Toronto-Dominion Bank (French: Banque Toronto-Dominion), doing business as TD Bank Group (French: Groupe Banque TD), is a Canadian multinational banking and financial services corporation headquartered in Toronto, Ontario. The bank and its subsidiaries are commonly known as simply TD and trading under the name Toronto-Dominion Bank. The bank was created on February 1, 1955, through the merger of the Bank of Toronto and The Dominion Bank, which were founded in 1855 and 1869; respectively. It is one of two Big Five banks of Canada founded in Toronto, the other being the Canadian Imperial Bank of Commerce. The TD Bank SWIFT code is TDOMCATTTOR and the TD institution number is 004.In 2021, according to Standard & Poor's, TD Bank Group was the largest bank in Canada by total assets and also by market capitalization, a top-10 bank in North America, and the 23rd largest bank in the world. In 2019, it was designated a global systemically important bank by the Financial Stability Board.The bank and its subsidiaries have over 89,000 employees and over 26 million clients worldwide. In Canada, the bank operates through its TD Canada Trust division and serves more than 11 million customers at over 1,091 branches. In the United States, the company operates through their subsidiary TD Bank, N.A., which was created through the merger of TD Banknorth and Commerce Bank. TD Bank serves more than 6.5 million customers in the United States with a network of over 1,200 branches in sixteen states and the District of Columbia.A.A.
Tabular foundation models (TFMs) such as TabPFN (Tabular Prior-Data Fitted Network) are designed to generalize across heterogeneous tabular datasets through in-context learning (ICL). They perform prediction in a single forward pass conditioned on labeled examples without dataset-specific parameter updates. This paradigm is particularly attractive in industrial domains (e.g., finance and healthcare) where tabular prediction is pervasive. Retraining a bespoke model for each new table can be costly or infeasible in these settings, while data quality issues such as irrelevant predictors, correlated feature groups, and label noise are common. In this paper, we provide strong empirical evidence that TabPFN is highly robust under these sub-optimal conditions. We study TabPFN and its attention mechanisms for binary classification problems with controlled synthetic perturbations that vary: (i) dataset width by injecting random uncorrelated features and by introducing nonlinearly correlated features, (ii) dataset size by increasing the number of training rows, and (iii) label quality by increasing the fraction of mislabeled targets. Beyond predictive performance, we analyze internal signals including attention concentration and attention-based feature ranking metrics. Across these parametric tests, TabPFN is remarkably resilient: ROC-AUC remains high, attention stays structured and sharp, and informative features are highly ranked by attention-based metrics. Qualitative visualizations with attention heatmaps, feature-token embeddings, and SHAP plots further support a consistent pattern across layers in which TabPFN increasingly concentrates on useful features while separating their signals from noise. Together, these findings suggest that TabPFN is a robust TFM capable of maintaining both predictive performance and coherent internal behavior under various scenarios of data imperfections.
Competitive balance in Formula One racing has different aspects. The existing literature measures uncertainty of outcome: concentration of wins, podium finishes, and season points among a few drivers or teams. The drama during the race, captured by measures of overtaking, has received attention recently. We propose another measure to capture the closeness of racing: lap-time dispersion, using detailed, lap-level data on each driver. To illustrate this measure, we compare lap-time dispersion in 16 races on the same tracks, under similar weather conditions, in the 2021 and 2022 seasons. Formula One made important rule changes prior to the 2022 season to improve competitive balance, focused on encouraging closer racing. Using quantile regression methods, we show that 2022 lap times decreased for the slowest drivers and increased for faster drivers, thus reducing lap-time dispersion, with the standard deviation of lap times and the Gini coefficient falling by 14.5% and 11.7%, respectively. The Lorenz curve for lap times also shifted significantly upward, indicating closer racing after the rule changes. Other aspects of competitive balance point in the same direction - lower concentration ratios for laps led and podium finishes - but the concentration ratio for wins rose substantially in 2022.
Large language models frequently generate code that appears correct on typical inputs yet fails on edge cases, invalid inputs, and other specification-defined corner conditions. A popular fix has the model write its own tests and repair until they pass, but the source of the gain is unclear: does it come from the tests merely existing, or from their grounding in a specification of what the code should do? We isolate this factor. Holding the tester, test budget, and repair loop fixed, we change a single prompt line that controls whether the tester receives the spec as a checklist of rules. The baseline is strong: it is already told to probe invalid inputs and edge cases. Grounding the tests in the spec produces correct code +38 percentage points more often than this baseline across three Claude tiers (Haiku 4.5, Sonnet 4.6, Opus 4.8), and +36 points on a held-out set. Grounding, not test quantity, is the primary driver: doubling the test budget barely helps, and combining eight independent ungrounded suites plateaus far below grounding. An ablation isolates the spec's content, not its format: given the spec as a plain paragraph the tester recovers 27 of 30 bugs, but asked to plan tests without the spec it recovers only 2 of 30. The effect survives stronger baselines: a property-based generator catches 28 of 30 bugs but invents out-of-spec requirements, and an AlphaCodium-style loop only matches the baseline. It replicates across vendors (GPT-5.3-codex +28, Gemini 3.5 Flash +19), with a task-level sign test over 18 tasks significant at p=0.002. Grounding improves both sensitivity and precision: it catches more real bugs and wrongly rejects far less correct code, cutting the false-alarm rate from 33
Finding similar bonds remains challenging in fixed-income analytics, as numerical financial attributes often overshadow categorical non-financial ones such as issuer sector and domicile. This paper shows that these categorical attributes dominate the predictability of spread curves and proposes embedding models to capture their semantic similarities, outperforming one-hot and many other baselines. Evaluated via sparse-issuer augmentation, the approach improves risk modeling and curve construction.
TabPFN is a transformer-based foundation model for tabular prediction that performs inference without task-specific training by conditioning on a support set and query inputs. Despite its strong empirical performance, its internal behavior on structurally difficult tabular geometries remains poorly understood. We study this behavior using zigzag persistent homology, treating TabPFN layer representations as evolving point clouds. We construct a controlled benchmark of synthetic tabular tasks with known true probabilities and varied intrinsic topology, including warped circles, tori, spheres, Hopf links, trefoil knots, and Swiss rolls. Across these tasks, we find that the topology of TabPFN's internal representation geometry is strongly associated with dataset-level reliability; for example, the zeroth homology group H_0 fragmentation count correlates positively with mean absolute residual across controlled tasks, and this association strengthens in a high-resolution warped circle case study at large sample size. Harder geometries induce a dual topological signature: increased H_1 loop activity and increased H_0 fragmentation, while the H_1 persistence becomes shorter-lived. These descriptors correlate with Bayes error, mean absolute residuals, and overconfidence. Our results suggest that zigzag persistence diagnoses the reliability of the inferred in-context task geometry and provides a context-level view of when TabPFN operates in topologically stressed regimes.
