Daily Papers

Source separation models either work on the spectrogram or waveform domain. In this work, we show how to perform end-to-end hybrid source separation, letting the model decide which domain is best suited for each source, and even combining both. The proposed hybrid version of the Demucs architecture won the Music Demixing Challenge 2021 organized by Sony. This architecture also comes with additional improvements, such as compressed residual branches, local attention or singular value regularization. Overall, a 1.4 dB improvement of the Signal-To-Distortion (SDR) was observed across all sources as measured on the MusDB HQ dataset, an improvement confirmed by human subjective evaluation, with an overall quality rated at 2.83 out of 5 (2.36 for the non hybrid Demucs), and absence of contamination at 3.04 (against 2.37 for the non hybrid Demucs and 2.44 for the second ranking model submitted at the competition).

Scaling Diffusion Transformers (DiTs) to hundreds of layers introduces a structural vulnerability: networks can enter a silent, mean-dominated collapse state that homogenizes token representations and suppresses centered variation. Through mechanistic auditing, we isolate the trigger event of this collapse as Mean Mode Screaming (MMS). MMS can occur even when training appears stable, with a mean-coherent backward shock on residual writers that opens deep residual branches and drives the network into a mean-dominated state. We show this behavior is driven by an exact decomposition of these gradients into mean-coherent and centered components, compounded by the structural suppression of attention-logit gradients through the null space of the Softmax Jacobian once values homogenize. To address this, we propose Mean-Variance Split (MV-Split) Residuals, which combine a separately gained centered residual update with a leaky trunk-mean replacement. On a 400-layer single-stream DiT, MV-Split prevents the divergent collapse that crashes the un-stabilized baseline; it tracks close to the baseline's pre-crash trajectory while remaining substantially better than token-isotropic gating methods such as LayerScale across the full schedule. Finally, we present a 1000-layer DiT as a scale-validation run at boundary scales, establishing that the architecture remains stably trainable at extreme depth.

We show that taking the width and depth to infinity in a deep neural network with skip connections, when branches are scaled by 1/depth (the only nontrivial scaling), result in the same covariance structure no matter how that limit is taken. This explains why the standard infinite-width-then-depth approach provides practical insights even for networks with depth of the same order as width. We also demonstrate that the pre-activations, in this case, have Gaussian distributions which has direct applications in Bayesian deep learning. We conduct extensive simulations that show an excellent match with our theoretical findings.

Image dehazing aims to restore image clarity and visual quality by reducing atmospheric scattering and absorption effects. While deep learning has made significant strides in this area, more and more methods are constrained by network depth. Consequently, lots of approaches have adopted parallel branching strategies. however, they often prioritize aspects such as resolution, receptive field, or frequency domain segmentation without dynamically partitioning branches based on the distribution of input features. Inspired by dynamic filtering, we propose using cascaded dynamic filters to create a multi-branch network by dynamically generating filter kernels based on feature map distribution. To better handle branch features, we propose a residual multiscale block (RMB), combining different receptive fields. Furthermore, we also introduce a dynamic convolution-based local fusion method to merge features from adjacent branches. Experiments on RESIDE, Haze4K, and O-Haze datasets validate our method's effectiveness, with our model achieving a PSNR of 43.21dB on the RESIDE-Indoor dataset. The code is available at https://github.com/dauing/CasDyF-Net.

The cost of hyperparameter tuning in deep learning has been rising with model sizes, prompting practitioners to find new tuning methods using a proxy of smaller networks. One such proposal uses muP parameterized networks, where the optimal hyperparameters for small width networks transfer to networks with arbitrarily large width. However, in this scheme, hyperparameters do not transfer across depths. As a remedy, we study residual networks with a residual branch scale of 1/text{depth} in combination with the muP parameterization. We provide experiments demonstrating that residual architectures including convolutional ResNets and Vision Transformers trained with this parameterization exhibit transfer of optimal hyperparameters across width and depth on CIFAR-10 and ImageNet. Furthermore, our empirical findings are supported and motivated by theory. Using recent developments in the dynamical mean field theory (DMFT) description of neural network learning dynamics, we show that this parameterization of ResNets admits a well-defined feature learning joint infinite-width and infinite-depth limit and show convergence of finite-size network dynamics towards this limit.

