. However, the distances between attribute values usually vary in different clusters induced by their different distributions, which has not been taken into account, thus leading to unreasonable distance measurement. Therefore, we propose a cluster-customized distance metric for categorical data clustering, which can competitively update distances based on different distributions of attributes in each cluster. In addition, we extend the proposed distance metric to the mixed data that contains both numerical and categorical attributes. Experiments demonstrate the efficacy of the proposed method, i.e., achieving an average ranking of around first in fourteen datasets. The source code is available at https://anonymous.4open.science/r/CADM-47D8/

We thank all three reviewers for their thorough reviews and constructive feedback. Otherwise, including additional second order information can make the results worse. "...CGD still requires that the step-size is bounded by one over the max diagonal entry of the Hessian...": Concern 1: Why not use full second order? See also our answer to Reviewer #7. Concern 3: Is CGD scalable?

High responsiveness and economic efficiency are critical objectives in supply chain transportation, both of which are influenced by strategic decisions on shipping mode. An integrated framework combining an efficient simulator with an intelligent decision-making algorithm can provide an observable, low-risk environment for transportation strategy design. An ideal simulation-decision framework must (1) generalize effectively across various settings, (2) reflect fine-grained transportation dynamics, (3) integrate historical experience with predictive insights, and (4) maintain tight integration between simulation feedback and policy refinement. We propose Sim-to-Dec framework to satisfy these requirements. Specifically, Sim-to-Dec consists of a generative simulation module, which leverages autoregressive modeling to simulate continuous state changes, reducing dependence on handcrafted domain-specific rules and enhancing robustness against data fluctuations; and a history-future dual-aware decision model, refined iteratively through end-to-end optimization with simulator interactions. Extensive experiments conducted on three real-world datasets demonstrate that Sim-to-Dec significantly improves timely delivery rates and profit.

This note presents a non-associative algebraic framework for the representation and computation of information items in high - dimensional space. This framework is consistent with the principles of spatial computing and with the empirical findings in cognitive science about memory. Computations are performed through a process of multiplication-like binding and non-associative interference-like bundling. Models that rely on associative bundling typically lose order information, which necessitates the use of auxiliary order structures, such as position markers, to represent sequential information that is important for cognitive tasks. In contrast, the non-associative bundling proposed allows the construction of sparse representations of arbitrarily long sequences that maintain their temporal structure across arbitrary lengths. The non-associative nature of the proposed framework results in the representation of a single sequence by two distinct states. The L-state, generated through left-associative bundling, continuously updates and emphasises a recency effect, while the R-state, formed through right-associative bundling, encodes finite sequences or chunks, capturing a primacy effect. The construction of these states may be associated with activity in the prefrontal cortex in relation to short-term memory and hippocampal encoding in long-term memory, respectively. The accuracy of retrieval is contingent upon a decision-making process that is based on the mutual information between the memory states and the cue. The model is able to replicate the Serial Position Curve, which reflects the empirical recency and primacy effects observed in cognitive experiments. Keywords: Memory states, high-dimensional computing (VSA), nonassociative bundling, spatial computing, mutual information, Serial Position Curve T o appear in Neural Computation, V ol 37, Issue 6, June 2025 1 Introduction In essence, the perception of an object is initialised with the activation of a sensory pole. This sensory activation has a rapid decay and lasts for only a few milliseconds.

Recommender systems involve an inherent trade-off between accuracy of recommendations and the extent to which users are willing to release information about their preferences. In this paper, we explore a two-tiered notion of privacy where there is a small set of "public" users who are willing to share their preferences openly, and a large set of "private" users who require privacy guarantees. We show theoretically and demonstrate empirically that a moderate number of public users with no access to private user information already suffices for reasonable accuracy. Moreover, we introduce a new privacy concept for gleaning relational information from private users while maintaining a first order deniability. We demonstrate gains from controlled access to private user preferences.

Recommender systems involve an inherent trade-off between accuracy of recommendations and the extent to which users are willing to release information about their preferences. In this paper, we explore a two-tiered notion of privacy where there is a small set of "public" users who are willing to share their preferences openly, and a large set of "private" users who require privacy guarantees. We show theoretically and demonstrate empirically that a moderate number of public users with no access to private user information already suffices for reasonable accuracy. Moreover, we introduce a new privacy concept for gleaning relational information from private users while maintaining a first order deniability. We demonstrate gains from controlled access to private user preferences.

With multiple iterations of updates, local statistical gradient descent (L-SGD) has been proven to be very effective in distributed machine learning schemes such as federated learning. In fact, many innovative works have shown that L-SGD with independent and identically distributed (IID) data can even outperform SGD. As a result, extensive efforts have been made to unveil the power of L-SGD. However, existing analysis failed to explain why the multiple local updates with small mini-batches of data (L-SGD) can not be replaced by the update with one big batch of data and a larger learning rate (SGD). In this paper, we offer a new perspective to understand the strength of L-SGD. We theoretically prove that, with IID data, L-SGD can effectively explore the second order information of the loss function. In particular, compared with SGD, the updates of L-SGD have much larger projection on the eigenvectors of the Hessian matrix with small eigenvalues, which leads to faster convergence. Under certain conditions, L-SGD can even approach the Newton method.

When individuals independently recollect events or retrieve facts from memory, how can we aggregate these retrieved memories to reconstruct the actual set of events or facts? In this research, we report the performance of individuals in a series of general knowledge tasks, where the goal is to reconstruct from memory the order of historic events, or the order of items along some physical dimension. We introduce two Bayesian models for aggregating order information based on a Thurstonian approach and Mallows model. Both models assume that each individuals reconstruction is based on either a random permutation of the unobserved ground truth, or by a pure guessing strategy. We apply MCMC to make inferences about the underlying truth and the strategies employed by individuals.