Datasets can be biased due to societal inequities, human biases, under-representation of minorities, etc. Our goal is to certify that models produced by a learning algorithm are pointwise-robust to dataset biases. This is a challenging problem: it entails learning models for a large, or even infinite, number of datasets, ensuring that they all produce the same prediction. We focus on decision-tree learning due to the interpretable nature of the models. Our approach allows programmatically specifying \emph{bias models} across a variety of dimensions (e.g., label-flipping or missing data), composing types of bias, and targeting bias towards a specific group. To certify robustness, we use a novel symbolic technique to evaluate a decision-tree learner on a large, or infinite, number of datasets, certifying that each and every dataset produces the same prediction for a specific test point. We evaluate our approach on datasets that are commonly used in the fairness literature, and demonstrate our approach's viability on a range of bias models.

Multi-fidelity modeling and learning is important in physical simulation related applications. It can leverage both low-fidelity and high-fidelity examples for training so as to reduce the cost of data generation yet still achieving good performance. While existing approaches only model finite, discrete fidelities, in practice, the feasible fidelity choice is often infinite, which can correspond to a continuous mesh spacing or finite element length. In this paper, we propose Infinite Fidelity Coregionalization (IFC). Given the data, our method can extract and exploit rich information within infinite, continuous fidelities to bolster the prediction accuracy. Our model can interpolate and/or extrapolate the predictions to novel fidelities that are not covered by the training data.

Infinite hidden Markov models provide a flexible framework for modelling time series with structural changes and complex dynamics, without requiring the number of latent states to be specified in advance. This flexibility is achieved through the hierarchical Dirichlet process prior, while efficient Bayesian inference is enabled by the beam sampler, which combines dynamic programming with slice sampling to truncate the infinite state space adaptively. Despite extensive methodological developments, the role of initialization in this framework has received limited attention. This study addresses this gap by systematically evaluating initialization strategies commonly used for finite hidden Markov models and assessing their suitability in the infinite setting. Results from both simulated and real datasets show that distance-based clustering initializations consistently outperform model-based and uniform alternatives, the latter being the most widely adopted in the existing literature.

Answers to these questions must begin by formalizing the specification for what a generative algorithm for language should be doing.

Hence, we prove the convergence in a finite manner. Lemma 4. The bounding operation in Algorithm 1 is finitely consistent. From Lemma 4, we have the bounding operation in Algorithm 1 is finitely consistent. Theorem 1. Algorithm 1 is convergent to the global optimal solution after a finite step From Lemma 6, we have Algorithm 1 terminates after finite steps. After bound tightening according to the "medoids on samples" constraint, Consequently, we have proved Theorem 1. 14 B Parallel results of large scale datasets Table 5 shows the parallel numerical results for large scale datasets with 10,000 to 2,458,285 samples.

The success of large language models (LLMs) has motivated formal theories of language generation and learning. We study the framework of \emph{language generation in the limit}, where an adversary enumerates strings from an unknown language $K$ drawn from a countable class, and an algorithm must generate unseen strings from $K$. Prior work showed that generation is always possible, and that some algorithms achieve positive lower density, revealing a \emph{validity--breadth} trade-off between correctness and coverage. We resolve a main open question in this line, proving a tight bound of $1/2$ on the best achievable lower density. We then strengthen the model to allow \emph{partial enumeration}, where the adversary reveals only an infinite subset $C \subseteq K$. We show that generation in the limit remains achievable, and if $C$ has lower density $α$ in $K$, the algorithm's output achieves density at least $α/2$, matching the upper bound. This generalizes the $1/2$ bound to the partial-information setting, where the generator must recover within a factor $1/2$ of the revealed subset's density. We further revisit the classical Gold--Angluin model of \emph{language identification} under partial enumeration. We characterize when identification in the limit is possible -- when hypotheses $M_t$ eventually satisfy $C \subseteq M \subseteq K$ -- and in the process give a new topological formulation of Angluin's characterization, showing that her condition is precisely equivalent to an appropriate topological space having the $T_D$ separation property.

In the late 19th century, Georg Cantor believed his new theory could help the Church understand the infinite nature of the divine. It might have escaped lay people at the time, but for some observers the ascension of Leo XIV as head of the Catholic Church this year was a reminder that the last time a Pope Leo sat in St. Peter's Chair in the Vatican, from 1878 to 1903, the modern view of infinity was born. Georg Cantor's completely original "naïve" set theory caused both revolution and revolt in mathematical circles, with some embracing his ideas and others rejecting them. Cantor was deeply disappointed with the negative reactions, of course, but never with his own ideas. Because he held firm to the belief that he had a main line to the absolute--that his ideas came direct from (the divine intellect).

Large Language Models (LLMs) like ChatGPT and LLaMA drive rapid progress in generative AI, yet their huge parameter scales create severe computational and environmental burdens. High training costs, energy use, and limited device deployment hinder accessibility. Existing compression - pruning, distillation, low-rank, and quantization - reduces size but ignores complex inter-layer correlations. We propose KARIPAP, a quantum-inspired tensor network compression using Infinite Projected Entangled Pair States (iPEPS) and Tensor Renormalization Group (TRG) contraction. Unlike 1D Matrix Product States, iPEPS captures multi-directional entanglement in attention and deep transformer layers. TRG ensures polynomial-time contraction, making tensorization feasible while preserving key correlation geometry. Experiments on LLaMA-2 7B show up to 93% memory and 70% parameter reduction, with 50% faster training, 25% faster inference, and only 2-3% accuracy loss. Layer-wise entanglement profiling reveals redundancy in deeper layers, confirming their suitability for tensor factorization. KARIPAP demonstrates that modern LLMs occupy low-dimensional entanglement manifolds, enabling scalable, energy-efficient, and quantum-aware AI architectures.

Vision-language models (VLMs) could power real-time assistants and autonomous agents, but they face a critical challenge: understanding near-infinite video streams without escalating latency and memory usage. Processing entire videos with full attention leads to quadratic computational costs and poor performance on long videos. Meanwhile, simple sliding window methods are also flawed, as they either break coherence or suffer from high latency due to redundant recomputation. In this paper, we introduce StreamingVLM, a model designed for real-time, stable understanding of infinite visual input. Our approach is a unified framework that aligns training with streaming inference. During inference, we maintain a compact KV cache by reusing states of attention sinks, a short window of recent vision tokens, and a long window of recent text tokens. This streaming ability is instilled via a simple supervised fine-tuning (SFT) strategy that applies full attention on short, overlapped video chunks, which effectively mimics the inference-time attention pattern without training on prohibitively long contexts. For evaluation, we build Inf-Streams-Eval, a new benchmark with videos averaging over two hours that requires dense, per-second alignment between frames and text. On Inf-Streams-Eval, StreamingVLM achieves a 66.18% win rate against GPT-4O mini and maintains stable, real-time performance at up to 8 FPS on a single NVIDIA H100. Notably, our SFT strategy also enhances general VQA abilities without any VQA-specific fine-tuning, improving performance on LongVideoBench by +4.30 and OVOBench Realtime by +5.96. Code is available at https://github.com/mit-han-lab/streaming-vlm.

Answers to these questions must begin by formalizing the specification for what a generative algorithm for language should be doing.