Recent work has made clear that the residual pathway is not mere optimization plumbing; it is part of the model's representational machinery. We agree, but argue that the cleanest way to organize this design space is through a two-axis view of the Transformer. A decoder evolves information along two ordered dimensions: sequence position and layer depth. Self-attention already provides adaptive mixing along the sequence axis, whereas the residual stream usually performs fixed addition along the depth axis. If we fix a token position and treat layer index as the ordered variable, then a causal depth-wise residual attention read is exactly the same local operator as causal short sliding-window attention (ShortSWA), except written over depth rather than over sequence. This is the core residual stream duality behind Transformer^2. This perspective also clarifies the recent literature. ELC-BERT and DenseFormer already show that learned aggregation over depth can outperform uniform residual accumulation, while Vertical Attention, DeepCrossAttention (DCA), MUDDFormer, and Attention Residuals move further toward explicit attention-based routing over earlier layers. The key point, however, is that operator-level duality does not imply systems-level symmetry. For large-scale autoregressive models, sequence-axis ShortSWA is usually the more hardware-friendly placement because it reuses token-side sliding-window kernels, KV-cache layouts, and chunked execution. If the goal is instead to change the shortcut itself, Deep Delta Learning (DDL) is the cleaner intervention because it modifies the residual operator directly rather than adding a separate cross-layer retrieval path. Our recommendation is therefore simple: use DDL when the shortcut is the object of interest, and use sequence-axis ShortSWA when the goal is local adaptive mixing.

Deep residual networks have emerged as a family of extremely deep architectures showing compelling accuracy and nice convergence behaviors. In this paper, we analyze the propagation formulations behind the residual building blocks, which suggest that the forward and backward signals can be directly propagated from one block to any other block, when using identity mappings as the skip connections and after-addition activation. A series of ablation experiments support the importance of these identity mappings. This motivates us to propose a new residual unit, which makes training easier and improves generalization. We report improved results using a 1001-layer ResNet on CIFAR-10 (4.62% error) and CIFAR-100, and a 200-layer ResNet on ImageNet. Code is available at: https://github.com/KaimingHe/resnet-1k-layers

Deep residual architectures, such as ResNet and the Transformer, have enabled models of unprecedented depth, yet a formal understanding of why depth is so effective remains an open question. A popular intuition, following Veit et al. (2016), is that these residual networks behave like ensembles of many shallower models. Our key finding is an explicit analytical formula that verifies this ensemble perspective, proving that increasing network depth is mathematically equivalent to expanding the size of this implicit ensemble. Furthermore, our expansion reveals a hierarchical ensemble structure in which the combinatorial growth of computation paths leads to an explosion in the output signal, explaining the historical necessity of normalization layers in training deep models. This insight offers a first principles explanation for the historical dependence on normalization layers and sheds new light on a family of successful normalization-free techniques like SkipInit and Fixup. However, while these previous approaches infer scaling factors through optimizer analysis or a heuristic analogy to Batch Normalization, our work offers the first explanation derived directly from the network's inherent functional structure. Specifically, our Residual Expansion Theorem reveals that scaling each residual module provides a principled solution to taming the combinatorial explosion inherent to these architectures. We further show that this scaling acts as a capacity controls that also implicitly regularizes the model's complexity.

One of the core pillars of efficient deep learning methods is architectural improvements such as the residual/skip connection, which has led to significantly better model convergence and quality. Since then the residual connection has become ubiquitous in not just convolutional neural networks but also transformer-based architectures, the backbone of LLMs. In this paper we introduce Learned Augmented Residual Layer (LAuReL) -- a novel generalization of the canonical residual connection -- with the goal to be an in-situ replacement of the latter while outperforming on both model quality and footprint metrics. Our experiments show that using \laurel can help boost performance for both vision and language models. For example, on the ResNet-50, ImageNet 1K task, it achieves 60% of the gains from adding an extra layer, while only adding 0.003% more parameters, and matches it while adding 2.6times fewer parameters.

