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How Powerful are Decoder-Only Transformer Neural Models?

In this article we prove that the general transformer neural model undergirding modern large language models (LLMs) is Turing complete under reasonable assumptions. This is the first work to directly address the Turing completeness of the underlying technology employed in GPT-x as past work has focused on the more expressive, full auto-encoder transformer architecture. From this theoretical analysis, we show that the sparsity/compressibility of the word embedding is an important consideration for Turing completeness to hold. We also show that Transformers are are a variant of B machines studied by Hao Wang.

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Forecaster: A Graph Transformer for Forecasting Spatial and Time-Dependent Data

Spatial and time-dependent data is of interest in many applications. This task is difficult due to its complex spatial dependency, long-range temporal dependency, data non-stationarity, and data heterogeneity. To address these challenges, we propose Forecaster, a graph Transformer architecture. Specifically, we start by learning the structure of the graph that parsimoniously represents the spatial dependency between the data at different locations. Based on the topology of the graph, we sparsify the Transformer to account for the strength of spatial dependency, long-range temporal dependency, data non-stationarity, and data heterogeneity. We evaluate Forecaster in the problem of forecasting taxi ride-hailing demand and show that our proposed architecture significantly outperforms the state-of-the-art baselines.

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ConTraNet: A single end-to-end hybrid network for EEG-based and EMG-based human machine interfaces

Objective: Electroencephalography (EEG) and electromyography (EMG) are two non-invasive bio-signals, which are widely used in human machine interface (HMI) technologies (EEG-HMI and EMG-HMI paradigm) for the rehabilitation of physically disabled people. Successful decoding of EEG and EMG signals into respective control command is a pivotal step in the rehabilitation process. Recently, several Convolutional neural networks (CNNs) based architectures are proposed that directly map the raw time-series signal into decision space and the process of meaningful features extraction and classification are performed simultaneously. However, these networks are tailored to the learn the expected characteristics of the given bio-signal and are limited to single paradigm. In this work, we addressed the question that can we build a single architecture which is able to learn distinct features from different HMI paradigms and still successfully classify them. Approach: In this work, we introduce a single hybrid model called ConTraNet, which is based on CNN and Transformer architectures that is equally useful for EEG-HMI and EMG-HMI paradigms. ConTraNet uses CNN block to introduce inductive bias in the model and learn local dependencies, whereas the Transformer block uses the self-attention mechanism to learn the long-range dependencies in the signal, which are crucial for the classification of EEG and EMG signals. Main results: We evaluated and compared the ConTraNet with state-of-the-art methods on three publicly available datasets which belong to EEG-HMI and EMG-HMI paradigms. ConTraNet outperformed its counterparts in all the different category tasks (2-class, 3-class, 4-class, and 10-class decoding tasks). Significance: The results suggest that ConTraNet is robust to learn distinct features from different HMI paradigms and generalizes well as compared to the current state of the art algorithms.

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Transformers as Graph-to-Graph Models

We argue that Transformers are essentially graph-to-graph models, with sequences just being a special case. Attention weights are functionally equivalent to graph edges. Our Graph-to-Graph Transformer architecture makes this ability explicit, by inputting graph edges into the attention weight computations and predicting graph edges with attention-like functions, thereby integrating explicit graphs into the latent graphs learned by pretrained Transformers. Adding iterative graph refinement provides a joint embedding of input, output, and latent graphs, allowing non-autoregressive graph prediction to optimise the complete graph without any bespoke pipeline or decoding strategy. Empirical results show that this architecture achieves state-of-the-art accuracies for modelling a variety of linguistic structures, integrating very effectively with the latent linguistic representations learned by pretraining.

