Multi-Head Attention

The discovery of exoplanets at scale has become one of the defining data science challenges in modern astrophysics. NASA's Transiting Exoplanet Survey Satellite (TESS) had catalogued over 7,800 planet candidates by early 2026, yet confirmation stands at fewer than 720. This paper introduces ExoNet, a multimodal deep learning framework that jointly processes phase-folded global and local light curve views alongside stellar parameter features through a calibrated late-fusion architecture combining 1D Convolutional Neural Networks, 8-head Multi-Head Attention over temporal feature maps, and a residual fusion head with post-hoc Temperature Scaling calibration. Trained on 7,585 labeled Kepler Objects of Interest, ExoNet achieves Test AUC = 0.9549 and 86.3% accuracy. Applied to 4,720 verified unconfirmed TESS Planet Candidates with TOI-TIC cross-identification verified against the NASA Exoplanet Archive, the model yields 1,754 high-confidence signals, 52 habitable-zone candidates, and six Earth-sized habitable-zone targets below 1.6 Earth radii. TOI-5728.01 and TOI-6716.01 emerge as the most Earth-like unconfirmed candidates. Full ablation confirms each modality improves AUC. Code and catalog are openly released.

To quantify the geometric expressivity of transformers, we introduce a tropical geometry framework to characterize their exact spatial partitioning capabilities. By modeling self-attention as a vector-valued tropical rational map, we prove it evaluates exactly to a Power Voronoi Diagram in the zero-temperature limit. Building on this equivalence, we establish a combinatorial rationale for Multi-Head Self-Attention (MHSA): via the Minkowski sum of Newton polytopes, multi-head aggregation expands the polyhedral complexity to $\mathcal{O}(N^H)$, overcoming the $\mathcal{O}(N)$ bottleneck of single heads. Extending this to deep architectures, we derive the first tight asymptotic bounds on the number of linear regions in transformers ($Θ(N^{d_{\text{model}}L})$), demonstrating a combinatorial explosion driven intrinsically by sequence length $N$, ambient embedding dimension $d_{\text{model}}$, and network depth $L$. Importantly, we guarantee that this idealized polyhedral skeleton is geometrically stable: finite-temperature soft attention preserves these topological partitions via exponentially tight differential approximation bounds.

The article proposes a new architecture based on Multi-head attention to solve the problem of morphological tagging for the Russian language. The preprocessing of the word vectors includes splitting the words into subtokens, followed by a trained procedure for aggregating the vectors of the subtokens into vectors for tokens. This allows to support an open dictionary and analyze morphological features taking into account parts of words (prefixes, endings, etc.). The open dictionary allows in future to analyze words that are absent in the training dataset. The performed computational experiment on the SinTagRus and Taiga datasets shows that for some grammatical categories the proposed architecture gives accuracy 98-99% and above, which outperforms previously known results. For nine out of ten words, the architecture precisely predicts all grammatical categories and indicates when the categories must not be analyzed for the word. At the same time, the model based on the proposed architecture can be trained on consumer-level graphics accelerators, retains all the advantages of Multi-head attention over RNNs (RNNs are not used in the proposed approach), does not require pretraining on large collections of unlabeled texts (like BERT), and shows higher processing speed than previous results.

We study a random model of deep multi-head self-attention in which the weights are resampled independently across layers and heads, as at initialization of training. Viewing depth as a time variable, the residual stream defines a discrete-time interacting particle system on the unit sphere. We prove that, under suitable joint scalings of the depth, the residual step size, and the number of heads, this dynamics admits a nontrivial homogenized limit. Depending on the scaling, the limit is either deterministic or stochastic with common noise; in the mean-field regime, the latter leads to a stochastic nonlinear Fokker--Planck equation for the conditional law of a representative token. In the Gaussian setting, the limiting drift vanishes, making the homogenized dynamics explicit enough to study representation collapse. This yields quantitative trade-offs between dimension, context length, and temperature, and identifies regimes in which clustering can be mitigated.

The pursuit of reducing the memory footprint of the self-attention mechanism in multi-headed self attention (MHA) spawned a rich portfolio of methods, e.g., group-query attention (GQA) and multi-head latent attention (MLA). The methods leverage specialized low-rank factorizations across embedding dimensions or attention heads. From the point of view of classical low-rank approximation, these methods are unconventional and raise questions of which objects they really approximate and how to interpret the low-rank behavior of the resulting representations. To answer these questions, this work proposes a generalized view on the weight objects in the self-attention layer and a factorization strategy, which allows us to construct a parameter efficient scheme, called Tucker Attention. Tucker Attention requires an order of magnitude fewer parameters for comparable validation metrics, compared to GQA and MLA, as evaluated in LLM and ViT test cases. Additionally, Tucker Attention~encompasses GQA, MLA, MHA as special cases and is fully compatible with flash-attention and rotary position embeddings (RoPE). This generalization strategy yields insights of the actual ranks achieved by MHA, GQA, and MLA, and further enables simplifications for MLA.

