Test-Time Training with KV Binding Is Secretly Linear Attention

Test-time training (TTT) views sequence modeling as an online learning problem in which fast weights are updated by an internal learning rule. Despite the growing number of TTT variants, existing approaches typically hard-code each variant separately, which makes it difficult to design new TTT methods and to isolate the role of each component. To address this, we propose Modular TTT, a framework that represents the inner learner as a directed acyclic graph and exposes the fast-weight network, loss function, learning rate, weight decay, and normalization as explicit design dimensions. Modular TTT automatically composes primitive-level train-view forward, train-view backward, and causal query-view rules into the full graph-level TTT computation, including the fast-weight state transition. Using Modular TTT, we systematically ablate the components of TTT and find that small learning-rate initialization, weight decay, and a single-layer nonlinearity improve performance, while MSE and inner-product losses perform similarly. Deeper fast-weight networks and normalization tend to hurt performance because they induce excessively large activations, while residual connections and gating provide little measurable benefit. Guided by these findings, we train the best resulting variant as 410M- and 1.45B-parameter models on 100B tokens, and observe training loss and benchmark performance comparable to Gated DeltaNet.

Recent Test-Time Training (TTT) architectures compress context into fast weights that are updated online and queried as memory. Existing TTT designs keep this memory private to each layer: it recurs only over time, and depth merely indexes L separate memories. We argue that memory ownership need not be tied to depth, and introduce Universal Test-Time Training (uTTT), in which all layers read and write one shared memory while retaining layer-specific backbone parameters. The shared memory thus recurs over two dimensions, time and depth, with chunks and layers as their units: a write by a deep layer in one chunk can be read by a shallow layer in the next. We instantiate this idea as uTTT-MoE and uTTT-Dense. uTTT-MoE routes each token head to a few experts in a pool shared by all layers; uTTT-Dense applies the whole shared memory at every layer without routing. In language modeling, uTTT-MoE reaches 15.5 and 27.9 RULER accuracy at 124M and 760M, 2.6 and 2.1 points above its layer-private counterpart at equal state and active compute, the highest among tested bounded-state models, with per-token loss matching or beating full attention. In novel view synthesis, sharing at fixed per-layer compute gains 0.92 dB in view-23 object PSNR in routed models and 0.76 dB in dense models.

While linear-complexity attention mechanisms offer a promising alternative to Softmax attention for overcoming the quadratic bottleneck, training such models from scratch remains prohibitively expensive. Inheriting weights from pretrained Transformers provides an appealing shortcut, yet the fundamental representational gap between Softmax and linear attention prevents effective weight transfer. In this work, we address this conversion challenge from two perspectives: architectural alignment and representational alignment. We identify Test-Time Training (TTT) as a linear-complexity architecture whose two-layer dynamic formulation is structurally aligned with Softmax attention, enabling direct inheritance of pretrained attention weights. To further align representational properties, including key shift-invariance and locality, we introduce key instance normalization and a lightweight locality enhancement module. We validate our approach by linearizing Stable Diffusion 3.5 and introduce SD3.5-T$^5$ (Transformer To Test Time Training). With only 1 hour of fine-tuning on 4$\times$H20 GPUs, SD3.5-T$^5$ achieves comparable text-to-image quality to the fine-tuned Softmax model, while accelerating inference by 1.32$\times$ and 1.47$\times$ at 1K and 2K resolutions. Code is available at https://github.com/LeapLabTHU/Transformer-to-TTT.