The rehearsal strategy is widely used to alleviate the catastrophic forgetting problem in class incremental learning (CIL) by preserving limited exemplars from previous tasks. With imbalanced sample numbers between old and new classes, the classifier learning can be biased. Existing CIL methods exploit the long-tailed (LT) recognition techniques, e.g., the adjusted losses and the data re-sampling methods, to handle the data imbalance issue within each increment task. In this work, the dynamic nature of data imbalance in CIL is shown and a novel Dynamic Residual Classifier (DRC) is proposed to handle this challenging scenario. Specifically, DRC is built upon a recent advance residual classifier with the branch layer merging to handle the model-growing problem. Moreover, DRC is compatible with different CIL pipelines and substantially improves them. Combining DRC with the model adaptation and fusion (MAF) pipeline, this method achieves state-of-the-art results on both the conventional CIL and the LT-CIL benchmarks. Extensive experiments are also conducted for a detailed analysis. The code is publicly available.

Deep residual networks were shown to be able to scale up to thousands of layers and still have improving performance. However, each fraction of a percent of improved accuracy costs nearly doubling the number of layers, and so training very deep residual networks has a problem of diminishing feature reuse, which makes these networks very slow to train. To tackle these problems, in this paper we conduct a detailed experimental study on the architecture of ResNet blocks, based on which we propose a novel architecture where we decrease depth and increase width of residual networks. We call the resulting network structures wide residual networks (WRNs) and show that these are far superior over their commonly used thin and very deep counterparts. For example, we demonstrate that even a simple 16-layer-deep wide residual network outperforms in accuracy and efficiency all previous deep residual networks, including thousand-layer-deep networks, achieving new state-of-the-art results on CIFAR, SVHN, COCO, and significant improvements on ImageNet. Our code and models are available at https://github.com/szagoruyko/wide-residual-networks

Deep Spiking Neural Networks (SNNs) present optimization difficulties for gradient-based approaches due to discrete binary activation and complex spatial-temporal dynamics. Considering the huge success of ResNet in deep learning, it would be natural to train deep SNNs with residual learning. Previous Spiking ResNet mimics the standard residual block in ANNs and simply replaces ReLU activation layers with spiking neurons, which suffers the degradation problem and can hardly implement residual learning. In this paper, we propose the spike-element-wise (SEW) ResNet to realize residual learning in deep SNNs. We prove that the SEW ResNet can easily implement identity mapping and overcome the vanishing/exploding gradient problems of Spiking ResNet. We evaluate our SEW ResNet on ImageNet, DVS Gesture, and CIFAR10-DVS datasets, and show that SEW ResNet outperforms the state-of-the-art directly trained SNNs in both accuracy and time-steps. Moreover, SEW ResNet can achieve higher performance by simply adding more layers, providing a simple method to train deep SNNs. To our best knowledge, this is the first time that directly training deep SNNs with more than 100 layers becomes possible. Our codes are available at https://github.com/fangwei123456/Spike-Element-Wise-ResNet.

Convolutional neural network (CNN) depth is of crucial importance for image super-resolution (SR). However, we observe that deeper networks for image SR are more difficult to train. The low-resolution inputs and features contain abundant low-frequency information, which is treated equally across channels, hence hindering the representational ability of CNNs. To solve these problems, we propose the very deep residual channel attention networks (RCAN). Specifically, we propose a residual in residual (RIR) structure to form very deep network, which consists of several residual groups with long skip connections. Each residual group contains some residual blocks with short skip connections. Meanwhile, RIR allows abundant low-frequency information to be bypassed through multiple skip connections, making the main network focus on learning high-frequency information. Furthermore, we propose a channel attention mechanism to adaptively rescale channel-wise features by considering interdependencies among channels. Extensive experiments show that our RCAN achieves better accuracy and visual improvements against state-of-the-art methods.