MANAR (Memory-augmented Attention with Navigational Abstract Conceptual Representation), contextualization layer generalizes standard multi-head attention (MHA) by instantiating the principles of Global Workspace Theory (GWT). While MHA enables unconstrained all-to-all communication, it lacks the functional bottleneck and global integration mechanisms hypothesized in cognitive models of consciousness. MANAR addresses this by implementing a central workspace through a trainable memory of abstract concepts and an Abstract Conceptual Representation (ACR). The architecture follows a two-stage logic that maps directly to GWT mechanics: (i) an integration phase, where retrieved memory concepts converge to form a collective "mental image" (the ACR) based on input stimuli; and (ii) a broadcasting phase, where this global state navigates and informs the contextualization of individual local tokens. We demonstrate that efficient linear-time scaling is a fundamental architectural byproduct of instantiating GWT functional bottleneck, as routing global information through a constant-sized ACR resolves the quadratic complexity inherent in standard attention. MANAR is a compatible re-parameterization of MHA with identical semantic roles for its projections, enabling knowledge transfer from pretrained transformers via weight-copy and thus overcoming the adoption barriers of structurally incompatible linear-time alternatives. MANAR enables non-convex contextualization, synthesizing representations that provably lie outside the convex hull of input tokens - a mathematical reflection of the creative synthesis described in GWT. Empirical evaluations confirm that MANAR matches or exceeds strong baselines across language (GLUE score of 85.1), vision (83.9% ImageNet-1K), and speech (2.7% WER on LibriSpeech), positioning it as an efficient and expressive alternative to quadratic attention.

The dense output projection in multi head attention scales quadratically with model dimension, contributing significantly to parameter count, memory footprint, and inference cost. We propose replacing this projection with a fixed, parameter free Walsh Hadamard Transform (WHT) followed by a diagonal affine transformation. This approach eliminates approximately 25 percent of attention parameters per block while maintaining global cross-head interaction through an orthogonal, norm-preserving transformation. Our results demonstrate that WHT augmented models exhibit a steeper validation loss curve relative to training FLOPs compared to dense baselines, suggesting superior compute utilization during training. Crucially, we show that efficiency gains including reduced memory footprint and increased throughput grow monotonically with model size, batch size, and sequence length. We evaluate performance across both prefill and decoding stages, finding that the structured transform consistently outperforms dense projections as complexity increases. Our findings indicate that replacing dense projections with structured transforms allows for more compute-efficient architectures that achieve lower loss than dense models at an equivalent training budget.

Multi-head attention enables transformer models to represent multiple attention patterns simultaneously. Empirically, head specialization emerges in distinct stages during training, while many heads remain redundant and learn similar representations. We propose a theoretical model capturing this phenomenon, based on the multi-index and single-location regression frameworks. In the first part, we analyze the training dynamics of multi-head softmax attention under SGD, revealing an initial unspecialized phase followed by a multi-stage specialization phase in which different heads sequentially align with latent signal directions. In the second part, we study the impact of attention activation functions on performance. We introduce the Bayes-softmax attention, which achieves optimal prediction performance in this setting.

Retrieval heads, a subset of attention heads in Transformers, were studied in English, showing its crucial role in retrieving information from the context. We expand the study of retrieval heads to multilingual context and find that while nearly half of all retrieval heads are often shared across multiple languages, language-specific retrieval heads also emerge. We further design a cross-lingual needle-in-the-haystack task, to identify $\textit{Retrieval Transition Heads (RTH)}$ that retrieve key information and further map it to target-language output. Our experiments reveal that RTHs do not always overlap with RH, and can be more vital for Chain-of-Thought reasoning in multilingual LLMs. Across four multilingual benchmarks (MMLU-ProX, MGSM, MLQA, and XQuAD) and two model families (Qwen2.5-7B Instruct and Llama3.1-8B Instruct), we demonstrate that masking RTH induces bigger performance drop than masking Retrieval Heads (RH). Specifically, for Llama3.1-8B Instruct, masking the top-25 RTHs results in an average 37.3-point drop (against 19.5-point drop from RH masking) in reasoning accuracy (MMLU-ProX, MGSM) and 9.0 F1-score reduction (against 5.1 drop for RH) in extractive QA (MLQA, XQuAD). Our work advances the understanding of multilingual LMs by isolating the attention heads responsible for mapping to target languages.

Multi-Head Attention (MHA) is the core computational primitive underlying modern Large Language Models (LLMs). However, MHA suffers from a fundamental linear scaling limitation: $H$ attention heads produce exactly $H$ independent attention matrices, with no communication between heads during attention computation. This becomes problematic for multi-step reasoning, where correct answers depend on aggregating evidence from multiple parts of the context and composing latent token-to-token relations over a chain of intermediate inferences. To address this, we propose Interleaved Head Attention (IHA), which enables cross-head mixing by constructing $P$ pseudo-heads per head (typically $P=H$), where each pseudo query/key/value is a learned linear combination of all $H$ original queries, keys and values respectively. Interactions between pseudo-query and pseudo-key heads induce up to $P^2$ attention patterns per head with modest parameter overhead $\mathcal{O}(H^2P)$. We provide theory showing improved efficiency in terms of number of parameters on the synthetic Polynomial task (IHA uses $Θ(\sqrt{k}n^2)$ parameters vs. $Θ(kn^2)$ for MHA) and on the synthetic order-sensitive CPM-3 task (IHA uses $\lceil\sqrt{N_{\max}}\rceil$ heads vs. $N_{\max}$ for MHA). On real-world benchmarks, IHA improves Multi-Key retrieval on RULER by 10-20% (4k-16k) and, after fine-tuning for reasoning on OpenThoughts, improves GSM8K by 5.8% and MATH-500 by 2.8% (Majority Vote) over full attention.