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NiNformer: A Network in Network Transformer with Token Mixing Generated Gating Function

The attention mechanism is the primary component of the transformer architecture; it has led to significant advancements in deep learning spanning many domains and covering multiple tasks. In computer vision, the attention mechanism was first incorporated in the Vision Transformer ViT, and then its usage has expanded into many tasks in the vision domain, such as classification, segmentation, object detection, and image generation. While the attention mechanism is very expressive and capable, it comes with the disadvantage of being computationally expensive and requiring datasets of considerable size for effective optimization. To address these shortcomings, many designs have been proposed in the literature to reduce the computational burden and alleviate the data size requirements. Examples of such attempts in the vision domain are the MLP-Mixer, the Conv-Mixer, the Perciver-IO, and many more attempts with different sets of advantages and disadvantages. This paper introduces a new computational block as an alternative to the standard ViT block. The newly proposed block reduces the computational requirements by replacing the normal attention layers with a Network in Network structure, therefore enhancing the static approach of the MLP-Mixer with a dynamic learning of element-wise gating function generated by a token mixing process. Extensive experimentation shows that the proposed design provides better performance than the baseline architectures on multiple datasets applied in the image classification task of the vision domain.

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Neural Organ Transplantation (NOT): Checkpoint-Based Modular Adaptation for Transformer Models

We introduce Neural Organ Transplantation (NOT), a modular adaptation framework that enables trained transformer layers to function as reusable transferable checkpoints for domain adaptation. Unlike conventional fine-tuning approaches that tightly couple trained parameters to specific model instances and training data, NOT extracts contiguous layer subsets ("donor organs") from pre-trained models, trains them independently on domain-specific data, and saves them as standalone checkpoint files that can be transplanted into compatible recipient models without access to the original training data. Through experiments on three decoder-only transformer architectures spanning 124M to 20B parameters (GPT-2, TinyLlama, and GPT-OSS), we demonstrate that donor transplantation substantially outperforms existing adaptation methods, achieving an order-of-magnitude improvement in perplexity over LoRA while training significantly faster. The method exhibits position dependence, with early insertion positions yielding optimal results. Cross-domain transfer at billion-parameter scale reveals unexpected regularization benefits. These findings demonstrate that transformer middle layers can support efficient modular transfer for decoder-only architectures, enabling privacy-preserving expertise sharing through checkpoint distribution. We note that this approach is currently limited to decoder-only models; preliminary experiments on encoder-based architectures show reduced effectiveness.

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Ripple Attention for Visual Perception with Sub-quadratic Complexity

Transformer architectures are now central to sequence modeling tasks. At its heart is the attention mechanism, which enables effective modeling of long-term dependencies in a sequence. Recently, transformers have been successfully applied in the computer vision domain, where 2D images are first segmented into patches and then treated as 1D sequences. Such linearization, however, impairs the notion of spatial locality in images, which bears important visual clues. To bridge the gap, we propose ripple attention, a sub-quadratic attention mechanism for vision transformers. Built upon the recent kernel-based efficient attention mechanisms, we design a novel dynamic programming algorithm that weights contributions of different tokens to a query with respect to their relative spatial distances in the 2D space in linear observed time. Extensive experiments and analyses demonstrate the effectiveness of ripple attention on various visual tasks.

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TransFusion: Cross-view Fusion with Transformer for 3D Human Pose Estimation

Estimating the 2D human poses in each view is typically the first step in calibrated multi-view 3D pose estimation. But the performance of 2D pose detectors suffers from challenging situations such as occlusions and oblique viewing angles. To address these challenges, previous works derive point-to-point correspondences between different views from epipolar geometry and utilize the correspondences to merge prediction heatmaps or feature representations. Instead of post-prediction merge/calibration, here we introduce a transformer framework for multi-view 3D pose estimation, aiming at directly improving individual 2D predictors by integrating information from different views. Inspired by previous multi-modal transformers, we design a unified transformer architecture, named TransFusion, to fuse cues from both current views and neighboring views. Moreover, we propose the concept of epipolar field to encode 3D positional information into the transformer model. The 3D position encoding guided by the epipolar field provides an efficient way of encoding correspondences between pixels of different views. Experiments on Human 3.6M and Ski-Pose show that our method is more efficient and has consistent improvements compared to other fusion methods. Specifically, we achieve 25.8 mm MPJPE on Human 3.6M with only 5M parameters on 256 x 256 resolution.