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 also train ResMLP models in a self-supervised setup, to further remove priors from employing a labelled dataset. Finally, by adapting our model to machine translation we achieve surprisingly good results. We share pre-trained models and our code based on the Timm library.

Residual connections are pivotal for deep neural networks, enabling greater depth by mitigating vanishing gradients. However, in standard residual updates, the module's output is directly added to the input stream. This can lead to updates that predominantly reinforce or modulate the existing stream direction, potentially underutilizing the module's capacity for learning entirely novel features. In this work, we introduce Orthogonal Residual Update: we decompose the module's output relative to the input stream and add only the component orthogonal to this stream. This design aims to guide modules to contribute primarily new representational directions, fostering richer feature learning while promoting more efficient training. We demonstrate that our orthogonal update strategy improves generalization accuracy and training stability across diverse architectures (ResNetV2, Vision Transformers) and datasets (CIFARs, TinyImageNet, ImageNet-1k), achieving, for instance, a +4.3\%p top-1 accuracy gain for ViT-B on ImageNet-1k.

The dominant industry response to AI-generated code quality problems is to deploy AI reviewers. This paper argues that this response is structurally circular when executable specifications are absent: without an external reference, both the generating agent and the reviewing agent reason from the same artefact, share the same training distribution, and exhibit correlated failures. The review checks code against itself, not against intent. Three hypotheses are developed. First, that correlated errors in homogeneous LLM pipelines echo rather than cancel, a claim supported by convergent empirical evidence from multiple 2025-2026 studies and by three small contrived experiments reported here. The first two experiments are same-family (Claude reviewing Claude-generated code); the third extends to a cross-family panel of four models from three families. All use a planted bug corpus rather than a natural defect sample; they are directional evidence, not a controlled demonstration. Second, that executable specifications perform a domain transition in the Cynefin sense, converting enabling constraints into governing constraints and moving the problem from the complex domain to the complicated domain, a transition that AI makes economically viable at scale. Third, that the defect classes lying outside the reach of executable specifications form a well-defined residual, which is the legitimate and bounded target for AI review. The combined argument implies an architecture: specifications first, deterministic verification pipeline second, AI review only for the structural and architectural residual. This is not a claim that AI review is valueless. It is a claim about what it is actually for, and about what happens when it is deployed without the foundation that makes it non-circular.

Large language model (LLM) scaling is hitting a wall. Widening models yields diminishing returns, and extending context length does not improve fundamental expressivity. In contrast, depth scaling offers theoretically superior expressivity, yet current Transformer architectures struggle to train reliably at extreme depths. We revisit the Post-LayerNorm (Post-LN) formulation, whose instability at scale caused its replacement by Pre-LN in modern LLMs. We show that the central failure mode of Post-LN arises from the ResNet-style residual pathway, which introduces gradient vanishing in deep networks. We present Keel, a Post-LN Transformer that replaces this residual path with a Highway-style connection. This modification preserves the gradient flow through the residual branch, preventing signal vanishing from the top layers to the bottom. Unlike prior methods, Keel enables stable training at extreme depths without requiring specialized initialization or complex optimization tricks. Keel trains robustly at depths exceeding 1000 layers and consistently improves perplexity and depth-scaling characteristics over Pre-LN. These findings indicate that Post-LN, when paired with a Highway-style connection, provides a simple and effective foundation for building deeply scalable LLMs, opening the possibility for future infinite-depth architectures.

Deep learning (DL) based semantic segmentation methods have been providing state-of-the-art performance in the last few years. More specifically, these techniques have been successfully applied to medical image classification, segmentation, and detection tasks. One deep learning technique, U-Net, has become one of the most popular for these applications. In this paper, we propose a Recurrent Convolutional Neural Network (RCNN) based on U-Net as well as a Recurrent Residual Convolutional Neural Network (RRCNN) based on U-Net models, which are named RU-Net and R2U-Net respectively. The proposed models utilize the power of U-Net, Residual Network, as well as RCNN. There are several advantages of these proposed architectures for segmentation tasks. First, a residual unit helps when training deep architecture. Second, feature accumulation with recurrent residual convolutional layers ensures better feature representation for segmentation tasks. Third, it allows us to design better U-Net architecture with same number of network parameters with better performance for medical image segmentation. The proposed models are tested on three benchmark datasets such as blood vessel segmentation in retina images, skin cancer segmentation, and lung lesion segmentation. The experimental results show superior performance on segmentation tasks compared to equivalent models including U-Net and residual U-Net (ResU-Net).

