Furthermore, their guarantees only hold in the realizable setting, requiring thatf is itself a size-s decision tree (i.e.opts = 0). There has been extensive work in the learning theory literature on learning the concept class of decision trees [EH89, Blu92, KM93, OS07, GKK08, HKY18, CM19]. This follows by combining the boundsInf(T) logs (see e.g.

Federated Retrieval (FR) routes queries across multiple external knowledge sources, to mitigate hallucinations of LLMs, when necessary external knowledge is distributed. However, existing methods struggle to retrieve high-quality and relevant documents for ambiguous queries, especially in cross-domain scenarios, which significantly limits their effectiveness in supporting downstream generation tasks. Inspired by Dynamic Information Flow (DIF), we propose DFAMS, a novel framework that leverages DIF to identify latent query intents and construct semantically aligned knowledge partitions for accurate retrieval across heterogeneous sources. Specifically, DFAMS probes the DIF in LLMs by leveraging gradient signals from a few annotated queries and employing Shapley value-based attribution to trace neuron activation paths associated with intent recognition and subdomain boundary detection. Then, DFAMS leverages DIF to train an alignment module via multi-prototype contrastive learning, enabling fine-grained intra-source modeling and inter-source semantic alignment across knowledge bases. Experimental results across five benchmarks show that DFAMS outperforms advanced FR methods by up to 14.37\% in knowledge classification accuracy, 5.38\% in retrieval recall, and 6.45\% in downstream QA accuracy, demonstrating its effectiveness in complex FR scenarios. Our code are anonymous available at https://anonymous.4open.science/r/DFAMS/

Transformers are deep architectures that define ``in-context maps'' which enable predicting new tokens based on a given set of tokens (such as a prompt in NLP applications or a set of patches for a vision transformer). In previous work, we studied the ability of these architectures to handle an arbitrarily large number of context tokens. To mathematically, uniformly analyze their expressivity, we considered the case that the mappings are conditioned on a context represented by a probability distribution which becomes discrete for a finite number of tokens. Modeling neural networks as maps on probability measures has multiple applications, such as studying Wasserstein regularity, proving generalization bounds and doing a mean-field limit analysis of the dynamics of interacting particles as they go through the network. In this work, we study the question what kind of maps between measures are transformers. We fully characterize the properties of maps between measures that enable these to be represented in terms of in-context maps via a push forward. On the one hand, these include transformers; on the other hand, transformers universally approximate representations with any continuous in-context map. These properties are preserving the cardinality of support and that the regular part of their Fréchet derivative is uniformly continuous. Moreover, we show that the solution map of the Vlasov equation, which is of nonlocal transport type, for interacting particle systems in the mean-field regime for the Cauchy problem satisfies the conditions on the one hand and, hence, can be approximated by a transformer; on the other hand, we prove that the measure-theoretic self-attention has the properties that ensure that the infinite depth, mean-field measure-theoretic transformer can be identified with a Vlasov flow.

We fine-tuned and compared several encoder-based Transformer large language models (LLM) to predict differential item functioning (DIF) from the item text. We then applied explainable artificial intelligence (XAI) methods to these models to identify specific words associated with DIF. The data included 42,180 items designed for English language arts and mathematics summative state assessments among students in grades 3 to 11. Prediction $R^2$ ranged from .04 to .32 among eight focal and reference group pairs. Our findings suggest that many words associated with DIF reflect minor sub-domains included in the test blueprint by design, rather than construct-irrelevant item content that should be removed from assessments. This may explain why qualitative reviews of DIF items often yield confusing or inconclusive results. Our approach can be used to screen words associated with DIF during the item-writing process for immediate revision, or help review traditional DIF analysis results by highlighting key words in the text. Extensions of this research can enhance the fairness of assessment programs, especially those that lack resources to build high-quality items, and among smaller subpopulations where we do not have sufficient sample sizes for traditional DIF analyses.

Since ChatGPT was introduced in November 2022, embedding (nearly) unnoticeable statistical signals into text generated by large language models (LLMs), also known as watermarking, has been used as a principled approach to provable detection of LLM-generated text from its human-written counterpart. In this paper, we introduce a general and flexible framework for reasoning about the statistical efficiency of watermarks and designing powerful detection rules. Inspired by the hypothesis testing formulation of watermark detection, our framework starts by selecting a pivotal statistic of the text and a secret key -- provided by the LLM to the verifier -- to enable controlling the false positive rate (the error of mistakenly detecting human-written text as LLM-generated). Next, this framework allows one to evaluate the power of watermark detection rules by obtaining a closed-form expression of the asymptotic false negative rate (the error of incorrectly classifying LLM-generated text as human-written). Our framework further reduces the problem of determining the optimal detection rule to solving a minimax optimization program. We apply this framework to two representative watermarks -- one of which has been internally implemented at OpenAI -- and obtain several findings that can be instrumental in guiding the practice of implementing watermarks. In particular, we derive optimal detection rules for these watermarks under our framework. These theoretically derived detection rules are demonstrated to be competitive and sometimes enjoy a higher power than existing detection approaches through numerical experiments.