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kMaX-DeepLab: k-means Mask Transformer

The rise of transformers in vision tasks not only advances network backbone designs, but also starts a brand-new page to achieve end-to-end image recognition (e.g., object detection and panoptic segmentation). Originated from Natural Language Processing (NLP), transformer architectures, consisting of self-attention and cross-attention, effectively learn long-range interactions between elements in a sequence. However, we observe that most existing transformer-based vision models simply borrow the idea from NLP, neglecting the crucial difference between languages and images, particularly the extremely large sequence length of spatially flattened pixel features. This subsequently impedes the learning in cross-attention between pixel features and object queries. In this paper, we rethink the relationship between pixels and object queries and propose to reformulate the cross-attention learning as a clustering process. Inspired by the traditional k-means clustering algorithm, we develop a k-means Mask Xformer (kMaX-DeepLab) for segmentation tasks, which not only improves the state-of-the-art, but also enjoys a simple and elegant design. As a result, our kMaX-DeepLab achieves a new state-of-the-art performance on COCO val set with 58.0% PQ, Cityscapes val set with 68.4% PQ, 44.0% AP, and 83.5% mIoU, and ADE20K val set with 50.9% PQ and 55.2% mIoU without test-time augmentation or external dataset. We hope our work can shed some light on designing transformers tailored for vision tasks. TensorFlow code and models are available at https://github.com/google-research/deeplab2 A PyTorch re-implementation is also available at https://github.com/bytedance/kmax-deeplab

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Transformers with Learnable Activation Functions

Activation functions can have a significant impact on reducing the topological complexity of input data and therefore improve the performance of the model. Selecting a suitable activation function is an essential step in neural model design. However, the choice of activation function is seldom discussed or explored in Transformer-based language models. Their activation functions are chosen beforehand and then remain fixed from pre-training to fine-tuning. As a result, the inductive biases they imposed on models cannot be adjusted during this long life cycle. Moreover, subsequently developed models (e.g., RoBERTa, BART, and GPT-3) often follow up prior work (e.g., BERT) to use the same activation function without justification. In this paper, we investigate the effectiveness of using Rational Activation Function (RAF), a learnable activation function, in the Transformer architecture. In contrast to conventional, predefined activation functions, RAFs can adaptively learn optimal activation functions during training according to input data. Our experiments show the RAF-based Transformer (RAFT) achieves a lower validation perplexity than a vanilla BERT with the GELU function. We further evaluate RAFT on downstream tasks in low- and full-data settings. Our results show that RAFT outperforms the counterpart model across the majority of tasks and settings. For instance, RAFT outperforms vanilla BERT on the GLUE benchmark by 5.71 points on average in low-data scenario (where 100 training examples are available) and by 2.05 points on SQuAD in full-data setting. Analysis of the shapes of learned RAFs further unveils that they substantially vary between different layers of the pre-trained model and mostly look very different from conventional activation functions. RAFT opens a new research direction for analyzing and interpreting pre-trained models according to the learned activation functions.

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Adapting Pre-trained Vision Transformers from 2D to 3D through Weight Inflation Improves Medical Image Segmentation

Given the prevalence of 3D medical imaging technologies such as MRI and CT that are widely used in diagnosing and treating diverse diseases, 3D segmentation is one of the fundamental tasks of medical image analysis. Recently, Transformer-based models have started to achieve state-of-the-art performances across many vision tasks, through pre-training on large-scale natural image benchmark datasets. While works on medical image analysis have also begun to explore Transformer-based models, there is currently no optimal strategy to effectively leverage pre-trained Transformers, primarily due to the difference in dimensionality between 2D natural images and 3D medical images. Existing solutions either split 3D images into 2D slices and predict each slice independently, thereby losing crucial depth-wise information, or modify the Transformer architecture to support 3D inputs without leveraging pre-trained weights. In this work, we use a simple yet effective weight inflation strategy to adapt pre-trained Transformers from 2D to 3D, retaining the benefit of both transfer learning and depth information. We further investigate the effectiveness of transfer from different pre-training sources and objectives. Our approach achieves state-of-the-art performances across a broad range of 3D medical image datasets, and can become a standard strategy easily utilized by all work on Transformer-based models for 3D medical images, to maximize performance.

