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Multimodal Large Language Models (MLLMs) exhibit strong visual understanding, yet the internal features that cause these behaviors remain difficult to identify, audit, or control. While applicable to post-hoc inspection, hidden states that are decomposed into interpretable feature directions using sparse autoencoders (SAEs) neither readily isolate which features are changed by multimodal training, nor are they directly useful for targeted control. We introduce MMDiff, a multimodal model-diffing framework that trains multimodal SAEs and turns them into feature-level interfaces for discovering and controlling multimodal behavior. MMDiff supports three uses: (i) feature isolation, by diffing a base-LM SAE against its multimodal-adapted counterpart to identify features altered by multimodal training; (ii) task-specific feature detection, via per-token contrastive firing analysis that isolates causal features; and (iii) feature-level control, by causally removing or steering the discovered feature directions. We train multimodal SAEs for three MLLM families, LLaVA-MORE, PaliGemma 2, and InternVL3.5, and evaluate on visual-spatial understanding, multimodal safety, and OCR. MMDiff discovers sparse, causally specific features whose removal selectively degrades target behaviors by an average of 12% on spatial tasks and 17% on OCR, and reduces attack success rate by 24% on multimodal safety attacks, with no impact on VQA performance. Steering these features improves spatial and OCR accuracy by +3.6% and +1.8% on average over a standard single-layer steering baseline. These results show that multimodal SAEs can serve not only as interpretability tools, but as mechanisms for auditing, steering, and controlling MLLMs behavior toward safer and more capable generations.

The search for new crystalline materials spans an enormous compositional and structural space. Generating candidates in this space requires modeling the relationships between elemental composition, crystallographic symmetry, and crystal geometry. The space group specifies the crystal's symmetry and determines the admissible Wyckoff positions and geometric degrees of freedom; fixing it in advance prevents this global symmetry choice from being revised using information from evolving Wyckoff occupations and elemental composition. We introduce DynaCrys, the first framework for complete crystal generation in which the space group co-evolves with Wyckoff occupations and elements. We develop physics-informed space-group diffusion that explicitly incorporates crystallographic group-subgroup relations, and a legality-constrained stochastic decoder that jointly samples compatible space groups, Wyckoff occupations, and elements, followed by symmetry-constrained geometry generation. In large-scale evaluations on standard benchmarks, DynaCrys achieves state-of-the-art performance in symmetry-aware crystal generation while supporting fast sampling.

Large language models (LLMs) are widely used in text-to-image (T2I) systems, but they are typically limited to text encoding, while denoising is handled by newly trained generative backbones. The emergence of representation autoencoders (RAEs) shifts the generation target toward semantically structured visual representations, creating a latent space that is more compatible with pretrained LLM priors. Inspired by multimodal LLMs (MLLMs), where an MLP projector is sufficient to align clean visual representations with a pretrained LLM, we repurpose the MLLM itself as a noisy representation encoder, extending this mechanism from clean to noisy inputs. We present RepFusion, which uses the resulting MLLM outputs as the conditioning signal for a diffusion transformer. In controlled comparisons at similar inference budgets, RepFusion outperforms baselines that devote comparable capacity to newly initialized denoisers. Reusing MLLM outputs across denoising steps further accelerates inference while retaining performance comparable to per-step MLLM recomputation. These results demonstrate that MLLMs provide strong priors for denoising visual representations.

The Path Avoiding Forbidden Pairs problem (PAFP) asks whether, in a directed graph $G$ with two of its vertices labeled $s,t$ and a set $\mathcal F$ of forbidden vertex pairs, there is an $s$--$t$ path that contains at most one endpoint from each pair in $\mathcal F$. We initiate the study of PAFP through a layer-based width measure. We first look at the directed union digraph $G\cup\mathcal F$, which is obtained by adding one arc per forbidden pair to $G$, oriented according to a fixed reachability-compatible order. Let the BFS layer $L_d$ be the set of vertices at directed shortest-path distance $d$ from $s$, and define the BFS-width from $s$ as $\max_d |L_d|$. We show that if $G\cup\mathcal F$ has BFS-width $b$ from $s$, and $p$ is the maximum, over BFS-layer cuts, of the smaller of the numbers of distinct heads and distinct tails of backward arcs crossing the cut, then PAFP is FPT parameterized by $b+p$. Here a backward arc goes from a later BFS layer to an earlier one. In contrast, we show that bounded BFS-width alone does not suffice: PAFP remains $\mathsf{NP}$-complete when the union digraph has BFS-width 2. We also study layer-based width parameters on the input graph. We show that if the input DAG has BFS-width at most $2$ and only $k$ backward input arcs, then PAFP can be decided in $2^k |I|^{O(1)}$ time, with unrestricted forbidden pairs, and this result is tight. Moreover, we study exact-length layers in the input graph, where the $d$-th exact-length layer consists of the vertices reachable from $s$ by a directed path of length exactly $d$. We show that for DAGs of exact-length width at most $2$, PAFP is polynomial-time decidable by a $2$-SAT encoding of fixed-length paths. Unlike previously known polynomial-time regimes our 2 input -graph tractability results simultaneously allow unrestricted forbidden pairs and input graphs with exponentially many $s$--$t$ paths.

