Species range maps (SRMs) are essential tools for research and policy-making in ecology, conservation, and environmental management.

Prompt engineering is crucial for leveraging the full potential of large language models (LLMs). While automatic prompt optimization offers a scalable alternative to costly manual design, generating effective prompts remains challenging. Existing methods often struggle to stably generate improved prompts, leading to low efficiency, and overlook that prompt optimization easily gets trapped in local optima. Addressing this, we propose GRACE, a framework that integrates two synergistic strategies: Gated Refinement and Adaptive Compression, achieving Efficient prompt optimization. The gated refinement strategy introduces a feedback regulation gate and an update rejection gate, which refine update signals to produce stable and effective prompt improvements. When optimization stagnates, the adaptive compression strategy distills the prompt's core concepts, restructuring the optimization trace and opening new paths. By strategically introducing information loss through refinement and compression, GRACE delivers substantial gains in performance and efficiency. In extensive experiments on 11 tasks across three practical domains, including BIG-Bench Hard (BBH), domain-specific, and general NLP tasks, GRACE achieves significant average relative performance improvements of 4.7%, 4.4% and 2.7% over state-of-the-art methods, respectively. Further analysis shows that GRACE achieves these gains using only 25% of the prompt generation budget required by prior methods, highlighting its high optimization efficiency and low computational overhead. Our code is available at https://github.com/Eric8932/GRACE.

Recent advances in word embeddings and language models use large-scale, unlabelled data and self-supervised learning to boost NLP performance. Multilingual models, often trained on web-sourced data like Wikipedia, face challenges: few low-resource languages are included, their data is often noisy, and lack of labeled datasets makes it hard to evaluate performance outside high-resource languages like English. In this dissertation, we focus on languages spoken in Sub-Saharan Africa where all the indigenous languages in this region can be regarded as low-resourced in terms of the availability of labelled data for NLP tasks and unlabelled data found on the web. We analyse the noise in the publicly available corpora, and curate a high-quality corpus, demonstrating that the quality of semantic representations learned in word embeddings does not only depend on the amount of data but on the quality of pre-training data. We demonstrate empirically the limitations of word embeddings, and the opportunities the multilingual pre-trained language model (PLM) offers especially for languages unseen during pre-training and low-resource scenarios. We further study how to adapt and specialize multilingual PLMs to unseen African languages using a small amount of monolingual texts. To address the under-representation of the African languages in NLP research, we developed large scale human-annotated labelled datasets for 21 African languages in two impactful NLP tasks: named entity recognition and machine translation. We conduct an extensive empirical evaluation using state-of-the-art methods across supervised, weakly-supervised, and transfer learning settings.

Large language models (LLMs) have demonstrated enhanced performance through the \textit{Thinking then Responding} paradigm, where models generate internal thoughts before final responses (aka, System 2 thinking). However, existing research lacks a systematic understanding of the mechanisms underlying how thinking patterns affect performance across model sizes. In this work, we conduct a comprehensive analysis of the impact of various thinking types on model performance and introduce ThinkPatterns-21k, a curated dataset comprising 21k instruction-response pairs (QA) collected from existing instruction-following datasets with five thinking types. For each pair, we augment it with five distinct internal thinking patterns: one unstructured thinking (monologue) and four structured variants (decomposition, self-ask, self-debate and self-critic), while maintaining the same instruction and response. Through extensive evaluation across different model sizes (3B-32B parameters), we have two key findings: (1) smaller models (<30B parameters) can benefit from most of structured thinking patterns, while larger models (32B) with structured thinking like decomposition would degrade performance and (2) unstructured monologue demonstrates broad effectiveness across different model sizes. Finally, we released all of our datasets, checkpoints, training logs of diverse thinking patterns to reproducibility, aiming to facilitate further research in this direction.

Regularized system identification has become a significant complement to more classical system identification. It has been numerically shown that kernel-based regularized estimators often perform better than the maximum likelihood estimator in terms of minimizing mean squared error (MSE). However, regularized estimators often require hyper-parameter estimation. This paper focuses on ridge regression and the regularized estimator by employing the empirical Bayes hyper-parameter estimator. We utilize the excess MSE to quantify the MSE difference between the empirical-Bayes-based regularized estimator and the maximum likelihood estimator for large sample sizes. We then exploit the excess MSE expressions to develop both a family of generalized Bayes estimators and a family of closed-form biased estimators. They have the same excess MSE as the empirical-Bayes-based regularized estimator but eliminate the need for hyper-parameter estimation. Moreover, we conduct numerical simulations to show that the performance of these new estimators is comparable to the empirical-Bayes-based regularized estimator, while computationally, they are more efficient.