With the increasing need to protect the privacy of sensitive user data while conducting meaningful data analysis, Differential Privacy (DP) [14] has become a popular solution. DP algorithms ensure that the impact of any single data sample on the output is limited, thus safeguarding individual privacy. Several works have obtained DP learning algorithms for various learning problems in both theory and practice. However, privacy does not come for free and often leads to a statistical (and sometimes computational) cost. The classical solution for non-private Probably Approximately Correct (PAC) learning [28] is via Empirical Risk Minimisation (ERM) that computes the best solution on the training data. Several works [3, 11] have shown that incorporating DP into ERM incurs a compulsory statistical cost that depends on the dimension of the problem. In the well-known setting of PAC learning with DP, Kasiviswanathan et al. [23] provided the first guarantees that all finite VC classes can be learned with a sample size that grows logarithmically in the size of the class. This line of research was advanced by subsequent works [4, 6, 17], resulting in the findings of Alon et al. [2] which established a surprising equivalence between non-private online learning and Approximate DP-PAC learning.

We study a model of machine teaching where the teacher mapping is constructed from a size function on both concepts and examples. The main question in machine teaching is the minimum number of examples needed for any concept, the so-called teaching dimension. A recent paper [7] conjectured that the worst case for this model, as a function of the size of the concept class, occurs when the consistency matrix contains the binary representations of numbers from zero and up. In this paper we prove their conjecture. The result can be seen as a generalization of a theorem resolving the edge isoperimetry problem for hypercubes [12], and our proof is based on a lemma of [10].

Isolation forest (iForest) has been emerging as arguably the most popular anomaly detector in recent years due to its general effectiveness across different benchmarks and strong scalability. Nevertheless, its linear axis-parallel isolation method often leads to (i) failure in detecting hard anomalies that are difficult to isolate in high-dimensional/non-linear-separable data space, and (ii) notorious algorithmic bias that assigns unexpectedly lower anomaly scores to artefact regions. These issues contribute to high false negative errors. Several iForest extensions are introduced, but they essentially still employ shallow, linear data partition, restricting their power in isolating true anomalies. Therefore, this paper proposes deep isolation forest. We introduce a new representation scheme that utilises casually initialised neural networks to map original data into random representation ensembles, where random axis-parallel cuts are subsequently applied to perform the data partition. This representation scheme facilitates high freedom of the partition in the original data space (equivalent to non-linear partition on subspaces of varying sizes), encouraging a unique synergy between random representations and random partition-based isolation. Extensive experiments show that our model achieves significant improvement over state-of-the-art isolation-based methods and deep detectors on tabular, graph and time series datasets; our model also inherits desired scalability from iForest.

It is of critical importance to be aware of the historical discrimination embedded in the data and to consider a fairness measure to reduce bias throughout the predictive modeling pipeline. Given various notions of fairness defined in the literature, investigating the correlation and interaction among metrics is vital for addressing unfairness. Practitioners and data scientists should be able to comprehend each metric and examine their impact on one another given the context, use case, and regulations. Exploring the combinatorial space of different metrics for such examination is burdensome. To alleviate the burden of selecting fairness notions for consideration, we propose a framework that estimates the correlation among fairness notions. Our framework consequently identifies a set of diverse and semantically distinct metrics as representative for a given context. We propose a Monte-Carlo sampling technique for computing the correlations between fairness metrics by indirect and efficient perturbation in the model space. Using the estimated correlations, we then find a subset of representative metrics. The paper proposes a generic method that can be generalized to any arbitrary set of fairness metrics. We showcase the validity of the proposal using comprehensive experiments on real-world benchmark datasets.

In this paper we propose Discretely Indexed flows (DIF) as a new tool for solving variational estimation problems. Roughly speaking, DIF are built as an extension of Normalizing Flows (NF), in which the deterministic transport becomes stochastic, and more precisely discretely indexed. Due to the discrete nature of the underlying additional latent variable, DIF inherit the good computational behavior of NF: they benefit from both a tractable density as well as a straightforward sampling scheme, and can thus be used for the dual problems of Variational Inference (VI) and of Variational density estimation (VDE). On the other hand, DIF can also be understood as an extension of mixture density models, in which the constant mixture weights are replaced by flexible functions. As a consequence, DIF are better suited for capturing distributions with discontinuities, sharp edges and fine details, which is a main advantage of this construction. Finally we propose a methodology for constructiong DIF in practice, and see that DIF can be sequentially cascaded, and cascaded with NF.