In AES-like ciphers, diffusion layers are commonly instantiated using MDS matrices, since their optimal branch number yields strong diffusion guarantees and underpins classical resistance arguments against differential and linear cryptanalysis. However, Daemen and Rijmen (2009) showed that linear layers may still exhibit related-differential structure beyond what the MDS criterion captures, and Bardeh and Rijmen (2022) demonstrated that this phenomenon can be exploited in attacks on reduced-round AES. In this work, we systematically investigate the conditions under which linear layers avoid or exhibit these differentials, identifying matrix classes for which such structure is unavoidable. We first prove that every non-MDS matrix admits a nontrivial pair of related differentials, showing that the MDS property is necessary for avoiding them. We then establish that every odd-order symmetric MDS matrix admits related differentials, which rules out broad families of Cauchy-based constructions. We also substantially strengthen the circulant case by proving that related differentials are unavoidable for every circulant matrix of order $n$ with $n \not\equiv \pm 2 \pmod{12}$. Finally, we revisit the characterization of $3 \times 3$ MDS matrices over $\mathbb{F}_{2^m}$ for the absence of related differentials, and derive an explicit necessary and sufficient criterion in terms of $15$ polynomial constraints.

Numerical methods and neural networks have transformed our understanding of nonlinear partial differential equations (PDEs), yet discovering mathematical representations that explain their dynamics remains largely an expert task. We introduce Agentic Symbolic Search (ASYS), in which coding agents construct and refine explicit approximations from a known PDE and supplied mathematical knowledge. ASYS couples evolutionary search over differentiable symbolic programs with gradient-based fitting, using the governing equation to evaluate candidates and guide their revision. For a singular generalized Constantin-Lax-Majda profile, ASYS infers a missing decay term that sets how fast the field approaches its singular-time limit, and builds a basis that fits the profile to a median error of $3.90\times10^{-5}\%$. For Fujita blow-up, separating diffusion from reaction and deriving a local response lowers the supplied formula's error from 55.5% to 0.0879%. For Allen-Cahn interfaces, a 14-parameter construction yields a mode-coupling law confirmed by independent simulations. These studies show how agentic search develops mathematical starting points into accurate, analyzable approximations.

Hardware executions of the quantum approximate optimization algorithm (QAOA) are often validated by comparing the device's mean cost with a simulation, a check that can miss what matters for optimization. Under global depolarization, the mean normalized gap and the floor-corrected probability of every set of bitstrings, the optimum included, retain the same fraction of their noiseless improvement over uniform sampling. We test this prediction with depth-2, transferred-angle QAOA circuits for binary subproblems of an alternating-direction decomposition on the IBM Heron processor \texttt{ibm\_marrakesh}, with and without dynamical decoupling and twirling. At 12 qubits, the main-family circuits retained 29\% to 46\% of their mean-gap improvement but only 5\% to 15\% of their probability of the optimum, lower on at least nine of ten instances per run. Near-optimal bitstrings were lost about as much as the optimum, whereas the avoidance of poor bitstrings was retained best. In the first submission, a device-matched noise model reproduced the pattern but overestimated the retention of the optimum five- to eightfold. On a rugged planted family, the device found the optimum in 62\% of 768-shot blocks (noiseless: 98\%), within the range of local heuristics. Validations of optimization circuits should report retention of the optimum and of near-optimal sets.

Robust visual classification often depends on localizing the main foreground objects in an image while ignoring contextual distractors. Surprisingly, we find that the last layer attention maps of smaller self-supervised ViTs localize foreground objects better than those of larger ViTs. However, we still need large ViTs, because they extract richer representations from each patch. To get the best of both worlds, good localization and rich representations, we propose $A^2$, a simple method that leverages this inverse scaling finding by decoupling where to look (a small attention model) from what to extract (a large embedding model): we crop around the attention peaks of a small model and embed the crops with a larger model. $A^2$ uses entirely pretrained features, requires no group labels, and does not require per-dataset attention or backbone training. Across 5 benchmarks, $A^2$ is competitive with backbone-matched loss-level methods like DFR, and outperforms end-to-end attention training under stronger distribution shifts.