Species range maps (SRMs) are essential tools for research and policy-making in ecology, conservation, and environmental management. However, traditional SRMs rely on the availability of environmental covariates and high-quality species location observation data, both of which can be challenging to obtain due to geographic inaccessibility and resource constraints. We propose a novel approach combining millions of citizen science species observations with textual descriptions from Wikipedia, covering habitat preferences and range descriptions for tens of thousands of species. Our framework maps locations, species, and text descriptions into a common space, facilitating the learning of rich spatial covariates at a global scale and enabling zero-shot range estimation from textual descriptions. Evaluated on held-out species, our zero-shot SRMs significantly outperform baselines and match the performance of SRMs obtained using tens of observations. Our approach also acts as a strong prior when combined with observational data, resulting in more accurate range estimation with less data. We present extensive quantitative and qualitative analyses of the learned representations in the context of range estimation and other spatial tasks, demonstrating the effectiveness of our approach.

It has recently been discovered that the conclusions of many highly influential econometrics studies can be overturned by removing a very small fraction of their samples (often less than $0.5\%$). These conclusions are typically based on the results of one or more Ordinary Least Squares (OLS) regressions, raising the question: given a dataset, can we certify the robustness of an OLS fit on this dataset to the removal of a given number of samples? Brute-force techniques quickly break down even on small datasets. Existing approaches which go beyond brute force either can only find candidate small subsets to remove (but cannot certify their non-existence) [BGM20, KZC21], are computationally intractable beyond low dimensional settings [MR22], or require very strong assumptions on the data distribution and too many samples to give reasonable bounds in practice [BP21, FH23]. We present an efficient algorithm for certifying the robustness of linear regressions to removals of samples. We implement our algorithm and run it on several landmark econometrics datasets with hundreds of dimensions and tens of thousands of samples, giving the first non-trivial certificates of robustness to sample removal for datasets of dimension $4$ or greater. We prove that under distributional assumptions on a dataset, the bounds produced by our algorithm are tight up to a $1 + o(1)$ multiplicative factor.

We consider the self-attention model - an interacting particle system on the unit sphere, which serves as a toy model for Transformers, the deep neural network architecture behind the recent successes of large language models. We prove the appearance of dynamic metastability conjectured in [GLPR23] - although particles collapse to a single cluster in infinite time, they remain trapped near a configuration of several clusters for an exponentially long period of time. By leveraging a gradient flow interpretation of the system, we also connect our result to an overarching framework of slow motion of gradient flows proposed by Otto and Reznikoff [OR07] in the context of coarsening and the Allen-Cahn equation. We finally probe the dynamics beyond the exponentially long period of metastability, and illustrate that, under an appropriate time-rescaling, the energy reaches its global maximum in finite time and has a staircase profile, with trajectories manifesting saddle-to-saddle-like behavior, reminiscent of recent works in the analysis of training dynamics via gradient descent for two-layer neural networks.

Savannahs are vital ecosystems whose sustainability is endangered by the spread of woody plants. This research targets the accurate mapping of fractional woody cover (FWC) at the species level in a South African savannah, using EnMAP hyperspectral data. Field annotations were combined with very high-resolution multispectral drone data to produce land cover maps that included three woody species. The high-resolution labelled maps were then used to generate FWC samples for each woody species class at the 30-m spatial resolution of EnMAP. Four machine learning regression algorithms were tested for FWC mapping on dry season EnMAP imagery. The contribution of multitemporal information was also assessed by incorporating as additional regression features, spectro-temporal metrics from Sentinel-2 data of both the dry and wet seasons. The results demonstrated the suitability of our approach for accurately mapping FWC at the species level. The highest accuracy rates achieved from the combined EnMAP and Sentinel-2 experiments highlighted their synergistic potential for species-level vegetation mapping.

Sparsifying transforms became in the last decades widely known tools for finding structured sparse representations of signals in certain transform domains. Despite the popularity of classical transforms such as DCT and Wavelet, learning optimal transforms that guarantee good representations of data into the sparse domain has been recently analyzed in a series of papers. Typically, the conditioning number and representation ability are complementary key features of learning square transforms that may not be explicitly controlled in a given optimization model. Unlike the existing approaches from the literature, in our paper, we consider a new sparsifying transform model that enforces explicit control over the data representation quality and the condition number of the learned transforms. We confirm through numerical experiments that our model presents better numerical behavior than the state-of-the-art.