#01Nov 12, 2026
cs.CL
ArchSpace: Recording, Reviewing, and Referencing LLM Architecture Research
Jie Wang, Tong Zhu, JiaHao Kuang and 8 more
Model architecture shapes the scaling behavior, training efficiency, and inference cost of LLMs, making it a central focus of both industry and academia. In industry, teams such as those behind DeepSeek, Qwen, and Kimi routinely introduce architectural innovations, yet public reports rarely document which ideas succeeded, which were abandoned, and why. In academia, limited compute and inconsistent baselines often restrict evaluations to small-scale, single-point comparisons, making it difficult to establish whether improvements hold at larger scales or translate into broader impact. ArchSpace addresses both gaps as a public platform for Recording, Reviewing, and Referencing Architecture Researc}: each proposal is recorded with its experiments and reasoning, reviewed by the community, and referenced by later work. To evaluate ideas before costly large-scale training, ArchSpace leverages scaling laws to predict model loss at larger scales from smaller experiments, a practice widely adopted in industry. We provide initial references that make the platform usable: Qwen3.5 and OLMo3 baselines, fitted scaling laws, and a reusable training recipe. Ideas validated through this review can in turn become new baselines, and ArchSpace thereby aims to broaden the range of ideas that shape the next generation of models.
#02Nov 12, 2026
cs.LG
Introducing Feedback Delays to Non-Delayed Adversarial MDPs: Optimal $\sqrt S$ and $\sqrt K$ Dependencies in Tabular and Linear AMDPs
Aarush Kulkarni, Khang Nguyen, William Chang and 1 more
We study regret minimization in episodic Adversarial Markov Decision Processes (AMDPs) with unknown transitions and bandit feedback. In tabular AMDPs with $S$ states, $A$ actions, and horizon $H$, the best known $K$-episode regret is $\tilde O(HS\sqrt{AK})$, whose $\sqrt S$ gap to the $Ω(H\sqrt{SAK})$ lower bound has long remained open. In linear AMDPs with $d$-dimensional features, after a five-year line of improvements starting from $K^{14/15}$, computationally efficient algorithms without a simulator or exploratory assumptions still only attain $\tilde O(K^{3/4})$ regret. A common challenge in both settings is to estimate the Q-function of a changing policy: past data comes from earlier policies that differ from (and are correlated with) the current one, while freezing the policy for future episodes worsens the dependency on $K$. We instead propose a general technique called introduced feedback delays: we estimate the Q-function of the policy using future episodes while still updating the policy, as if the feedback were delayed. While feedback delays are usually an obstacle imposed by the environment, here they are introduced voluntarily and, perhaps surprisingly, come at no extra cost. We develop Geometric Resampling with Rejection (GRR) to account for policy changes during the delay, and threshold the visitation probabilities to avoid long delays on rarely visited state-action pairs. With this unified technique, our policy optimization algorithms achieve, with high probability, $\tilde O(\text{poly}(H)\sqrt{SAK})$ regret in tabular AMDPs, resolving the open problem; and $\tilde O(\text{poly}(d,H)\sqrt K)$ regret in linear AMDPs, giving the first efficient algorithm optimal in $K$. They also naturally extend to delayed AMDPs with a total feedback delay $\mathfrak D$, yielding the first bounds optimal in $S$ and $\mathfrak D$ (tabular) and in $K$ and $\mathfrak D$ (linear).
#03Nov 12, 2026
cs.AI
Classical Energies Learn to Reason 1,000x Faster than Looped Models
Benjamin Hoover, Hugh Blayney, James C. R. Whittington
Looped models have emerged as a prominent paradigm for reasoning, with successes on simple reasoning puzzles such as Sudoku-Extreme and Maze-Unique. However, these models can be unstable, slow to train, and use many parameters and FLOPs to solve simple puzzles. Descent on an energy not only mitigates these issues but also offers advantages: built-in early stopping, compute that adapts to problem difficulty, fast training without differentiating through a solver, and interpretable weights that learn the constraints of the puzzle. Here we demonstrate this with a learned version of Hopfield & Tank's energy from the 80s, which we term CRAM, solves 99.996% of Sudoku-Extreme and 100% of Maze-Unique test puzzles after 42 ms and 132 ms of training on one GPU, at least 1,000x faster than looped models on these tasks. CRAM also matches baseline looped models at their highest accuracy on Sudoku-Extreme using at least 282x fewer inference FLOPs. Our work suggests two things. First, that energies are an extremely promising direction for training reasoning from data. Second, a caution against using trivially solvable benchmarks like Sudoku and Maze to test the scalability of looped reasoning techniques.
#04Nov 12, 2026
math.ST
Linear Regression with Self-Selection Bias in Polynomial Time
Felix Zhou
We revisit the problem of estimating $k$ linear regressors with self-selection bias in $n$ dimensions up to error $\varepsilon$ with the maximum self-selection criterion, as introduced by Cherapanamjeri, Daskalakis, Ilyas, and Zampetakis [CDIZ23, STOC]. Our main result is a $\mathrm{poly}(n,k,1/\varepsilon)$ time algorithm for the unknown-index variant of this problem, thereby improving upon the running times of the best known algorithms due to Gaitonde and Mossel [GM24] and Kalavasis, Mehrotra, and Zhou [KMZ26, COLT] with exponential dependence on $k$. Our algorithm succeeds in the presence of correlated noise between regressors, which captures the related setting of max-affine regression. Consequently, we also give the first polynomial-time algorithm for this problem, improving on the prior works of Ghosh, Pananjady, Guntuboyina, and Ramchandran [GPGR22, IEEE Transactions on Information Theory] and Gaitonde and Mossel [GM24] with exponential dependence on $k$. Prior works exhaustively search over a $k$-dimensional subspace spanned by the regressors, using conditional moments of the response to test candidates. In contrast, our algorithm is driven by an improved understanding of the moments of the covariates. We show that, restricting to observations with large response values, the degree-$(\log n)$ Hermite moment of the covariates approximately decomposes as a sum of tensor powers of the regressors. The first step of our algorithm can be viewed as a tensor decomposition algorithm for these implicitly represented high-order tensors, which outputs unit vectors parallel to the regressors. A secondary step based on a simple variant of ordinary least squares extracts estimates for the regressors given these unit vectors. We believe our analytic insight and algorithmic components may have applications to designing efficient algorithms for other latent-variable problems.
#05Nov 12, 2026
cs.LG
Internalizing Investment Mandates: A Neurosymbolic RL Approach to Portfolio Allocation
Zeynep Yıldız, Satchit Chatterji, Ercan Atam and 1 more
Institutional portfolios operate under investment policy statements that specify asset allocation constraints, often conditioned on market regime information. Deep reinforcement learning has been shown to optimize financial performance but typically does not enforce rule compliance, making it unsuitable for real-world deployment. Existing neurosymbolic methods such as Probabilistic Logic Policy Gradient (PLPG) offer constraint-satisfying reinforcement learning (RL) via differentiable symbolic supervision but assume a finite, discrete action space. We present a PLPG-inspired continuous allocation method that estimates the probability that the policy's own executed action satisfies the investment mandate, using reparameterized Monte Carlo sampling, and adds it to the training objective. No post-hoc enforcement mechanism intercepts actions at inference time and compliance is learned by the agent. Audited directly on deterministic mean actions with no correction, the policy reduces violations of a six-rule regime-conditional mandate from 96-98% for unconstrained RL and 33.4% for a reward-penalty baseline to 4.8%, showing that a continuous-action neurosymbolic policy can substantially internalize a symbolic mandate.