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Erik Aas

Publications and source records attributed to Erik Aas.

12 recordsLinked to original sources

Shieldstral

We introduce Shieldstral, a 3B-parameter policy-adaptive multimodal safety classifier that matches or outperforms models nearly 7$\times$ its size on text safety benchmarks and sets a new state of the art on multimodal safety classification. Shieldstral formulates content moderation as a binary question-answering task. This simple formulation unifies diverse moderation tasks into a single yes/no problem, enabling heterogeneous safety datasets with divergent taxonomies to be consolidated under one training framework. We present the data construction recipe, covering curation and generation of approximately 54.1M samples and a fine-grained evaluation set to evaluate policy adaptability. Together, these enable a small adaptive model to match or outperform much larger models.

cs.CL

Robostral Navigate

Deploying navigation systems at scale requires a recipe that minimizes sensor assumptions, generalizes across robot embodiments, and trains efficiently. Yet, today's best systems depend on depth sensors, multi-camera rigs, or pre-built maps, limiting the hardware they support and increasing deployment cost. We introduce Robostral Navigate, an 8B vision-language model built around this scalability objective. The model consumes only a stream of monocular RGB images - the most ubiquitous sensor across robotic platforms and predicts waypoints by pointing to the next target location in the current camera view. Operating purely in image space, rather than robot-specific coordinates, makes the policy naturally robust to changes in camera intrinsics and scene scale, enabling deployment across wheeled, legged, and aerial robots without recalibration. We generate 2.4 million trajectories across 350k simulated scenes to reduce the reliance on real-world data collection and scale easily. We further introduce a prefix-caching training recipe that packs entire episodes into single training sequences, reducing training tokens by 22x and cutting training time from months to days. A tree-based attention mask prevents conditioning on previous ground-truth actions, encouraging visually grounded action prediction, and reinforcement learning is used to further improve exploration and recovery capabilities. On the Room-to-Room and Room-Across-Room in Continuous Environments (R2R-CE and RxR-CE) benchmarks, Robostral Navigate sets a new state of the art. On R2R-CE, it achieves a 77.4% success rate, surpassing the best monocular method by 10.5 points and the strongest depth- or multi-camera system by 5.3 points despite using only a single RGB camera. On RxR-CE, it reaches 75.1% success rate, outperforming all monocular baselines.

cs.RO

Limiting directions for random walks in classical affine Weyl groups

Let $W$ be a finite Weyl group and $\widetilde W$ the corresponding affine Weyl group. A random element of $\widetilde W$ can be obtained as a reduced random walk on the alcoves of $\widetilde W$. By a theorem of Lam (Ann. Prob. 2015), such a walk almost surely approaches one of $|W|$ many directions. We compute these directions when $W$ is $B_n$, $C_n$ and $D_n$ and the random walk is weighted by Kac and dual Kac labels. This settles Lam's questions for types $B$ and $C$ in the affirmative and for type $D$ in the negative. The main tool is a combinatorial two row model for a totally asymmetric simple exclusion process called the $D^*$-TASEP, with four parameters. By specializing the parameters in different ways, we obtain TASEPs for each of the Weyl groups mentioned above. Computing certain correlations in these TASEPs gives the desired limiting directions.

math.PR

Multiline queues with spectral parameters

Using the description of multiline queues as functions on words, we introduce the notion of a spectral weight of a word by defining a new weighting on multiline queues. We show that the spectral weight of a word is invariant under a natural action of the symmetric group, giving a proof of the commutativity conjecture of Arita, Ayyer, Mallick, and Prolhac. We give a determinant formula for the spectral weight of a word, which gives a proof of a conjecture of the first author and Linusson.