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Comparing Generalization in Learning with Limited Numbers of Exemplars: Transformer vs. RNN in Attractor Dynamics

ChatGPT, a widely-recognized large language model (LLM), has recently gained substantial attention for its performance scaling, attributed to the billions of web-sourced natural language sentences used for training. Its underlying architecture, Transformer, has found applications across diverse fields, including video, audio signals, and robotic movement. %The crucial question this raises concerns the Transformer's generalization-in-learning (GIL) capacity. However, this raises a crucial question about Transformer's generalization in learning (GIL) capacity. Is ChatGPT's success chiefly due to the vast dataset used for training, or is there more to the story? To investigate this, we compared Transformer's GIL capabilities with those of a traditional Recurrent Neural Network (RNN) in tasks involving attractor dynamics learning. For performance evaluation, the Dynamic Time Warping (DTW) method has been employed. Our simulation results suggest that under conditions of limited data availability, Transformer's GIL abilities are markedly inferior to those of RNN.

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MIMONets: Multiple-Input-Multiple-Output Neural Networks Exploiting Computation in Superposition

With the advent of deep learning, progressively larger neural networks have been designed to solve complex tasks. We take advantage of these capacity-rich models to lower the cost of inference by exploiting computation in superposition. To reduce the computational burden per input, we propose Multiple-Input-Multiple-Output Neural Networks (MIMONets) capable of handling many inputs at once. MIMONets augment various deep neural network architectures with variable binding mechanisms to represent an arbitrary number of inputs in a compositional data structure via fixed-width distributed representations. Accordingly, MIMONets adapt nonlinear neural transformations to process the data structure holistically, leading to a speedup nearly proportional to the number of superposed input items in the data structure. After processing in superposition, an unbinding mechanism recovers each transformed input of interest. MIMONets also provide a dynamic trade-off between accuracy and throughput by an instantaneous on-demand switching between a set of accuracy-throughput operating points, yet within a single set of fixed parameters. We apply the concept of MIMONets to both CNN and Transformer architectures resulting in MIMOConv and MIMOFormer, respectively. Empirical evaluations show that MIMOConv achieves about 2-4 x speedup at an accuracy delta within [+0.68, -3.18]% compared to WideResNet CNNs on CIFAR10 and CIFAR100. Similarly, MIMOFormer can handle 2-4 inputs at once while maintaining a high average accuracy within a [-1.07, -3.43]% delta on the long range arena benchmark. Finally, we provide mathematical bounds on the interference between superposition channels in MIMOFormer. Our code is available at https://github.com/IBM/multiple-input-multiple-output-nets.

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YZS-model: A Predictive Model for Organic Drug Solubility Based on Graph Convolutional Networks and Transformer-Attention

Accurate prediction of drug molecule solubility is crucial for therapeutic effectiveness and safety. Traditional methods often miss complex molecular structures, leading to inaccuracies. We introduce the YZS-Model, a deep learning framework integrating Graph Convolutional Networks (GCN), Transformer architectures, and Long Short-Term Memory (LSTM) networks to enhance prediction precision. GCNs excel at capturing intricate molecular topologies by modeling the relationships between atoms and bonds. Transformers, with their self-attention mechanisms, effectively identify long-range dependencies within molecules, capturing global interactions. LSTMs process sequential data, preserving long-term dependencies and integrating temporal information within molecular sequences. This multifaceted approach leverages the strengths of each component, resulting in a model that comprehensively understands and predicts molecular properties. Trained on 9,943 compounds and tested on an anticancer dataset, the YZS-Model achieved an $R^2$ of 0.59 and an RMSE of 0.57, outperforming benchmark models ($R^2$ of 0.52 and RMSE of 0.61). In an independent test, it demonstrated an RMSE of 1.05, improving accuracy by 45.9%. The integration of these deep learning techniques allows the YZS-Model to learn valuable features from complex data without predefined parameters, handle large datasets efficiently, and adapt to various molecular types. This comprehensive capability significantly improves predictive accuracy and model generalizability. Its precision in solubility predictions can expedite drug development by optimizing candidate selection, reducing costs, and enhancing efficiency. Our research underscores deep learning's transformative potential in pharmaceutical science, particularly for solubility prediction and drug design.

