Randomized controlled trials typically assume that prognostic covariates are known and available at no cost. In practice, obtaining high-dimensional pretreatment data is costly, forcing a trade-off between covariate-adaptive precision and a measurement budget. We introduce Dynamic Adaptive Rerandomization via Thompson Sampling (DARTS), which treats covariate acquisition as a sequential optimization problem embedded within a design-based causal inference task. A budgeted combinatorial Thompson sampler learns which covariates are most prognostic across successive batches; selected covariates then drive rerandomization and regression adjustment to reduce batch-level average treatment effect variance. Our primary theoretical contribution is a decoupling result: adaptive covariate selection based on past batches preserves batch-level randomization validity, and the cumulative inverse-variance weighted estimator achieves at least nominal asymptotic coverage. We further derive a Bayes risk bound for the acquisition layer that matches the minimax lower bound up to logarithmic factors. Empirically, DARTS systematically concentrates the budget on informative features, significantly closing the efficiency gap to oracle designs while maintaining strict inferential validity.

High dimensional sampling is an important computational tool in statistics and other computational disciplines, with applications ranging from Bayesian statistical uncertainty quantification, metabolic modeling in systems biology to volume computation. We present $\textsf{PolytopeWalk}$, a new scalable Python library designed for uniform sampling over polytopes. The library provides an end-to-end solution, which includes preprocessing algorithms such as facial reduction and initialization methods. Six state-of-the-art MCMC algorithms on polytopes are implemented, including the Dikin, Vaidya, and John Walk. Additionally, we introduce novel sparse constrained formulations of these algorithms, enabling efficient sampling from sparse polytopes of the form $K_2 = \{x \in \mathbb{R}^d \ | \ Ax = b, x \succeq_k 0\}$. This implementation maintains sparsity in $A$, ensuring scalability to high dimensional settings $(d > 10^5)$. We demonstrate the improved sampling efficiency and per-iteration cost on both Netlib datasets and structured polytopes. $\textsf{PolytopeWalk}$ is available at github.com/ethz-randomwalk/polytopewalk with documentation at polytopewalk.readthedocs.io .

Automatically generating symbolic music-music scores tailored to specific human needs-can be highly beneficial for musicians and enthusiasts. Recent studies have shown promising results using extensive datasets and advanced transformer architectures. However, these state-of-the-art models generally offer only basic control over aspects like tempo and style for the entire composition, lacking the ability to manage finer details, such as control at the level of individual bars. While fine-tuning a pre-trained symbolic music generation model might seem like a straightforward method for achieving this finer control, our research indicates challenges in this approach. The model often fails to respond adequately to new, fine-grained bar-level control signals. To address this, we propose two innovative solutions. First, we introduce a pre-training task designed to link control signals directly with corresponding musical tokens, which helps in achieving a more effective initialization for subsequent fine-tuning. Second, we implement a novel counterfactual loss that promotes better alignment between the generated music and the control prompts. Together, these techniques significantly enhance our ability to control music generation at the bar level, showing a 13.06\% improvement over conventional methods. Our subjective evaluations also confirm that this enhanced control does not compromise the musical quality of the original pre-trained generative model.

To generate coherent responses, language models infer unobserved meaning from their input text sequence. One potential explanation for this capability arises from theories of delay embeddings in dynamical systems, which prove that unobserved variables can be recovered from the history of only a handful of observed variables. To test whether language models are effectively constructing delay embeddings, we measure the capacities of sequence models to reconstruct unobserved dynamics. We trained 1-layer transformer decoders and state-space sequence models on next-step prediction from noisy, partially-observed time series data. We found that each sequence layer can learn a viable embedding of the underlying system. However, state-space models have a stronger inductive bias than transformers-in particular, they more effectively reconstruct unobserved information at initialization, leading to more parameter-efficient models and lower error on dynamics tasks.

Multivariate time-series (MTS) forecasting is a paramount and fundamental problem in many real-world applications. The core issue in MTS forecasting is how to effectively model complex spatial-temporal patterns. In this paper, we develop a modular and interpretable forecasting framework, which seeks to individually model each component of the spatial-temporal patterns. We name this framework SCNN, short for Structured Component-based Neural Network. SCNN works with a pre-defined generative process of MTS, which arithmetically characterizes the latent structure of the spatial-temporal patterns. In line with its reverse process, SCNN decouples MTS data into structured and heterogeneous components and then respectively extrapolates the evolution of these components, the dynamics of which is more traceable and predictable than the original MTS. Extensive experiments are conducted to demonstrate that SCNN can achieve superior performance over state-of-the-art models on three real-world datasets. Additionally, we examine SCNN with different configurations and perform in-depth analyses of the properties of SCNN.

Imagine you are working on some problem in which you have to do some computation which takes a lot of time in a conventional way. I was working on a project and came across a problem solved through the vectorization process. I will not able to share the exact problem but will give you some ideas so you can solve your own problem by following these steps. For instance, you have a numpy array of 300 size, which is basically a vector, and you want to find cosine similarity with all other vectors, roughly 150000 vectors. Wow, that sounds like a lot of computation. But let's define our Cosine Similarity Function Now let's define our Vectors The total exact time is 4.34531307220459 sec We can reduce the time by using the vectorization process, but first, let's try to make some ground for this.

As we know, PyTorch is a popular, open source ML framework and an optimized tensor library developed by researchers at Facebook AI, used widely in deep learning and AI Research. The torch package contains data structures for multi-dimensional tensors (N-dimensional arrays) and mathematical operations over these are defined. In this blog post, we seek to cover some of the useful functions that the torch package provides for tensor manipulation, by looking at working examples for each and an example when the function doesn't work as expected. This function concatenates the given sequence of tensors along the given dimension. All tensors must either have the same shape (except in the concatenating dimension) or be empty.