The influential Residual Networks designed by He et al. remain the gold-standard architecture in numerous scientific publications. They typically serve as the default architecture in studies, or as baselines when new architectures are proposed. Yet there has been significant progress on best practices for training neural networks since the inception of the ResNet architecture in 2015. Novel optimization & data-augmentation have increased the effectiveness of the training recipes. In this paper, we re-evaluate the performance of the vanilla ResNet-50 when trained with a procedure that integrates such advances. We share competitive training settings and pre-trained models in the timm open-source library, with the hope that they will serve as better baselines for future work. For instance, with our more demanding training setting, a vanilla ResNet-50 reaches 80.4% top-1 accuracy at resolution 224x224 on ImageNet-val without extra data or distillation. We also report the performance achieved with popular models with our training procedure.

The Branch-and-bound (B&B) algorithm is the main solver for Mixed Integer Linear Programs (MILPs), where the selection of branching variable is essential to computational efficiency. However, traditional heuristics for branching often fail to generalize across heterogeneous problem instances, while existing learning-based methods such as imitation learning (IL) suffers from dependence on expert demonstration quality, and reinforcement learning (RL) struggles with limitations in sparse rewards and dynamic state representation challenges. To address these issues, we propose ReviBranch, a novel deep RL framework that constructs revived trajectories by reviving explicit historical correspondences between branching decisions and their corresponding graph states along search-tree paths. During training, ReviBranch enables agents to learn from complete structural evolution and temporal dependencies within the branching process. Additionally, we introduce an importance-weighted reward redistribution mechanism that transforms sparse terminal rewards into dense stepwise feedback, addressing the sparse reward challenge. Extensive experiments on different MILP benchmarks demonstrate that ReviBranch outperforms state-of-the-art RL methods, reducing B&B nodes by 4.0% and LP iterations by 2.2% on large-scale instances. The results highlight the robustness and generalizability of ReviBranch across heterogeneous MILP problem classes.

Post-training data plays a pivotal role in shaping the capabilities of Large Language Models (LLMs), yet datasets are often treated as isolated artifacts, overlooking the systemic connections that underlie their evolution. To disentangle these complex relationships, we introduce the concept of data lineage to the LLM ecosystem and propose an automated multi-agent framework to reconstruct the evolutionary graph of dataset development. Through large-scale lineage analysis, we characterize domain-specific structural patterns, such as vertical refinement in math-oriented datasets and horizontal aggregation in general-domain corpora. Moreover, we uncover pervasive systemic issues, including structural redundancy induced by implicit dataset intersections and the propagation of benchmark contamination along lineage paths. To demonstrate the practical value of lineage analysis for data construction, we leverage the reconstructed lineage graph to create a lineage-aware diversity-oriented dataset. By anchoring instruction sampling at upstream root sources, this approach mitigates downstream homogenization and hidden redundancy, yielding a more diverse post-training corpus. We further highlight lineage-centric analysis as an efficient and robust topological alternative to sample-level dataset comparison for large-scale data ecosystems. By grounding data construction in explicit lineage structures, our work advances post-training data curation toward a more systematic and controllable paradigm.

