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Very high resolution (VHR) mapping through remote sensing (RS) imagery presents a new opportunity to inform decision-making and sustainable practices in countless domains. Efficient processing of big VHR data requires automated tools applicable to numerous geographic regions and features. Contemporary RS studies address this challenge by employing deep learning (DL) models for specific datasets or features, which limits their applicability across contexts. The present research aims to overcome this limitation by introducing EcoMapper, a scalable solution to segment arbitrary features in VHR RS imagery. EcoMapper fully automates processing of geospatial data, DL model training, and inference. Models trained with EcoMapper successfully segmented two distinct features in a real-world UAV dataset, achieving scores competitive with prior studies which employed context-specific models. To evaluate EcoMapper, many additional models were trained on permutations of principal field survey characteristics (FSCs). A relationship was discovered allowing derivation of optimal ground sampling distance from feature size, termed Cording Index (CI). A comprehensive methodology for field surveys was developed to ensure DL methods can be applied effectively to collected data. The EcoMapper code accompanying this work is available at //github.com/hcording/ecomapper .

Accelerated failure time (AFT) models are frequently used to model survival data, providing a direct quantification of the relationship between event times and covariates. These models allow for the acceleration or deceleration of failure times through a multiplicative factor that accounts for the effect of covariates. While existing literature provides numerous methods for fitting AFT models with time-fixed covariates, adapting these approaches to scenarios involving both time-varying covariates and partly interval-censored data remains challenging. Motivated by a randomised clinical trial dataset on advanced melanoma patients, we propose a maximum penalised likelihood approach for fitting a semiparametric AFT model to survival data with partly interval-censored failure times. This method also accommodates both time-fixed and time-varying covariates. We utilise Gaussian basis functions to construct a smooth approximation of the non-parametric baseline hazard and fit the model using a constrained optimisation approach. The effectiveness of our method is demonstrated through extensive simulations. Finally, we illustrate the relevance of our approach by applying it to a dataset from a randomised clinical trial involving patients with advanced melanoma.

To manage exceptions, software relies on a key architectural guarantee, precision: that exceptions appear to execute between instructions. However, this definition, dating back over 60 years, fundamentally assumes a sequential programmers model. Modern architectures such as Arm-A with programmer-observable relaxed behaviour make such a naive definition inadequate, and it is unclear exactly what guarantees programmers have on exception entry and exit. In this paper, we clarify the concepts needed to discuss exceptions in the relaxed-memory setting -- a key aspect of precisely specifying the architectural interface between hardware and software. We explore the basic relaxed behaviour across exception boundaries, and the semantics of external aborts, using Arm-A as a representative modern architecture. We identify an important problem, present yet unexplored for decades: pinning down what it means for exceptions to be precise in a relaxed setting. We describe key phenomena that any definition should account for. We develop an axiomatic model for Arm-A precise exceptions, tooling for axiomatic model execution, and a library of tests. Finally we explore the relaxed semantics of software-generated interrupts, as used in sophisticated programming patterns, and sketch how they too could be modelled.

Large language models (LLMs) demonstrate an impressive ability to utilise information within the context of their input sequences to appropriately respond to data unseen by the LLM during its training procedure. This ability is known as in-context learning (ICL). Humans and non-human animals demonstrate similar abilities, however their neural architectures differ substantially from LLMs. Despite this, a critical component within LLMs, the attention mechanism, resembles modern associative memory models, widely used in and influenced by the computational neuroscience community to model biological memory systems. Using this connection, we introduce an associative memory model capable of performing ICL. We use this as inspiration for a novel residual stream architecture which allows information to directly flow between attention heads. We test this architecture during training within a two-layer Transformer and show its ICL abilities manifest more quickly than without this modification. We then apply our architecture in small language models with 8 million parameters, focusing on attention head values, with results also indicating improved ICL performance at this larger and more naturalistic scale.

Language models (LMs) have been widely used to generate text on the Internet. The generated text is often collected into the training corpus of the next generations of LMs. Previous work has experimentally found that LMs collapse when trained on recursively generated text. This paper contributes to existing knowledge from two aspects. We present a theoretical proof of LM collapse. Our proof reveals the cause of LM collapse and proves that all auto-regressive LMs will definitely collapse. We present a new finding: the performance of LMs gradually declines when trained on recursively generated text until they perform no better than a randomly initialized LM. The trained LMs produce large amounts of repetitive text and perform poorly across a wide range of natural language tasks. The above proof and new findings deepen our understanding of LM collapse and offer valuable insights that may inspire new training techniques to mitigate this threat.