In many settings where LLM post-training is desirable, high-quality answers are recognizable but difficult to score with explicit rewards. Reinforcement learning with verifiable rewards (RLVR) is limited to tasks where an explicit correctness signal is available. Prior adversarial approaches to training reasoning LLMs either complement verifiable rewards with co-trained critics or require reference reasoning traces. We ask whether a co-trained LLM judge can turn reference answers alone into the sole reward for on-policy post-training of reasoning LLMs. We call this method Reinforced Adversarial Learning (RAL). We first validate RAL on three verifiable tasks (integer multiplication, code-based arithmetic-expression synthesis, and SMILES-to-formula translation), using the verifiers only for evaluation. With sufficiently capable judges and enough training, RAL matches direct RLVR. We then apply RAL to scientific abstract generation in two settings. In the first setting, RAL guides the generator to produce abstracts in the scientific domain of the reference abstracts, even though the prompt leaves that domain unspecified. In the second setting, we generate abstracts for U.S. National Institutes of Health grant proposals conditioned on the grant title. Human scientists and an ensemble of LLM judges find our generations harder to distinguish from real abstracts than those of frontier-LLM baselines. These results suggest a path toward post-training reasoning models in scientific and other high-value domains, where increasingly capable judges infer hard-to-specify reward functions from example answers.

In this work, we propose a method to automatically find the regularization parameter for low-rank MMSE filters based on a Kronecker-product representation, using an approximate leave-one-out (ALO) cross-validation metric. We formulate the problem in a constrained form that covers both error minimization and interference suppression, and explore the link between regularization and rank selection. The proposed method is validated on system identification and antenna beamforming problems, showing significant gains over commonly used methods.

Byte-level language models such as the Byte Latent Transformer (BLT) group bytes into patches and run their large global model once per patch. BLT starts a patch where a small model's next-byte entropy is high. We show that under tight patch budgets this rule has a blind spot: positions whose type the preceding text fixes but whose value must be computed, such as the number after "= " in a worked math solution. A nearly certain digit keeps the next byte's entropy near or below log2(10) = 3.32 bits, about BLT-1B's threshold for a 10% budget. In Meta's BLT-1B with patch starts on 10% of bytes, the entropy rule puts a patch start at 16% of the computed results in GSM8K solutions and gets 19.0% of them exactly right given the true preceding text; a boundary after each "=" at the same patch count gets 51.8%, and entropy combined with a label-free boundary-dependence signal gets 67.1% (default layout at 26% of bytes: 76.8%). The gap survives adapting BLT-1B to the budget with low-rank adapters (32.9% vs 72.7%, three runs per rule). In byte models trained from scratch at a 10% budget on a 1.9 GB math corpus, it is not detectable at 1M parameters, appears on final answers at 12M and on both targets at 50M, as training data grow too: at 50M boundary dependence gets 35.9% of computed results against 13.9% for entropy and 78.9% of final answers against 59.0% (3 seeds each), although final answers mostly copy the solution's last number and entropy starts a patch at every one. In BLT-1B the blind spot narrows at larger budgets (entropy covers about 90% of the values right after "= " at 20% of bytes) and in the same solutions rewritten as prose, where a patch start at each value still pays. Boundary dependence, the change in the model's own loss when a patch start is removed or added, measured per two-byte context on text in the same format, finds these positions without labels.

We propose a provably correct Monte Carlo tree search (MCTS) algorithm for solving risk-aware Markov decision processes (MDPs) with entropic risk measure (ERM) objectives. We provide a non-asymptotic analysis of our proposed algorithm, showing that the algorithm: (i) is correct in the sense that the empirical ERM obtained at the root node converges to the optimal ERM; and (ii) enjoys polynomial regret concentration. Our algorithm successfully exploits the dynamic programming formulations for solving risk-aware MDPs with ERM objectives introduced by previous works in the context of an upper confidence bound-based tree search algorithm. Finally, we provide a set of illustrative experiments to evaluate our risk-aware MCTS method, showing it successfully trades off between risk-neutral and risk-averse behavior.

