By proof of Theorem 1, we have HCIL(x) = HWP(x)+HTP(x). Equal contribution The work was done when this author was visiting Bing Liu's group at University of Illinois at Chicago Correspondance author. According to proof of Theorem 4 ii), we have HTP(x) η. Note that ODIN is not applicable to iCaRL and Mnemonics as they are not based on softmax but some distance functions. The result for C100-10T are reported in the main paper. For the postprocessing method ODIN, we only reported the results on C100-10T due to space limitations. Tab. 5 shows the results on the other datasets. A continual learning method with a better AUC shows a better CIL performance than other methods with lower AUC.

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Therapeutic antibodies are an essential and rapidly expanding drug modality.

Therapeutic antibodies are an essential and rapidly flourishing drug modality. The binding specificity between antibodies and antigens is decided by complementarity-determining regions (CDRs) at the tips of these Y-shaped proteins. In this paper, we propose a \textbf{h}ierarchical \textbf{t}raining \textbf{p}aradigm (HTP) for the antibody sequence-structure co-design. HTP consists of four levels of training stages, each corresponding to a specific protein modality within a particular protein domain. Through carefully crafted tasks in different stages, HTP seamlessly and effectively integrates geometric graph neural networks (GNNs) with large-scale protein language models to excavate evolutionary information from not only geometric structures but also vast antibody and non-antibody sequence databases, which determines ligand binding pose and strength. Empirical experiments show HTP sets the new state-of-the-art performance in the co-design problem as well as the fix-backbone design. Our research offers a hopeful path to unleash the potential of deep generative architectures and seeks to illuminate the way forward for the antibody sequence and structure co-design challenge.

This paper introduces the Harmonic Token Projection (HTP), a reversible and deterministic framework for generating text embeddings without training, vocabularies, or stochastic parameters. Unlike neural embeddings that rely on statistical co-occurrence or optimization, HTP encodes each token analytically as a harmonic trajectory derived from its Unicode integer representation, establishing a bijective and interpretable mapping between discrete symbols and continuous vector space. The harmonic formulation provides phase-coherent projections that preserve both structure and reversibility, enabling semantic similarity estimation from purely geometric alignment. Experimental evaluation on the Semantic Textual Similarity Benchmark (STS-B) and its multilingual extension shows that HTP achieves a Spearman correlation of \r{ho} = 0.68 in English, maintaining stable performance across ten languages with negligible computational cost and sub-millisecond latency per sentence pair. This demonstrates that meaningful semantic relations can emerge from deterministic geometry, offering a transparent and efficient alternative to data-driven embeddings. Keywords: Harmonic Token Projection, reversible embedding, deterministic encoding, semantic similarity, multilingual representation.

Large language models produce powerful text embeddings, but their causal attention mechanism restricts the flow of information from later to earlier tokens, degrading representation quality. While recent methods attempt to solve this by prepending a single summary token, they over-compress information, hence harming performance on long documents. We propose Hierarchical Token Prepending (HTP), a method that resolves two critical bottlenecks. To mitigate attention-level compression, HTP partitions the input into blocks and prepends block-level summary tokens to subsequent blocks, creating multiple pathways for backward information flow. To address readout-level over-squashing, we replace last-token pooling with mean-pooling, a choice supported by theoretical analysis. HTP achieves consistent performance gains across 11 retrieval datasets and 30 general embedding benchmarks, especially in long-context settings. As a simple, architecture-agnostic method, HTP enhances both zero-shot and finetuned models, offering a scalable route to superior long-document embeddings.

Therapeutic antibodies are an essential and rapidly flourishing drug modality. The binding specificity between antibodies and antigens is decided by complementarity-determining regions (CDRs) at the tips of these Y-shaped proteins. In this paper, we propose a \textbf{h}ierarchical \textbf{t}raining \textbf{p}aradigm (HTP) for the antibody sequence-structure co-design. HTP consists of four levels of training stages, each corresponding to a specific protein modality within a particular protein domain. Through carefully crafted tasks in different stages, HTP seamlessly and effectively integrates geometric graph neural networks (GNNs) with large-scale protein language models to excavate evolutionary information from not only geometric structures but also vast antibody and non-antibody sequence databases, which determines ligand binding pose and strength.