Additional Feedback: This paper studies a variant of Fisher et al's unseen species problem, namely, predicting the number of new symbols that appears at least \mu times in the future (unobserved) sample of size a \times n on the basis of the existing sample of size n. This extends the results of Orlitsky et al. [22] focusing on \mu 1, the original setting in Fisher et al. The main findings are - Theorem 1: an estimator is constructed using the smoothing technique from [22] that achieves a normalized prediction error of n {-\Omega(1/a)} provided a O(log n/mu) - Theorem 2: a minimax lower bound n {-O(1/a)} is shown, provided a \Omega(log n/mu). Both the construction and the analysis follow closely those in [22]. Namely, the upper bound is obtained by following the recipe of smoothed estimator (by modifying the unbiased estimator) and the analysis uses Poisson sampling and relies on Bessel function to control the bias from cancellation; the lower bound is obtained by a reduction to the support size estimation problem.

DNA barcodes are crucial in biodiversity analysis for building automatic identification systems that recognize known species and discover unseen species. Unlike human genome modeling, barcode-based invertebrate identification poses challenges in the vast diversity of species and taxonomic complexity. Among Transformer-based foundation models, BarcodeBERT excelled in species-level identification of invertebrates, highlighting the effectiveness of self-supervised pretraining on barcode-specific datasets. Recently, structured state space models (SSMs) have emerged, with a time complexity that scales sub-quadratically with the context length. SSMs provide an efficient parameterization of sequence modeling relative to attention-based architectures. Given the success of Mamba and Mamba-2 in natural language, we designed BarcodeMamba, a performant and efficient foundation model for DNA barcodes in biodiversity analysis. We conducted a comprehensive ablation study on the impacts of self-supervised training and tokenization methods, and compared both versions of Mamba layers in terms of expressiveness and their capacity to identify "unseen" species held back from training. Our study shows that BarcodeMamba has better performance than BarcodeBERT even when using only 8.3% as many parameters, and improves accuracy to 99.2% on species-level accuracy in linear probing without fine-tuning for "seen" species. In our scaling study, BarcodeMamba with 63.6% of BarcodeBERT's parameters achieved 70.2% genus-level accuracy in 1-nearest neighbor (1-NN) probing for unseen species. The code repository to reproduce our experiments is available at https://github.com/bioscan-ml/BarcodeMamba.

As part of an ongoing worldwide effort to comprehend and monitor insect biodiversity, this paper presents the BIOSCAN-5M Insect dataset to the machine learning community and establish several benchmark tasks. BIOSCAN-5M is a comprehensive dataset containing multi-modal information for over 5 million insect specimens, and it significantly expands existing image-based biological datasets by including taxonomic labels, raw nucleotide barcode sequences, assigned barcode index numbers, and geographical information. We propose three benchmark experiments to demonstrate the impact of the multi-modal data types on the classification and clustering accuracy. First, we pretrain a masked language model on the DNA barcode sequences of the BIOSCAN-5M dataset, and demonstrate the impact of using this large reference library on species- and genus-level classification performance. Second, we propose a zero-shot transfer learning task applied to images and DNA barcodes to cluster feature embeddings obtained from self-supervised learning, to investigate whether meaningful clusters can be derived from these representation embeddings. Third, we benchmark multi-modality by performing contrastive learning on DNA barcodes, image data, and taxonomic information. This yields a general shared embedding space enabling taxonomic classification using multiple types of information and modalities. The code repository of the BIOSCAN-5M Insect dataset is available at https://github.com/zahrag/BIOSCAN-5M.

Measuring biodiversity is crucial for understanding ecosystem health. While prior works have developed machine learning models for the taxonomic classification of photographic images and DNA separately, in this work, we introduce a multimodal approach combining both, using CLIP-style contrastive learning to align images, DNA barcodes, and textual data in a unified embedding space. This allows for accurate classification of both known and unknown insect species without task-specific fine-tuning, leveraging contrastive learning for the first time to fuse DNA and image data. Our method surpasses previous single-modality approaches in accuracy by over 11% on zero-shot learning tasks, showcasing its effectiveness in biodiversity studies.

Estimating the number of unseen species is an important problem in many scientific endeavors. Its most popular formulation, introduced by Fisher, uses $n$ samples to predict the number $U$ of hitherto unseen species that would be observed if $t\cdot n$ new samples were collected. Of considerable interest is the largest ratio $t$ between the number of new and existing samples for which $U$ can be accurately predicted. In seminal works, Good and Toulmin constructed an intriguing estimator that predicts $U$ for all $t\le 1$, thereby showing that the number of species can be estimated for a population twice as large as that observed. Subsequently Efron and Thisted obtained a modified estimator that empirically predicts $U$ even for some $t>1$, but without provable guarantees. We derive a class of estimators that $\textit{provably}$ predict $U$ not just for constant $t>1$, but all the way up to $t$ proportional to $\log n$. This shows that the number of species can be estimated for a population $\log n$ times larger than that observed, a factor that grows arbitrarily large as $n$ increases. We also show that this range is the best possible and that the estimators' mean-square error is optimal up to constants for any $t$. Our approach yields the first provable guarantee for the Efron-Thisted estimator and, in addition, a variant which achieves stronger theoretical and experimental performance than existing methodologies on a variety of synthetic and real datasets. The estimators we derive are simple linear estimators that are computable in time proportional to $n$. The performance guarantees hold uniformly for all distributions, and apply to all four standard sampling models commonly used across various scientific disciplines: multinomial, Poisson, hypergeometric, and Bernoulli product.