Graph Neural Networks (GNNs) have emerged as a powerful, differentiable class of learning models for graph-structured systems. Their ability to generalize across topologies opens the prospect of a surrogate for combined structural and parametric optimization, which classical metamodels cannot offer. Supply chains are a natural target, yet the use of GNN surrogates for supply chain problems is largely unexplored. This paper lays the foundation, presents initial steps, and discusses key research directions. As a foundation, we formulate the problem and create a large public training dataset of programmatically generated supply chain graphs with input parameters and steady-state performance metrics obtained using our SupplyNetPy simulation library. As initial steps, we explore GNN architectures that work well as surrogates for node- and network-level predictions, and analyze their accuracy-compute trade-off against simulation. Most importantly, we outline the exciting directions this opens, namely gradient-based optimization over topology, fast design-space exploration, and sensitivity analysis.

Recent advances in one-step text-to-image generation have enabled real-time synthesis with remarkable efficiency and quality. Previous reinforcement learning methods for one-step generators combine image-space reward optimization with diffusion noisy-space distribution matching. This paradigm brings challenges due to a mismatch between terminal reward optimization and the underlying generative dynamics. As a result, optimization tends to exploit stochastic degrees of freedom, often improving reward at the expense of image fidelity. To address this issue, we propose Diff-Instruct with Diffused Reward (DIDR), a data-free trajectory-level alignment framework derived from Integral KL minimization. DIDR propagates the RLHF-optimal reward-tilted clean-image distribution across all noise levels along the diffusion trajectory. We show that this objective admits the same minimizer as clean-image RLHF, while naturally inducing the Diffused Reward Score (DRS), which acts as a reward-driven correction to the reference score function. To make this practical, we further introduce the Diffused Reward Proxy (DRP), an efficient estimator of DRS based on differentiable short-step denoising. Extensive experiments demonstrate that DIDR consistently Pareto-dominates existing one-step SDXL baselines. Moreover, when transferred to a 6B DiT backbone (Z-Image), DIDR surpasses its 50-step teacher in preference alignment while requiring only a single generation step. Code: https://github.com/Junyi-W/DIDR

Several public scripts for formulaic alpha mining store prices adjusted to the snapshot's last day, so a past day's stored price changes with every later split or dividend and formulas that do not cancel the adjustment factor depend on future corporate actions. We formalise a change of adjustment anchor as a per-stock group action and give a two-sorted type system that soundly certifies anchor invariance from a formula's syntax, under a declared field-adjustment contract and idealised operator semantics; its second sort admits log-returns, and a linear-time checker plugs into any miner. In a re-anchoring audit on Chinese A-shares, pools that five published methods mined in our benchmark pipeline score a mean information coefficient (IC) 0.005 higher on the stored representation than on a cutoff-anchored one, about 14% of their IC. The mean signed change for certified pools is about -0.001, and pools mined on past-anchored data stay sensitive. On the Chinese development folds, certification shows no detectable predictive cost or gain; the estimated minimum detectable difference is about 0.017 IC across cells on pool ICs of 0.03-0.04. We also trace an erroneous index-membership entry to public Qlib data snapshots and show that re-mining exposes the effect of such data defects, which re-evaluating fixed pools understates.

Data annotation is an essential but costly aspect of developing machine learning-based technology, requiring multiple human workers to repeatedly label each data point in a data set. We explore the tradeoff between annotation accuracy and cost by identifying minority reports---worker responses disagreeing with the reference majority-vote label---that may indicate unnecessary redundancy, and can therefore be proactively pruned before they are executed. We develop a theoretical framework for choosing the number of repeated annotations required for a task and pruning policies at a target label quality. We estimate minority-report risk on two computer vision datasets re-annotated through a professional platform, then evaluate a rolling policy on the assignment stream to prune over 35% of repeats while preserving more than 99.9% of reference majority-vote labels.

This paper introduces SupplyNetPy, an open-source, well-documented Python library for modeling and discrete-event simulation of supply chain networks with arbitrary multi-echelon structures. It supports multiple replenishment policies, perishable inventory, node disruptions, and stochastic demand and lead times. All components are extensible via inheritance. Users describe a supply chain as a graph with node and link attributes, while the library handles simulation, providing logs and extensive node and network level performance reports. This paper presents the motivation, design, key features, and architecture of SupplyNetPy, along with detailed validation results (against analytical benchmarks, a commercial tool, and a published case study). A key motivation behind SupplyNetPy's development is programmatic generation and simulation of complex models, enabling design-space exploration, what-if analysis, training data generation, and supply chain digital twins.