We study nonconvex optimization in high dimensions through Langevin dynamics, focusing on the multi-spiked tensor PCA problem. This tensor estimation problem involves recovering $r$ hidden signal vectors (spikes) from noisy Gaussian tensor observations using maximum likelihood estimation. We study the number of samples required for Langevin dynamics to efficiently recover the spikes and determine the necessary separation condition on the signal-to-noise ratios (SNRs) for exact recovery, distinguishing the cases $p \ge 3$ and $p=2$, where $p$ denotes the order of the tensor. In particular, we show that the sample complexity required for recovering the spike associated with the largest SNR matches the well-known algorithmic threshold for the single-spike case, while this threshold degrades when recovering all $r$ spikes. As a key step, we provide a detailed characterization of the trajectory and interactions of low-dimensional projections that capture the high-dimensional dynamics.

We develop a machine learning algorithm to turn around stratification in Monte Carlo sampling. We use a different way to divide the domain space of the integrand, based on the height of the function being sampled, similar to what is done in Lebesgue integration. This means that isocontours of the function define regions that can have any shape depending on the behavior of the function. We take advantage of the capacity of neural networks to learn complicated functions in order to predict these complicated divisions and preclassify large samples of the domain space. From this preclassification we can select the required number of points to perform a number of tasks such as variance reduction, integration and even event selection. The network ultimately defines the regions with what it learned and is also used to calculate the multi-dimensional volume of each region.

We prove, for stably computably enumerable formal systems, direct analogues of the first and second incompleteness theorems of G\"odel. A typical stably computably enumerable set is the set of Diophantine equations with no integer solutions, and in particular such sets are generally not computably enumerable. And so this gives the first extension of the second incompleteness theorem to non classically computable formal systems. Let's motivate this with a somewhat physical application. Let $\mathcal{H} $ be the suitable infinite time limit (stabilization in the sense of the paper) of the mathematical output of humanity, specializing to first order sentences in the language of arithmetic (for simplicity), and understood as a formal system. Suppose that all the relevant physical processes in the formation of $\mathcal{H} $ are Turing computable. Then as defined $\mathcal{H} $ may \emph{not} be computably enumerable, but it is stably computably enumerable. Thus, the classical G\"odel disjunction applied to $\mathcal{H} $ is meaningless, but applying our incompleteness theorems to $\mathcal{H} $ we then get a sharper version of G\"odel's disjunction: assume $\mathcal{H} \vdash PA$ then either $\mathcal{H} $ is not stably computably enumerable or $\mathcal{H} $ is not 1-consistent (in particular is not sound) or $\mathcal{H} $ cannot prove a certain true statement of arithmetic (and cannot disprove it if in addition $\mathcal{H} $ is 2-consistent).

We present ResMLP, an architecture built entirely upon multi-layer perceptrons for image classification. It is a simple residual network that alternates (i) a linear layer in which image patches interact, independently and identically across channels, and (ii) a two-layer feed-forward network in which channels interact independently per patch. When trained with a modern training strategy using heavy data-augmentation and optionally distillation, it attains surprisingly good accuracy/complexity trade-offs on ImageNet. We will share our code based on the Timm library and pre-trained models.

Hashing has been widely used in approximate nearest search for large-scale database retrieval for its computation and storage efficiency. Deep hashing, which devises convolutional neural network architecture to exploit and extract the semantic information or feature of images, has received increasing attention recently. In this survey, several deep supervised hashing methods for image retrieval are evaluated and I conclude three main different directions for deep supervised hashing methods. Several comments are made at the end. Moreover, to break through the bottleneck of the existing hashing methods, I propose a Shadow Recurrent Hashing(SRH) method as a try. Specifically, I devise a CNN architecture to extract the semantic features of images and design a loss function to encourage similar images projected close. To this end, I propose a concept: shadow of the CNN output. During optimization process, the CNN output and its shadow are guiding each other so as to achieve the optimal solution as much as possible. Several experiments on dataset CIFAR-10 show the satisfying performance of SRH.