Modern Transformers Are Implicit Hybrids: From Functional Differentiation to Principled Hybrid Architecture Design

Hybrid architectures combining Full Attention (FA) and Linear Attention (LA) are increasingly prominent, yet their allocation remains heuristic. We seek an evidence-grounded basis in head-level functional organization learned by RoPE-based Transformers. Behavioral probes do not yield a complete taxonomy, so we propose two intervention metrics: RoPE Frequency Importance Score (RFIS), measuring how each frequency affects a head's attention distribution, and RoPE Positional Dependence (RPD), isolating dependence on rotary positional modulation. On Qwen3-series models and Llama3.1, RFIS suggests and RPD verifies a complete taxonomy of retrieval and positional heads separated by a salient mid-low-frequency band. Controlled Transformers show that this boundary follows the training-length positional scale; we term it the Global Positional Band (GPBand). The analysis suggests a potential cause of zero-shot length-extrapolation failure and yields two principles: positional modeling should operate only locally, with global access through position-independent retrieval; and both functions should be assigned at head granularity with layer-specific allocation. We instantiate them in Head-wise Hybrid Architecture (HwH), using NoPE FA for global retrieval and LA for local positional modeling. With an FA-to-LA ratio below 1:3, HwH retains strong language modeling and commonsense reasoning while improving retrieval and substantially strengthening zero-shot long-context extrapolation over Transformer, LA, and a layer-wise hybrid baseline. Ablations validate both principles and component roles, highlighting principled hybrid architecture design as a promising route toward future foundation models.

Graphical Design of Interpretable Architectures

Designing, implementing, and comparing interpretable architectures requires a formal language to represent them. The most common representations fall short in one of two ways. Symbolic equations give no global view of an architecture at a glance. Probabilistic graphical models and flowcharts do not describe actual tensor manipulations, thus hiding key insights and limiting reproducibility. To close this gap, we introduce a graphical notation for designing interpretable AI architectures, adapted from Penrose tensor notation. This graphical notation gives a global view of an architecture and maps one to one onto PyTorch einsum code. We first use this notation to describe architectures that are interpretable by construction, including concept bottlenecks, sparse probes, prototype networks, neural additive models, and mixtures of linear models. We then diagram the key architectural components of Steerling-8B, a frontier interpretable language model. The diagram yields global insights into the architecture (e.g., showing that Steerling is a residual model), a geometric interpretation of each individual operation, and a direct translation into 33 lines of PyTorch code.

Unifying Graph Neural Networks Through a Common Layer Equation

Graph neural networks are commonly described through family-specific equations whose notation obscures shared computations and structural differences. We introduce a common layer equation that represents covered architectures through seven components: an update domain, channel set, propagation bank, per-channel message maps, channel-fusion operator, ego/residual map, and update map. The central factorization separates where information moves, encoded by the propagation bank, from what moves, encoded by the message maps. Function-valued fillings extend the same equation across local message passing, attention, spectral filtering, global communication, relation-specific channels, higher-order domains, and geometric messages. We make this unification explicit and checkable through worked reductions of canonical layers and component assignments spanning seven nonexclusive architectural families. A fixed slot discipline assigns operations by computational role and defines the framework's coverage boundary. The decomposition also yields component-level theoretical insights: under endpoint-local messages and node-local updates, operator support bounds one-layer dependencies, and one-layer global mixing requires a full effective operator row under the stated hypotheses. The resulting framework organizes more than 200 architectures in a common design space, enables component-wise comparison and generation of structurally consistent architectures, and connects propagation choices to oversmoothing, oversquashing, heterophily, and expressivity. It further exposes the empirical inverse problem of mapping measurable graph and task properties to validated component choices.

V-Simba: Unleashing the Architectural Potential of RL in Visual Continuous Control

Improving sample efficiency remains a core challenge in reinforcement learning (RL), especially in real-world settings like robotics, where data collection is costly. This challenge is pronounced in visual RL, where high-dimensional inputs often obscure learning signals. While prior work in visual RL has focused on algorithmic solutions, such as better dynamics models or exploration strategies, recent advances in state-based RL show that architectural design alone can lead to significant gains in sample efficiency. This raises an important question: Can these architectural principles transfer to visual RL? In response, we introduce V-Simba, a simple yet effective visual RL architecture inspired by the Simba architecture from state-based RL. Built on top of Soft Actor-Critic (SAC) with data augmentation, V-Simba modifies the architecture by adding normalization layers to stabilize training and using pointwise convolutions to reduce computation. Despite its simplicity, V-Simba matches or outperforms the state-of-the-art methods across the DMC, Adroit, and Meta-World benchmarks, while being more computationally efficient than DrQ-v2. We make our code publicly available at https://github.com/DAVIAN-Robotics/V-Simba.

