TorR: Towards Brain-Inspired Task-Oriented Reasoning via Cache-Oriented Algorithm-Architecture Co-design

The increasing popularity of reasoning models -- language models that output a series of reasoning or thought tokens before producing an answer -- is justified, in part, by theoretical results showing that chain-of-thought (CoT) transformers can simulate Turing machines, and thus perform arbitrary computation. However, the Turing machine, while suitable for complexity-theoretic analysis, is not convenient, intuitive, or efficient for discussing algorithms. Algorithms are typically designed and analyzed at a higher level of abstraction, captured by the Word RAM model with random-access memory and unit-cost operations on $\bigO(\log n)$-bit words. As a result, Word RAM algorithms can be substantially more efficient than their Turing machine counterparts, raising the question: Can CoT transformers efficiently simulate Word RAM algorithms? For instance, can they sort $n$ items in $\bigO(n \log n)$ steps or run Dijkstra's algorithm in $\bigO(E + V \log V)$ steps? We answer affirmatively, up to poly-logarithmic overhead. We first establish this for finite-precision transformers with poly-logarithmic width and rightmost unique hard attention, then strengthen the result to two more practical settings with finite width and log-precision: continuous CoT, where reasoning takes the form of vectors rather than tokens, and a hybrid architecture in which transformer layers sit atop a recurrent (linear RNN) layer. In all three cases, we find that CoT can efficiently simulate any Word RAM algorithm with only a poly-logarithmic overhead in $n$. This overhead reduces to log-square when the Word RAM has a ``flat'' instruction set, and only logarithmic for multiplication-free flat instructions -- in stark contrast to known CoT simulations of Turing machines, which require quadratic overhead over Word RAM.

Recursive reasoning models solve hard structured tasks with a few million parameters by iterating a latent state, but deploying them on edge hardware means compressing them -- and quantization noise compounds across recursive cycles rather than accumulating over output tokens, so single-pass intuitions fail. Here, we ask what survives. Across a full precision sweep and three tasks, aggressive compression preserves local prediction but destroys global reasoning: pruning, distillation, and linear attention drive puzzle-exact accuracy to zero while cell accuracy holds. Naive INT4 is different: its damage is architectural, striking MLP-mixing recursion but not attention on the same task, and per-channel calibration reverses it without retraining, where quantization-aware training does not. We also introduce carry-trajectory fidelity, the cosine similarity to the full-precision reasoning path, as a label-free signal that predicts both the damage and the recovery before any task evaluation, with a threshold that transfers across tasks. The result is a deployment recipe: flash-streamed embeddings remove a 99.4 MB bottleneck, one recursive cycle matches full-depth accuracy at 6x fewer FLOPs, and calibrated INT4 brings the backbone to 3.3 MB, inside a 4 MB budget.

We present RiO-DETR: DETR for Real-time Oriented Object Detection, the first real-time oriented detection transformer to the best of our knowledge. Adapting DETR to oriented bounding boxes (OBBs) poses three challenges: semantics-dependent orientation, angle periodicity that breaks standard Euclidean refinement, and an enlarged search space that slows convergence. RiO-DETR resolves these issues with task-native designs while preserving real-time efficiency. First, we propose Content-Driven Angle Estimation by decoupling angle from positional queries, together with Rotation-Rectified Orthogonal Attention to capture complementary cues for reliable orientation. Second, Decoupled Periodic Refinement combines bounded coarse-to-fine updates with a Shortest-Path Periodic Loss for stable learning across angular seams. Third, Oriented Dense O2O injects angular diversity into dense supervision to speed up angle convergence at no extra cost. Extensive experiments on DOTA-1.0, DIOR-R, and FAIR-1M-2.0 demonstrate RiO-DETR establishes a new speed--accuracy trade-off for real-time oriented detection. GitHub Repository: https://github.com/RicePasteM/RiO-DETR.