Transformer residual layers are approximated as an explicit Euler scheme for a controlled hidden-state flow whose mean-field limit is a first-order transport control problem with Pontryagin terminal condition given by the softmax residual.
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mHC: Manifold-Constrained Hyper-Connections
38 Pith papers cite this work. Polarity classification is still indexing.
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abstract
Recently, studies exemplified by Hyper-Connections (HC) have extended the ubiquitous residual connection paradigm established over the past decade by expanding the residual stream width and diversifying connectivity patterns. While yielding substantial performance gains, this diversification fundamentally compromises the identity mapping property intrinsic to the residual connection, which causes severe training instability and restricted scalability, and additionally incurs notable memory access overhead. To address these challenges, we propose Manifold-Constrained Hyper-Connections (mHC), a general framework that projects the residual connection space of HC onto a specific manifold to restore the identity mapping property, while incorporating rigorous infrastructure optimization to ensure efficiency. Empirical experiments demonstrate that mHC is effective for training at scale, offering tangible performance improvements and superior scalability. We anticipate that mHC, as a flexible and practical extension of HC, will contribute to a deeper understanding of topological architecture design and suggest promising directions for the evolution of foundational models.
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2026 38roles
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Depth-Attention mixes values from earlier layers into the current attention value by having the query attend to previous-layer keys at the same position, yielding lower perplexity and up to 2.3 points higher average accuracy than vanilla transformers on Qwen3-style models with negligible extra FLOPs
TBP-mHC proposes parameterizations of the Birkhoff polytope via transportation polytopes that achieve exact double stochasticity for hyper-connections using only (n-1)^2 degrees of freedom.
Delta Attention Residuals attend over per-sublayer deltas instead of cumulative hidden states, producing higher-contrast attention weights and 1.7-8.2% validation perplexity gains over standard and attention residuals across 220M-7.6B models.
An efficiently computable HS-Jacobian acts as a conservative mapping for projections onto polyhedral sets, supporting provably convergent Adam-based end-to-end training of linearly constrained deep neural networks.
FLUID is a continuous-time transformer using Liquid Attention Networks to model attention as stable ODE solutions that interpolate between discrete SDPA and CT-RNNs, with an explicit sink gate and liquid hyper-connections for better information flow.
SATFormer uses a context-dependent gate for selective reuse of early Transformer representations, improving validation loss and zero-shot accuracy especially on retrieval benchmarks.
Skip-connected MLPs and residual-free MLPs of equal width represent generically disjoint function classes for common activations, with explicit impossibility proofs and a non-generic absorption condition for ReLU and GELU.
A new SFT framework for MoE models combines bias-driven sparsification with gated condenser experts to retain long-tailed expert information, outperforming DenseMixer and ESFT by over 2.5% on math reasoning and commonsense QA benchmarks.
LoopCTR trains CTR models with recursive layer reuse and process supervision so that zero-loop inference outperforms baselines on public and industrial datasets.
Deep Delta Learning replaces additive residual updates with a gated delta-rule that selectively overwrites residual content along learned directions, improving language modeling quality over standard ResNet-style accumulation.
Derives mechanism-based monitors from module functional roles and validates them via fault-injection experiments showing early detection of LLM training instability.
Smoothly activated DNNs (feedforward and residual) achieve non-asymptotic uniform convergence rates that mitigate the curse of dimensionality by adaptively using hierarchical composition structure of the target function.
DAR replaces residual addition in DiTs with learnable, timestep-adaptive aggregation of sublayer outputs, yielding 2.11 FID improvement on SiT-XL/2 and 8.75x faster convergence on ImageNet 256x256.
SNLP achieves up to 2.58x wall-clock speedup on 0.5B Transformers via architecture-specific Newton corrections (IDN/HCN) that enable layer-parallel inference while preserving perplexity in milder settings.
AOT-POT adaptively reshapes complex PDE solution operators via input-dependent transformations and parallel stream mixing to enable effective large-scale pre-training, yielding SOTA results on 12 benchmarks with minimal added parameters.
SODA unifies several modern optimizers under optimistic dual averaging and supplies a 1/k decay wrapper that improves performance without weight decay tuning.
The EΔ-MHC-Geo Transformer achieves input-adaptive unconditionally orthogonal residual connections via a Cayley-based rotation that works for all parameters, combined with a learned hybrid gate for reflections.
Graph Normalization is a convergent dynamical system that approximates MWIS by always reaching a binary maximum independent set via majorization-minimization and evolutionary game equivalence.
HypEHR is a hyperbolic embedding model for EHR data that uses Lorentzian geometry and hierarchy-aware pretraining to answer clinical questions nearly as well as large language models but with much smaller size.
DsmNet substitutes Laplacian matrices with approximated doubly stochastic matrices in GNNs, using Neumann truncation and residual mass compensation to achieve O(K|E|) efficiency and bound Dirichlet energy decay for reduced over-smoothing.
ResBM achieves 128x activation compression in pipeline-parallel transformer training by adding a residual bottleneck module that preserves a low-rank identity path, with no major loss in convergence or added overhead.
LPC-SM is a hybrid architecture separating local attention, persistent memory, predictive correction, and control with ONT for memory writes, showing loss reductions on 158M-parameter models up to 4096-token contexts.
SiameseNorm is a two-stream architecture that reconciles Pre-Norm and Post-Norm in Transformers by coupling streams via shared residual blocks, yielding performance gains with maintained stability on language, vision, and diffusion models.
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Efficient and provably convergent end-to-end training of deep neural networks with linear constraints
An efficiently computable HS-Jacobian acts as a conservative mapping for projections onto polyhedral sets, supporting provably convergent Adam-based end-to-end training of linearly constrained deep neural networks.
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mHC-SSM: Manifold-Constrained Hyper-Connections for State Space Language Models with Stream-Specialized Adapters
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