math.CO

The exact phase diagram for a semipermeable TASEP with nonlocal boundary jumps

We consider a finite one-dimensional totally asymmetric simple exclusion process (TASEP) with four types of particles, $\{1,0,\bar{1},*\}$, in contact with reservoirs. Particles of species $0$ can neither enter nor exit the lattice, and those of species $*$ are constrained to lie at the first and last site. Particles of species $1$ enter from the left reservoir into either the first or second site, move rightwards, and leave from either the last or penultimate site. Conversely, particles of species $\bar{1}$ enter from the right reservoir into either the last or penultimate site, move leftwards, and leave from either the first or last site. This dynamics is motivated by a natural random walk on the Weyl group of type D. We compute the exact nonequilibrium steady state distribution using a matrix ansatz building on earlier work of Arita. We then give explicit formulas for the nonequilibrium partition function as well as densities and currents of all species in the steady state, and derive the phase diagram.

cond-mat.stat-mech

Continuous Multi-line Queues and TASEP

In this paper, we study a distribution of labeled particles on a continuous ring. It arises in three different ways, all related to the multi-type TASEP on a ring. We prove formulas for the probability density function for some permutations and give conjectures for a larger class. We give a complete conjecture for the probability of two particles i, j being next to each other on the cycle, for which we prove some cases. We also find that two natural events associated to the process have exactly the same probability expressed as a Vandermonde determinant. It is unclear whether this is just a coincidence or a consequence of a deeper connection.

math.CO

TASEP in any Weyl Group

We investigate a Markov chain defined by Thomas Lam, which generalizes the multi-type TASEP on a ring to any Weyl group. For groups of type C we define an analogue of the multiline queues of Ferrari and Martin (which compute the stationary distribution for the classical TASEP). While our construction does not suffice for finding the stationary distribution, the construction gives the stationary distribution of a certain projection of Lam's chain. Also, our approach is incremental, in the sense that the construction appears to fit into a pattern of 'conjugation matrices', which remains to be fully worked out. Finally, we prove a theorem for the classical TASEP which fits into the picture of viewing TASEP in a permutation-free way.

math.CO

The Double Eulerian Polynomial and Inversion Tables

We show that the pair (des, ides) of statistics on the set of permu- tations has the same distribution as the pair (asc, row) of statistics on the set of inversion tables, proving a conjecture of Visontai. The common generating function of these pairs is the double Eulerian polynomial.

math.CO

A product formula for the TASEP on a ring

For a random permutation sampled from the stationary distribution of the TASEP on a ring, we show that, conditioned on the event that the first entries are strictly larger than the last entries, the order of the first entries is independent of the order of the last entries. The proof uses multi-line queues as defined by Ferrari and Martin, and the theorem has an enumerative combinatorial interpretation in that setting. Finally, we present a conjecture for the case where the small and large entries are not separated.

math.PR

Stationary probability of the identity for the TASEP on a ring

Consider the following Markov chain on permutations of length $n$. At each time step we choose a random position. If the letter at that position is smaller than the letter immediately to the left (cyclically) then these letters swap positions. Otherwise nothing happens, corresponding to a loop in the Markov chain. This is the circular TASEP. We compute the average proportion of time the chain spends at the identity permutation (and, in greater generality, at sorted words). This answers a conjecture by Thomas Lam.

math.PR

Limit points of the iterative scaling procedure

The iterative scaling procedure (ISP) is an algorithm which computes a sequence of matrices, starting from some given matrix. The objective is to find a matrix 'proportional' to the given matrix, having given row and column sums. In many cases, for example if the initial matrix is strictly positive, the sequence is convergent. In the general case, it is known that the sequence has at most two limit points. When these are distinct, convergence can be slow. We give an efficient algorithm which finds these limit points, invoking the ISP only on instances for which the procedure is convergent.

math.ST

Path correlations in a randomly oriented complete bipartite graph

In a randomly oriented graph containing vertices $x$ and $y$, denote by $\{x\to y\}$ the event that there is a directed path from $x$ to $y$. We study the correlation between the events $\{x\to y\}$ and $\{y\to z\}$ for a (large) oriented complete bipartite graph with orientation chosen uniformly at random. We classify the cases of positive and negative correlation respectively in terms of the relative proportions of the sizes of the color classes of the graph.

math.PR