Large language model inference is both memory-intensive and time-consuming, often requiring distributed algorithms to efficiently scale. Various model parallelism strategies are used in multi-gpu training and inference to partition computation across multiple devices, reducing memory load and computation time. However, using model parallelism necessitates communication of information between GPUs, which has been a major bottleneck and limits the gains obtained by scaling up the number of devices. We introduce Ladder Residual, a simple architectural modification applicable to all residual-based models that enables straightforward overlapping that effectively hides the latency of communication. Our insight is that in addition to systems optimization, one can also redesign the model architecture to decouple communication from computation. While Ladder Residual can allow communication-computation decoupling in conventional parallelism patterns, we focus on Tensor Parallelism in this paper, which is particularly bottlenecked by its heavy communication. For a Transformer model with 70B parameters, applying Ladder Residual to all its layers can achieve 30% end-to-end wall clock speed up at inference time with TP sharding over 8 devices. We refer the resulting Transformer model as the Ladder Transformer. We train a 1B and 3B Ladder Transformer from scratch and observe comparable performance to a standard dense transformer baseline. We also show that it is possible to convert parts of the Llama-3.1 8B model to our Ladder Residual architecture with minimal accuracy degradation by only retraining for 3B tokens.

Reinforcement Learning with Verifiable Rewards (RLVR) enhances reasoning of Large Language Models (LLMs) but usually exhibits limited generation diversity due to the over-incentivization of positive rewards. Although methods like Negative Sample Reinforcement (NSR) mitigate this issue by upweighting penalty from negative samples, they may suppress the semantic distributions shared between positive and negative responses. To boost reasoning ability without losing diversity, this paper proposes negative sample projection Residual Reinforcement Learning (ResRL) that decouples similar semantic distributions among positive and negative responses. We theoretically link Lazy Likelihood Displacement (LLD) to negative-positive head-gradient interference and derive a single-forward proxy that upper-bounds representation alignment to guide conservative advantage reweighting. ResRL then projects negative-token hidden representations onto an SVD-based low-rank positive subspace and uses projection residuals to modulate negative gradients, improving reasoning while preserving diversity and outperforming strong baselines on average across twelve benchmarks spanning Mathematics, Code, Agent Tasks, and Function Calling. Notably, ResRL surpasses NSR on mathematical reasoning by 9.4\% in Avg@16 and 7.0\% in Pass@128. Code is available at https://github.com/1229095296/ResRL.git.

Accurate segmentation of brain tumors plays a key role in the diagnosis and treatment of brain tumor diseases. It serves as a critical technology for quantifying tumors and extracting their features. With the increasing application of deep learning methods, the computational burden has become progressively heavier. To achieve a lightweight model with good segmentation performance, this study proposes the MBDRes-U-Net model using the three-dimensional (3D) U-Net codec framework, which integrates multibranch residual blocks and fused attention into the model. The computational burden of the model is reduced by the branch strategy, which effectively uses the rich local features in multimodal images and enhances the segmentation performance of subtumor regions. Additionally, during encoding, an adaptive weighted expansion convolution layer is introduced into the multi-branch residual block, which enriches the feature expression and improves the segmentation accuracy of the model. Experiments on the Brain Tumor Segmentation (BraTS) Challenge 2018 and 2019 datasets show that the architecture could maintain a high precision of brain tumor segmentation while considerably reducing the calculation overhead.Our code is released at https://github.com/Huaibei-normal-university-cv-laboratory/mbdresunet

We present Hierarchical Residual Networks (HiResNets), deep convolutional neural networks with long-range residual connections between layers at different hierarchical levels. HiResNets draw inspiration on the organization of the mammalian brain by replicating the direct connections from subcortical areas to the entire cortical hierarchy. We show that the inclusion of hierarchical residuals in several architectures, including ResNets, results in a boost in accuracy and faster learning. A detailed analysis of our models reveals that they perform hierarchical compositionality by learning feature maps relative to the compressed representations provided by the skip connections.

In this work we identify the dormant neuron phenomenon in deep reinforcement learning, where an agent's network suffers from an increasing number of inactive neurons, thereby affecting network expressivity. We demonstrate the presence of this phenomenon across a variety of algorithms and environments, and highlight its effect on learning. To address this issue, we propose a simple and effective method (ReDo) that Recycles Dormant neurons throughout training. Our experiments demonstrate that ReDo maintains the expressive power of networks by reducing the number of dormant neurons and results in improved performance.