Mobius Learning: Cyclic Depth Folding in Transformers

Transformer-based language models organize computation along an ordered depth axis, where shallow and deep blocks often develop distinct representational roles. We challenge the conventional view that these roles must remain tied to a block's position in the ordered sequence. We introduce Mobius Learning, a training architecture based on cyclic depth folding, in which different data streams follow cyclically shifted block orders. The same block group is therefore applied early in the block sequence for some data streams and late for others, so it is optimized in both shallow and deep roles, a phenomenon we call depth-role superposition. Surprisingly, in four-worker experiments with a modded GPT-2 small (124M) model trained on 2.5B FineWeb tokens using Muon, Mobius Learning achieves lower validation loss than a fixed-order looped Transformer at larger numbers of Transformer block-sequence passes. This counterintuitive result shows that a block group need not remain confined to one fixed shallow or deep role within the block sequence and opens a new design space based on cyclic depth folding. Crucially, this structure makes Mobius Learning particularly well suited to memory-constrained distributed training: raw training data remain local, while each worker stores one block group rather than the complete Transformer block stack.

The State-Prediction Separation Hypothesis

Transformers use the same forward computation stream to both predict the next token and store useful state for future token predictions. We formulate the \emph{state-prediction separation hypothesis}: disentangling the two roles yields better language modeling performance. We design a Transformer variant that uses two computation streams to separate the two functions, and conduct pretraining experiments across various scales. Our experiments show that state-prediction separation consistently offers better data and compute efficiencies, improving validation loss and outperforming standard Transformers by 2--3 percentage points on average on downstream tasks. We also conduct extensive empirical analysis that rules out potential confounders and demonstrates the fundamental difference in the gradients our design entails.

Decoupled Vision-Language System for Multimodal Understanding and Generation

We introduce a new architecture design for multimodal large language models (MLLMs), Libra, capable of both multimodal understanding and generation. Libra architecture contains one vision system and one language system, connected by cross-modal bridges. This design decouples self-modal modeling and cross-modal interaction, enabling each modality to learn its unique representations while maintaining effective cross-modal comprehension. The decoupling is mainly achieved in a switch attention module and a switch FFN module, which dynamically routes the computation flow for self-modal modeling and cross-modal interaction scenarios. We evaluate the effectiveness in two important settings: \textbf{Libra-1} for the understanding-only image-to-text setting, and \textbf{Libra-2} for unified image-to-text understanding and text-to-image generation. In addition to the architecture design, we discuss various improvements on tokenization, positional encoding, and supervision. Experiments demonstrate that the dedicated Libra design enables mutual improvements on multimodal understanding and generation, achieving strong performance on both understanding and generation benchmarks.

Tapered Language Models

Modern language models, including transformer, recurrent, and memory-based variants, share a common chassis: a stack of identical layers in which parameters are allocated uniformly across depth. This is a default inherited from the original transformer and largely unchanged since, yet a growing body of evidence suggests that layers contribute non-uniformly to the final output, with later layers refining the residual stream rather than transforming it. We ask whether parameter capacity should reflect this asymmetry. Our controlled experiment shows that, under a fixed budget, allocating more capacity to earlier layers and less to later layers improves perplexity over a uniform-width baseline, while the reverse allocation hurts. Building on this result, we introduce Tapered Language Models (TLMs), an architectural principle in which a parameter-bearing component is monotonically tapered across depth under a fixed total budget. MLPs are the natural site for this instantiation: they dominate parameter count across all modern LM families and expose width as a single, clean axis of variation. Across three model scales and four architectures (Transformer, Gated Attention, Hope-attention, and Titans), tapering MLP width via a smooth cosine schedule consistently improves perplexity and downstream benchmark performance over uniform baselines, at no additional parameter or compute cost. These findings establish depth-aware capacity allocation as a simple, architecture-agnostic axis of language model design, a free lever hidden in plain sight.

Assistants, Not Architects: The Role of LLMs in Networked Systems Design

Designing the architecture of modern networked systems requires navigating a large, combinatorial space of hardware, systems, and configuration choices with complex cross-layer interactions. Architects must balance competing objectives such as performance, cost, and deployability while satisfying compatibility and resource constraints, often relying on scattered rules-of-thumb drawn from benchmarks, papers, documentation, and expert experience. This raises a natural question: can large language models (LLMs) reliably perform this kind of architectural reasoning? We find that they cannot. While LLMs produce plausible configurations, they frequently miss critical constraints, encode incorrect assumptions, and exhibit ``stickiness'' to familiar patterns. A natural workaround--iterative validation via simulation or experimentation--is often prohibitively expensive at scale and, in many cases, infeasible, particularly when comparing hardware-dependent alternatives. Motivated by this gap, we present Kepler, a lightweight reasoning framework for architecture design that combines structured, expert-driven specifications with SMT-based optimization. Kepler encodes architecturally significant properties--requirements, incompatibilities, and qualitative trade-offs--about systems, hardware, and workloads as constraints, and synthesizes feasible designs that optimize user-defined objectives. It operates at an abstract level, capturing ``rules-of-thumb'' rather than detailed system behavior, enabling tractable reasoning while preserving key interactions, and provides explanations for its decisions. Through experiments and case studies, we show that Kepler uncovers interactions missed by LLMs and supports systematic, explainable design exploration.