This paper studies simple transformers trained on a high-order Markov chain, where the model must incorporate information from multiple past positions, each with different statistical importance. We show that transformers learn the task incrementally, with each stage corresponding to learning how to copy information from a subset of positions via a sparse attention pattern. Notably, the learning dynamics transition from a competitive phase, where all heads focus on the statistically most important positions, to a cooperative phase, where different heads specialize in different patterns. We model these dynamics with simplified differential equations and prove stage-wise convergence of the resulting system. Functionally, these stages correspond to a sequence of increasingly expressive misspecified models, with the full model class reached only at the end. Overall, we give a theoretical account of how structured attention patterns and head specialization emerge in stages without an explicit curriculum, with implications for generalization in sequential tasks.

Modern large language models increasingly require long contexts for reasoning and multi-document tasks, but attention's quadratic complexity creates a severe computational bottleneck. We present Block Sparse Flash Attention (BSFA), a drop-in replacement that accelerates long-context inference while preserving model quality. Unlike methods that predict importance before computing scores, BSFA computes exact query-key similarities to select the top-k most important value blocks for each query. By comparing per-block maximum scores against calibrated thresholds, we skip approximately 50% of the computation and memory transfers for pruned blocks. Our training-free approach requires only a one-time threshold calibration on a small dataset to learn the per-layer and per-head attention score distributions. We provide a CUDA kernel implementation that can be used as a drop-in replacement for FlashAttention. On Llama-3.1-8B, BSFA achieves up to 1.13x end-to-end speedup on LongBench with only a 1.1% accuracy drop, and up to 1.24x on Needle-in-a-Haystack retrieval at a 1% accuracy drop. The attention kernel itself accelerates by up to 1.38x. We compare BSFA against five recent sparse attention baselines (SpargeAttention, MInference, FlexPrefill, XAttention, and BLASST), and verify the method on Qwen2.5-7B and on A6000 and H100 GPUs. The implementation is available at https://github.com/Danielohayon/Block-Sparse-Flash-Attention.

Attention is a core operation in large language models (LLMs). We present BD Attention (BDA), a lossless algorithmic reformulation of attention. BDA is enabled by a simple matrix identity from Basis Decomposition (BD), which restructures multi-head projections into a compact form while preserving exact outputs. Unlike I/O-aware system optimizations such as FlashAttention, BDA provides a mathematically guaranteed acceleration that is architecture-agnostic. On DeepSeek-V2-Lite (16B, FP16), BDA requires only 4s of offline preparation with no retraining required and, on modern GPUs, achieves 34% faster key/value projections and 25% smaller weights, while increasing perplexity (PPL) by just 0.02% (FP16) or 0.0004% (FP32), a negligible effect on model performance. These results position BDA as a theoretically exact method for lossless attention acceleration that is complementary to existing engineering-level optimizations. Our code is available at https://github.com/abcbdf/basis-decomposition-official.

Large language models (LLMs) routinely fail to output the correct option in multiple-choice question answering (MCQA) while encoding the answer internally. We expose this latent knowledge via the Query--Key (QK) score, defined for an attention head as the inner product between the last-token query and the key at the end-of-line token following option $i$, evaluated before rotary positional embedding is applied. Its argmax identifies a universal class of select-and-copy heads in middle layers that perform option selection through semantic query--key alignment, mechanistically distinct from induction and copy-suppression heads (Olsson et al., 2022): they are invariant to label symbols, and solve a synthetic task with zero surface overlap---properties no positional-copy account explains and that critically require stripping RoPE. Across 24 models from 1.5B to 72B parameters (LLaMA-2/3/3.1/3.3, Qwen-2.5, Gemma, Phi-3.5, DeepSeek-R1-Distill), a single head's QK-score exceeds the model's own zero-shot accuracy by up to $+27.4$ pp on HellaSwag and $+49.8$ pp on HaluDialogue; causal zero-ablation collapses MCQA accuracy to near-random. To remove any dependence on labeled validation data, we introduce an unsupervised HeadScore that ranks heads from unlabeled inputs and recovers the supervised top-$k$ heads on every tested model. Against four positional-debiasing baselines (e.g., PriDe, Wiegrefe, Wang), QK-score is complementary by construction: debiasing re-weights output logits, whereas QK-score reads the model's selection from a middle-layer head before decoding. We release a one-line drop-in HeadScore script and per-model head indices, making every result one-command reproducible across all 24 models and four benchmarks.