Residual connections are central to modern deep learning architectures, enabling the training of very deep networks by mitigating gradient vanishing. Hyper-Connections recently generalized residual connections by introducing multiple connection strengths at different depths, thereby addressing the seesaw effect between gradient vanishing and representation collapse. However, Hyper-Connections increase memory access costs by expanding the width of hidden states. In this paper, we propose Frac-Connections, a novel approach that divides hidden states into multiple parts rather than expanding their width. Frac-Connections retain partial benefits of Hyper-Connections while reducing memory consumption. To validate their effectiveness, we conduct large-scale experiments on language tasks, with the largest being a 7B MoE model trained on up to 3T tokens, demonstrating that Frac-Connections significantly outperform residual connections.

Residual connections with PreNorm are standard in modern LLMs, yet they accumulate all layer outputs with fixed unit weights. This uniform aggregation causes uncontrolled hidden-state growth with depth, progressively diluting each layer's contribution. We propose Attention Residuals (AttnRes), which replaces this fixed accumulation with softmax attention over preceding layer outputs, allowing each layer to selectively aggregate earlier representations with learned, input-dependent weights. To address the memory and communication overhead of attending over all preceding layer outputs for large-scale model training, we introduce Block AttnRes, which partitions layers into blocks and attends over block-level representations, reducing the memory footprint while preserving most of the gains of full AttnRes. Combined with cache-based pipeline communication and a two-phase computation strategy, Block AttnRes becomes a practical drop-in replacement for standard residual connections with minimal overhead. Scaling law experiments confirm that the improvement is consistent across model sizes, and ablations validate the benefit of content-dependent depth-wise selection. We further integrate AttnRes into the Kimi Linear architecture (48B total / 3B activated parameters) and pre-train on 1.4T tokens, where AttnRes mitigates PreNorm dilution, yielding more uniform output magnitudes and gradient distribution across depth, and improves downstream performance across all evaluated tasks.

Deeper neural networks are more difficult to train. We present a residual learning framework to ease the training of networks that are substantially deeper than those used previously. We explicitly reformulate the layers as learning residual functions with reference to the layer inputs, instead of learning unreferenced functions. We provide comprehensive empirical evidence showing that these residual networks are easier to optimize, and can gain accuracy from considerably increased depth. On the ImageNet dataset we evaluate residual nets with a depth of up to 152 layers---8x deeper than VGG nets but still having lower complexity. An ensemble of these residual nets achieves 3.57% error on the ImageNet test set. This result won the 1st place on the ILSVRC 2015 classification task. We also present analysis on CIFAR-10 with 100 and 1000 layers. The depth of representations is of central importance for many visual recognition tasks. Solely due to our extremely deep representations, we obtain a 28% relative improvement on the COCO object detection dataset. Deep residual nets are foundations of our submissions to ILSVRC & COCO 2015 competitions, where we also won the 1st places on the tasks of ImageNet detection, ImageNet localization, COCO detection, and COCO segmentation.

Polyploidization is an important evolutionary process which affects organisms ranging from plants to fish and fungi. The signal left behind by it is in the form of a species' ploidy level (number of complete chromosome sets found in a cell) which is inherently non-treelike. Currently available tools for reconstructing the evolutionary past of a polyploid dataset generally start with a multi-labelled tree obtained for a dataset of interest and then derive a (phylogenetic) network from that tree in some way that reflects that past by interpreting the networks's vertices of indegree at least two as polyploidization events. Since obtaining such a tree can be computationally expensive it is paramount to have alternative approaches available that allow one to shed light into the reticulate evolutionary past of a polyploid dataset. SPRINT aims to reconstruct the evolutionary past of a polyploid dataset in terms of a binary network which realises the dataset's ploidy profile (vector of ploidy levels of the dataset's taxa) and requires the fewest number of polyploidization events. It does this by representing the ploidy level of a species x in terms of the number of directed paths from the root of the network to the leaf of the network labelled by x. SPRINT is distributed on GitHub: https://github.com/lmaher1/SPRINT.