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Spacetime $E(n)$-Transformer: Equivariant Attention for Spatio-temporal Graphs

We introduce an $E(n)$-equivariant Transformer architecture for spatio-temporal graph data. By imposing rotation, translation, and permutation equivariance inductive biases in both space and time, we show that the Spacetime $E(n)$-Transformer (SET) outperforms purely spatial and temporal models without symmetry-preserving properties. We benchmark SET against said models on the charged $N$-body problem, a simple physical system with complex dynamics. While existing spatio-temporal graph neural networks focus on sequential modeling, we empirically demonstrate that leveraging underlying domain symmetries yields considerable improvements for modeling dynamical systems on graphs.

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Ehrenfeucht-Haussler Rank and Chain of Thought

The notion of \emph{rank} of a Boolean function has been a cornerstone in PAC learning theory, enabling quasipolynomial-time learning algorithms for polynomial-size decision trees. We present a novel characterization of rank, grounded in the well-known Transformer architecture. We show that the rank of a function $f$ corresponds to the minimum number of \emph{Chain of Thought} (CoT) steps required by a single-layer Transformer with hard attention to compute $f$. Based on this characterization we establish tight bounds on the number of CoT steps required for specific problems, showing that \(\ell\)-fold function composition necessitates exactly \(\ell\) CoT steps. Furthermore, we analyze the problem of identifying the position of the \(k\)-th occurrence of 1 in a Boolean sequence, proving that it requires \(k\) CoT steps. Finally, we introduce the notion of the multi-head rank that captures multi-head single-layer transformers, and perform the analysis of PAC-learnability of the classes of functions with bounded multi-head rank.

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Architectural Trade-offs in Small Language Models Under Compute Constraints

We present a systematic empirical study of small language models under strict compute constraints, analyzing how architectural choices and training budget interact to determine performance. Starting from a linear next-token predictor, we progressively introduce nonlinearities, self-attention, and multi-layer transformer architectures, evaluating each on character-level modeling of Tiny Shakespeare and word-level modeling of Penn Treebank (PTB) and WikiText-2. We compare models using test negative log-likelihood (NLL), parameter count, and approximate training FLOPs to characterize accuracy-efficiency trade-offs. Our results show that attention-based models dominate MLPs in per-FLOP efficiency even at small scale, while increasing depth or context without sufficient optimization can degrade performance. We further examine rotary positional embeddings (RoPE), finding that architectural techniques successful in large language models do not necessarily transfer to small-model regimes.

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InfoFlow: A Framework for Multi-Layer Transformer Analysis

While the approximation properties of single-layer Transformer architectures have been studied in recent works, a rigorous theoretical understanding of the multi-layer setting remains limited. In this work, we establish that multi-layer Transformers possess fundamentally different approximation capabilities from single-layer ones: for certain retrieval tasks, any single-layer Transformer requires least $Ω(\varepsilon^{-k})$ parameters to achieve precision $\varepsilon$, where $k$ grows linearly with sequence length $T$, whereas a two-layer Transformer with a single head per layer achieves the same approximation precision with at most $O (\varepsilon^{-1})$ parameters. To understand this separation, we identify two structural mechanisms underlying multi-layer approximation. Specifically, softmax attention can only efficiently retrieve the token attaining the maximum attention score, incurring exponential-in-length parameter cost for $k$-th largest retrieval with $k \geq 2$. Moreover, the parameter cost of decoding coupled information scales with the size of the retrieved token set. Motivated by these findings, we propose InfoFlow, a framework for multi-layer Transformers. The framework tracks an information set of accessible input positions at each token and layer, assigning an explicit approximation rate to each mode of information propagation. This abstraction recovers known approximation bounds, remains consistent with experimental observations on trained networks, and yields concrete predictions in settings where direct theoretical analysis is currently intractable. Our results provide a principled framework for reasoning about the approximation efficiency of multi-layer Transformers.

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